From 028ffa6e9a0379c5ca9d11ae74901534b9f5edf6 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Tue, 20 Apr 2021 07:18:24 +0200 Subject: [PATCH 001/186] Getting rid of "React version not specified" warning while linting. --- .eslintrc | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/.eslintrc b/.eslintrc index 076399682c..e1c40a0adb 100644 --- a/.eslintrc +++ b/.eslintrc @@ -11,5 +11,10 @@ "class-methods-use-this": "off", "arrow-body-style": "off", "no-loop-func": "off" + }, + "settings": { + "react": { + "version": "latest" + } } } From f0b246a5214f6f392ea4ec19a9fd550a8b26fcbb Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Tue, 20 Apr 2021 17:47:33 +0200 Subject: [PATCH 002/186] Adding a Seam Carving algorithm with Dynamic Programming implementation. (#693) * Adding a Seam Carving algorithm with Dynamic Programming implementation. * Adding a Seam Carving algorithm with Dynamic Programming implementation. * Adding a Seam Carving algorithm with Dynamic Programming implementation. * Testing Husky integration. * Testing Husky integration. --- .husky/.gitignore | 1 + .husky/pre-commit | 5 + .huskyrc.json | 5 - README.md | 3 + package-lock.json | 2650 +++++++++-------- package.json | 6 +- .../image-processing/seam-carving/README.md | 509 ++++ .../seam-carving/README.ru-RU.md | 509 ++++ .../__tests__/resizeImageWidth.test.js | 51 + .../__tests__/test-image-after.jpg | Bin 0 -> 6088 bytes .../__tests__/test-image-before.jpg | Bin 0 -> 3395 bytes .../seam-carving/resizeImageWidth.js | 253 ++ .../image-processing/utils/imageData.js | 39 + 13 files changed, 2838 insertions(+), 1193 deletions(-) create mode 100644 .husky/.gitignore create mode 100755 .husky/pre-commit delete mode 100644 .huskyrc.json create mode 100644 src/algorithms/image-processing/seam-carving/README.md create mode 100644 src/algorithms/image-processing/seam-carving/README.ru-RU.md create mode 100644 src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js create mode 100644 src/algorithms/image-processing/seam-carving/__tests__/test-image-after.jpg create mode 100644 src/algorithms/image-processing/seam-carving/__tests__/test-image-before.jpg create mode 100644 src/algorithms/image-processing/seam-carving/resizeImageWidth.js create mode 100644 src/algorithms/image-processing/utils/imageData.js diff --git a/.husky/.gitignore b/.husky/.gitignore new file mode 100644 index 0000000000..31354ec138 --- /dev/null +++ b/.husky/.gitignore @@ -0,0 +1 @@ +_ diff --git a/.husky/pre-commit b/.husky/pre-commit new file mode 100755 index 0000000000..bec1c08a1a --- /dev/null +++ b/.husky/pre-commit @@ -0,0 +1,5 @@ +#!/bin/sh +. "$(dirname "$0")/_/husky.sh" + +# npm run lint +# npm run test diff --git a/.huskyrc.json b/.huskyrc.json deleted file mode 100644 index 6e9b7b23b7..0000000000 --- a/.huskyrc.json +++ /dev/null @@ -1,5 +0,0 @@ -{ - "hooks": { - "pre-commit": "npm run lint && npm run test" - } -} diff --git a/README.md b/README.md index 8bb2bf3cdf..71b0798fbe 100644 --- a/README.md +++ b/README.md @@ -152,6 +152,8 @@ a set of rules that precisely define a sequence of operations. * `B` [NanoNeuron](https://github.com/trekhleb/nano-neuron) - 7 simple JS functions that illustrate how machines can actually learn (forward/backward propagation) * `B` [k-NN](src/algorithms/ml/knn) - k-nearest neighbors classification algorithm * `B` [k-Means](src/algorithms/ml/k-means) - k-Means clustering algorithm +* **Image Processing** + * `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - content-aware image resizing algorithm * **Uncategorized** * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower) * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - in-place algorithm @@ -203,6 +205,7 @@ algorithm is an abstraction higher than a computer program. * `B` [Unique Paths](src/algorithms/uncategorized/unique-paths) * `B` [Rain Terraces](src/algorithms/uncategorized/rain-terraces) - trapping rain water problem * `B` [Recursive Staircase](src/algorithms/uncategorized/recursive-staircase) - count the number of ways to reach to the top + * `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - content-aware image resizing algorithm * `A` [Levenshtein Distance](src/algorithms/string/levenshtein-distance) - minimum edit distance between two sequences * `A` [Longest Common Subsequence](src/algorithms/sets/longest-common-subsequence) (LCS) * `A` [Longest Common Substring](src/algorithms/string/longest-common-substring) diff --git a/package-lock.json b/package-lock.json index aeeed97b47..93de7f66c9 100644 --- a/package-lock.json +++ b/package-lock.json @@ -23,41 +23,40 @@ } }, "@babel/code-frame": { - "version": "7.10.4", - "resolved": "https://registry.npmjs.org/@babel/code-frame/-/code-frame-7.10.4.tgz", - 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"ci": "npm run lint && npm run coverage" + "ci": "npm run lint && npm run coverage", + "prepare": "husky install" }, "repository": { "type": "git", @@ -37,13 +38,14 @@ "@babel/cli": "7.12.10", "@babel/preset-env": "7.12.11", "@types/jest": "26.0.19", + "canvas": "^2.7.0", "eslint": "7.16.0", "eslint-config-airbnb": "18.2.1", "eslint-plugin-import": "2.22.1", "eslint-plugin-jest": "24.1.3", "eslint-plugin-jsx-a11y": "6.4.1", "eslint-plugin-react": "7.21.5", - "husky": "4.3.6", + "husky": "6.0.0", "jest": "26.6.3" }, "dependencies": {} diff --git a/src/algorithms/image-processing/seam-carving/README.md b/src/algorithms/image-processing/seam-carving/README.md new file mode 100644 index 0000000000..87004f7abe --- /dev/null +++ b/src/algorithms/image-processing/seam-carving/README.md @@ -0,0 +1,509 @@ +# Content-aware image resizing in JavaScript + +![Content-aware image resizing in JavaScript](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/01-cover-02.png) + +> There is an [interactive version of this post](https://trekhleb.dev/blog/2021/content-aware-image-resizing-in-javascript/) available where you can upload and resize your custom images. + +## TL;DR + +There are many great articles written about the *Seam Carving algorithm* already, but I couldn't resist the temptation to explore this elegant, powerful, and *yet simple* algorithm on my own, and to write about my personal experience with it. Another point that drew my attention (as a creator of [javascript-algorithms](https://github.com/trekhleb/javascript-algorithms) repo) was the fact that *Dynamic Programming (DP)* approach might be smoothly applied to solve it. And, if you're like me and still on your "learning algorithms" journey, this algorithmic solution may enrich your personal DP arsenal. + +So, with this article I want to do three things: + +1. Provide you with an interactive **content-aware resizer** so that you could play around with resizing your own images +2. Explain the idea behind the **Seam Carving algorithm** +3. Explain the **dynamic programming approach** to implement the algorithm (we'll be using TypeScript for it) + +### Content-aware image resizing + +*Content-aware image resizing* might be applied when it comes to changing the image proportions (i.e. reducing the width while keeping the height) and when losing some parts of the image is not desirable. Doing the straightforward image scaling in this case would distort the objects in it. To preserve the proportions of the objects while changing the image proportions we may use the [Seam Carving algorithm](https://perso.crans.org/frenoy/matlab2012/seamcarving.pdf) that was introduced by *Shai Avidan* and *Ariel Shamir*. + +The example below shows how the original image width was reduced by 50% using *content-aware resizing* (left image) and *straightforward scaling* (right image). In this particular case, the left image looks more natural since the proportions of the balloons were preserved. + +![Content-aware image resizing](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/01-resizing-options.png) + +The Seam Carving algorithm's idea is to find the *seam* (continuous sequence of pixels) with the lowest contribution to the image content and then *carve* (remove) it. This process repeats over and over again until we get the required image width or height. In the example below you may see that the hot air balloon pixels contribute more to the content of the image than the sky pixels. Thus, the sky pixels are being removed first. + +![JS IMAGE CARVER DEMO](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/10-demo-01.gif) + +Finding the seam with the lowest energy is a computationally expensive task (especially for large images). To make the seam search faster the *dynamic programming* approach might be applied (we will go through the implementation details below). + +### Objects removal + +The importance of each pixel (so-called pixel's energy) is being calculated based on its color (`R`, `G`, `B`, `A`) difference between two neighbor pixels. Now, if we set the pixel energy to some really low level artificially (i.e. by drawing a mask on top of them), the Seam Carving algorithm would perform an **object removal** for us for free. + +![JS IMAGE CARVER OBJECT REMOVAL DEMO](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/10-demo-02.gif) + +### JS IMAGE CARVER demo + +I've created the [JS IMAGE CARVER](https://trekhleb.dev/js-image-carver/) web-app (and also [open-sourced it on GitHub](https://github.com/trekhleb/js-image-carver)) that you may use to play around with resizing of your custom images. + +### More examples + +Here are some more examples of how the algorithm copes with more complex backgrounds. + +Mountains on the background are being shrunk smoothly without visible seams. + +![Resizing demo with more complex backgrounds](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/11-demo-01.png) + +The same goes for the ocean waves. The algorithm preserved the wave structure without distorting the surfers. + +![Resizing demo with more complex backgrounds](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/11-demo-02.png) + +We need to keep in mind that the Seam Carving algorithm is not a silver bullet, and it may fail to resize the images where *most of the pixels are edges* (look important to the algorithm). In this case, it starts distorting even the important parts of the image. In the example below the content-aware image resizing looks pretty similar to a straightforward scaling since for the algorithm all the pixels look important, and it is hard for it to distinguish Van Gogh's face from the background. + +![Example when the algorithm does not work as expected](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/12-demo-01.png) + +## How Seam Carving algorithms works + +Imagine we have a `1000 x 500 px` picture, and we want to change its size to `500 x 500 px` to make it square (let's say the square ratio would better fit the Instagram feed). We might want to set up several **requirements to the resizing process** in this case: + +- *Preserve the important parts of the image* (i.e. if there were 5 trees before the resizing we want to have 5 trees after resizing as well). +- *Preserve the proportions* of the important parts of the image (i.e. circle car wheels should not be squeezed to the ellipse wheels) + +To avoid changing the important parts of the image we may find the **continuous sequence of pixels (the seam)**, that goes from top to bottom and has *the lowest contribution to the content* of the image (avoids important parts) and then remove it. The seam removal will shrink the image by 1 pixel. We will then repeat this step until the image will get the desired width. + +The question is how to define *the importance of the pixel* and its contribution to the content (in the original paper the authors are using the term **energy of the pixel**). One of the ways to do it is to treat all the pixels that form the edges as important ones. In case if a pixel is a part of the edge its color would have a greater difference between the neighbors (left and right pixels) than the pixel that isn't a part of the edge. + +![Pixels color difference](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/30-pixel-energy-comparison.png) + +Assuming that the color of a pixel is represented by *4* numbers (`R` - red, `G` - green, `B` - blue, `A` - alpha) we may use the following formula to calculate the color difference (the pixel energy): + +![Pixel energy formula](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/20-energy-formula.png) + +Where: + +- `mEnergy` - *Energy* (importance) of the *middle* pixel (`[0..626]` if rounded) +- `lR` - *Red* channel value for the *left* pixel (`[0..255]`) +- `mR` - *Red* channel value for the *middle* pixel (`[0..255]`) +- `rR` - *Red* channel value for the *right* pixel (`[0..255]`) +- `lG` - *Green* channel value for the *left* pixel (`[0..255]`) +- and so on... + +In the formula above we're omitting the alpha (transparency) channel, for now, assuming that there are no transparent pixels in the image. Later we will use the alpha channel for masking and for object removal. + +![Example of pixel energy calculation](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/30-pixel-energy-calculation-example.png) + +Now, since we know how to find the energy of one pixel, we can calculate, so-called, **energy map** which will contain the energies of each pixel of the image. On each resizing step the energy map should be re-calculated (at least partially, more about it below) and would have the same size as the image. + +For example, on the 1st resizing step we will have a `1000 x 500` image and a `1000 x 500` energy map. On the 2nd resizing step we will remove the seam from the image and re-calculate the energy map based on the new shrunk image. Thus, we will get a `999 x 500` image and a `999 x 500` energy map. + +The higher the energy of the pixel the more likely it is a part of an edge, and it is important for the image content and the less likely that we need to remove it. + +To visualize the energy map we may assign a brighter color to the pixels with the higher energy and darker colors to the pixels with the lower energy. Here is an artificial example of how the random part of the energy map might look like. You may see the bright line which represents the edge and which we want to preserve during the resizing. + +![Energy map sketch](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/30-energy-map-padding.png) + +Here is a real example of the energy map for the demo image you saw above (with hot air balloons). + +![Energy map example](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/40-energy-map.png) + +You may play around with your custom images and see how the energy map would look like in the [interactive version of the post](https://trekhleb.dev/blog/2021/content-aware-image-resizing-in-javascript/). + +We may use the energy map to find the seams (one after another) with the lowest energy and by doing this to decide which pixels should be ultimately deleted. + +![Searching the seam](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/41-seam-search.png) + +Finding the seam with the lowest energy is not a trivial task and requires exploring many possible pixel combinations before making the decision. We will apply the dynamic programming approach to speed it up. + +In the example below, you may see the energy map with the first lowest energy seam that was found for it. + +![Energy map example with seam](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/40-energy-map-with-seam.png) + +In the examples above we were reducing the width of the image. A similar approach may be taken to reduce the image height. We need to "rotate" the approach though: + +- start using *top* and *bottom* pixel neighbors (instead of *left* and *right* ones) to calculate the pixel energy +- when searching for a seam we need to move from *left* to *right* (instead of from *up* to *bottom*) + +## Implementation in TypeScript + +> You may find the source code, and the functions mentioned below in the [js-image-carver](https://github.com/trekhleb/js-image-carver) repository. + +To implement the algorithm we will be using TypeScript. If you want a JavaScript version, you may ignore (remove) type definitions and their usages. + +For simplicity reasons let's implement the seam carving algorithm only for the image *width* reduction. + +### Content-aware width resizing (the entry function) + +First, let's define some common types that we're going to use while implementing the algorithm. + +```typescript +// Type that describes the image size (width and height). +type ImageSize = { w: number, h: number }; + +// The coordinate of the pixel. +type Coordinate = { x: number, y: number }; + +// The seam is a sequence of pixels (coordinates). +type Seam = Coordinate[]; + +// Energy map is a 2D array that has the same width and height +// as the image the map is being calculated for. +type EnergyMap = number[][]; + +// Type that describes the image pixel's RGBA color. +type Color = [ + r: number, // Red + g: number, // Green + b: number, // Blue + a: number, // Alpha (transparency) +] | Uint8ClampedArray; +``` + +On the high level the algorithm consists of the following steps: + +1. Calculate the **energy map** for the current version of the image. +2. Find the **seam** with the lowest energy based on the energy map (this is where we will apply Dynamic Programming). +3. **Delete the seam** with the lowest energy seam from the image. +4. **Repeat** until the image width is reduced to the desired value. + +```typescript +type ResizeImageWidthArgs = { + img: ImageData, // Image data we want to resize. + toWidth: number, // Final image width we want the image to shrink to. +}; + +type ResizeImageWidthResult = { + img: ImageData, // Resized image data. + size: ImageSize, // Resized image size (w x h). +}; + +// Performs the content-aware image width resizing using the seam carving method. +export const resizeImageWidth = ( + { img, toWidth }: ResizeImageWidthArgs, +): ResizeImageWidthResult => { + // For performance reasons we want to avoid changing the img data array size. + // Instead we'll just keep the record of the resized image width and height separately. + const size: ImageSize = { w: img.width, h: img.height }; + + // Calculating the number of pixels to remove. + const pxToRemove = img.width - toWidth; + if (pxToRemove < 0) { + throw new Error('Upsizing is not supported for now'); + } + + let energyMap: EnergyMap | null = null; + let seam: Seam | null = null; + + // Removing the lowest energy seams one by one. + for (let i = 0; i < pxToRemove; i += 1) { + // 1. Calculate the energy map for the current version of the image. + energyMap = calculateEnergyMap(img, size); + + // 2. Find the seam with the lowest energy based on the energy map. + seam = findLowEnergySeam(energyMap, size); + + // 3. Delete the seam with the lowest energy seam from the image. + deleteSeam(img, seam, size); + + // Reduce the image width, and continue iterations. + size.w -= 1; + } + + // Returning the resized image and its final size. + // The img is actually a reference to the ImageData, so technically + // the caller of the function already has this pointer. But let's + // still return it for better code readability. + return { img, size }; +}; +``` + +The image that needs to be resized is being passed to the function in [ImageData](https://developer.mozilla.org/en-US/docs/Web/API/ImageData) format. You may draw the image on the canvas and then extract the ImageData from the canvas like this: + +```javascript +const ctx = canvas.getContext('2d'); +const imgData = ctx.getImageData(0, 0, imgWidth, imgHeight); +``` + +> The way of uploading and drawing images in JavaScript is out of scope for this article, but you may find the complete source code of how it may be done using React in [js-image-carver](https://github.com/trekhleb/js-image-carver) repo. + +Let's break down each step ony be one and implement the `calculateEnergyMap()`, `findLowEnergySeam()` and `deleteSeam()` functions. + +### Calculating the pixel's energy + +Here we apply the color difference formula described above. For the left and right borders (when there are no left or right neighbors), we ignore the neighbors and don't take them into account during the energy calculation. + +```typescript +// Calculates the energy of a pixel. +const getPixelEnergy = (left: Color | null, middle: Color, right: Color | null): number => { + // Middle pixel is the pixel we're calculating the energy for. + const [mR, mG, mB] = middle; + + // Energy from the left pixel (if it exists). + let lEnergy = 0; + if (left) { + const [lR, lG, lB] = left; + lEnergy = (lR - mR) ** 2 + (lG - mG) ** 2 + (lB - mB) ** 2; + } + + // Energy from the right pixel (if it exists). + let rEnergy = 0; + if (right) { + const [rR, rG, rB] = right; + rEnergy = (rR - mR) ** 2 + (rG - mG) ** 2 + (rB - mB) ** 2; + } + + // Resulting pixel energy. + return Math.sqrt(lEnergy + rEnergy); +}; +``` + +### Calculating the energy map + +The image we're working with has the [ImageData](https://developer.mozilla.org/en-US/docs/Web/API/ImageData) format. It means that all the pixels (and their colors) are stored in a flat (*1D*) [Uint8ClampedArray](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Uint8ClampedArray) array. For readability purposes let's introduce the couple of helper functions that will allow us to work with the Uint8ClampedArray array as with a *2D* matrix instead. + +```typescript +// Helper function that returns the color of the pixel. +const getPixel = (img: ImageData, { x, y }: Coordinate): Color => { + // The ImageData data array is a flat 1D array. + // Thus we need to convert x and y coordinates to the linear index. + const i = y * img.width + x; + const cellsPerColor = 4; // RGBA + // For better efficiency, instead of creating a new sub-array we return + // a pointer to the part of the ImageData array. + return img.data.subarray(i * cellsPerColor, i * cellsPerColor + cellsPerColor); +}; + +// Helper function that sets the color of the pixel. +const setPixel = (img: ImageData, { x, y }: Coordinate, color: Color): void => { + // The ImageData data array is a flat 1D array. + // Thus we need to convert x and y coordinates to the linear index. + const i = y * img.width + x; + const cellsPerColor = 4; // RGBA + img.data.set(color, i * cellsPerColor); +}; +``` + +To calculate the energy map we go through each image pixel and call the previously described `getPixelEnergy()` function against it. + +```typescript +// Helper function that creates a matrix (2D array) of specific +// size (w x h) and fills it with specified value. +const matrix = (w: number, h: number, filler: T): T[][] => { + return new Array(h) + .fill(null) + .map(() => { + return new Array(w).fill(filler); + }); +}; + +// Calculates the energy of each pixel of the image. +const calculateEnergyMap = (img: ImageData, { w, h }: ImageSize): EnergyMap => { + // Create an empty energy map where each pixel has infinitely high energy. + // We will update the energy of each pixel. + const energyMap: number[][] = matrix(w, h, Infinity); + for (let y = 0; y < h; y += 1) { + for (let x = 0; x < w; x += 1) { + // Left pixel might not exist if we're on the very left edge of the image. + const left = (x - 1) >= 0 ? getPixel(img, { x: x - 1, y }) : null; + // The color of the middle pixel that we're calculating the energy for. + const middle = getPixel(img, { x, y }); + // Right pixel might not exist if we're on the very right edge of the image. + const right = (x + 1) < w ? getPixel(img, { x: x + 1, y }) : null; + energyMap[y][x] = getPixelEnergy(left, middle, right); + } + } + return energyMap; +}; +``` + +> The energy map is going to be recalculated on every resize iteration. It means that it will be recalculated, let's say, 500 times if we need to shrink the image by 500 pixels which is not optimal. To speed up the energy map calculation on the 2nd, 3rd, and further steps, we may re-calculate the energy only for those pixels that are placed around the seam that is going to be removed. For simplicity reasons this optimization is omitted here, but you may find the example source-code in [js-image-carver](https://github.com/trekhleb/js-image-carver) repo. + +### Finding the seam with the lowest energy (Dynamic Programming approach) + +> I've described some Dynamic Programming basics in [Dynamic Programming vs Divide-and-Conquer](https://trekhleb.dev/blog/2018/dynamic-programming-vs-divide-and-conquer/) article before. There is a DP example based on the minimum edit distance problem. You might want to check it out to get some more context. + +The issue we need to solve now is to find the path (the seam) on the energy map that goes from top to bottom and has the minimum sum of pixel energies. + +#### The naive approach + +The naive approach would be to check all possible paths one after another. + +![The naive approach](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/50-naive-approach.png) + +Going from top to bottom, for each pixel, we have 3 options (↙︎ go down-left, ↓ go down, ↘︎ go down-right). This gives us the time complexity of `O(w * 3^h)` or simply `O(3^h)`, where `w` and `h` are the width and the height of the image. This approach looks slow. + +#### The greedy approach + +We may also try to choose the next pixel as a pixel with the lowest energy, hoping that the resulting seam energy will be the smallest one. + +![The greedy approach](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/51-greedy-approach.png) + +This approach gives not the worst solution, but it cannot guarantee that we will find the best available solution. On the image above you may see how the greedy approach chose `5` instead of `10` at first and missed the chain of optimal pixels. + +The good part about this approach is that it is fast, and it has a time complexity of `O(w + h)`, where `w` and `h` are the width and the height of the image. In this case, the cost of the speed is the low quality of resizing. We need to find a minimum value in the first row (traversing `w` cells) and then we explore only 3 neighbor pixels for each row (traversing `h` rows). + +#### The dynamic programming approach + +You might have noticed that in the naive approach we summed up the same pixel energies over and over again while calculating the resulting seams' energy. + +![Repeated problems](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/52-dp-repeated-problems.png) + +In the example above you see that for the first two seams we are re-using the energy of the shorter seam (which has the energy of `235`). Instead of doing just one operation `235 + 70` to calculate the energy of the 2nd seam we're doing four operations `(5 + 0 + 80 + 150) + 70`. + +> This fact that we're re-using the energy of the previous seam to calculate the current seam's energy might be applied recursively to all the shorter seams up to the very top 1st row seam. When we have such overlapping sub-problems, [it is a sign](https://trekhleb.dev/blog/2018/dynamic-programming-vs-divide-and-conquer/) that the general problem *might* be optimized by dynamic programming approach. + +So, we may **save the energy of the current seam** at the particular pixel in an additional `seamsEnergies` table to make it re-usable for calculating the next seams faster (the `seamsEnergies` table will have the same size as the energy map and the image itself). + +Let's also keep in mind that for one particular pixel on the image (i.e. the bottom left one) we may have *several* values of the previous seams energies. + +![What seam to choose](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/53-dp-what-to-choose.png) + +Since we're looking for a seam with the lowest resulting energy it would make sense to pick the previous seam with the lowest resulting energy as well. + +![Seams energies example](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/56-dp-seams-energies-example.png) + +In general, we have three possible previous seems to choose from: + +![Three options to choose from](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/55-dp-three-options.png) + +You may think about it this way: + +- The cell `[1][x]`: contains the lowest possible energy of the seam that starts somewhere on the row `[0][?]` and ends up at cell `[1][x]` +- **The current cell** `[2][3]`: contains the lowest possible energy of the seam that starts somewhere on the row `[0][?]` and ends up at cell `[2][3]`. To calculate it we need to sum up the energy of the current pixel `[2][3]` (from the energy map) with the `min(seam_energy_1_2, seam_energy_1_3, seam_energy_1_4)` + +If we fill the `seamsEnergies` table completely, then the minimum number in the lowest row would be the lowest possible seam energy. + +Let's try to fill several cells of this table to see how it works. + +![Seams energies map traversal](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/57-dp-seams-energies-traversal.png) + +After filling out the `seamsEnergies` table we may see that the lowest energy pixel has an energy of `50`. For convenience, during the `seamsEnergies` generation for each pixel, we may save not only the energy of the seam but also the coordinates of the previous lowest energy seam. This will give us the possibility to reconstruct the seam path from the bottom to the top easily. + +The time complexity of DP approach would be `O(w * h)`, where `w` and `h` are the width and the height of the image. We need to calculate energies for *every* pixel of the image. + +Here is an example of how this logic might be implemented: + +```typescript +// The metadata for the pixels in the seam. +type SeamPixelMeta = { + energy: number, // The energy of the pixel. + coordinate: Coordinate, // The coordinate of the pixel. + previous: Coordinate | null, // The previous pixel in a seam. +}; + +// Finds the seam (the sequence of pixels from top to bottom) that has the +// lowest resulting energy using the Dynamic Programming approach. +const findLowEnergySeam = (energyMap: EnergyMap, { w, h }: ImageSize): Seam => { + // The 2D array of the size of w and h, where each pixel contains the + // seam metadata (pixel energy, pixel coordinate and previous pixel from + // the lowest energy seam at this point). + const seamsEnergies: (SeamPixelMeta | null)[][] = matrix(w, h, null); + + // Populate the first row of the map by just copying the energies + // from the energy map. + for (let x = 0; x < w; x += 1) { + const y = 0; + seamsEnergies[y][x] = { + energy: energyMap[y][x], + coordinate: { x, y }, + previous: null, + }; + } + + // Populate the rest of the rows. + for (let y = 1; y < h; y += 1) { + for (let x = 0; x < w; x += 1) { + // Find the top adjacent cell with minimum energy. + // This cell would be the tail of a seam with lowest energy at this point. + // It doesn't mean that this seam (path) has lowest energy globally. + // Instead, it means that we found a path with the lowest energy that may lead + // us to the current pixel with the coordinates x and y. + let minPrevEnergy = Infinity; + let minPrevX: number = x; + for (let i = (x - 1); i <= (x + 1); i += 1) { + if (i >= 0 && i < w && seamsEnergies[y - 1][i].energy < minPrevEnergy) { + minPrevEnergy = seamsEnergies[y - 1][i].energy; + minPrevX = i; + } + } + + // Update the current cell. + seamsEnergies[y][x] = { + energy: minPrevEnergy + energyMap[y][x], + coordinate: { x, y }, + previous: { x: minPrevX, y: y - 1 }, + }; + } + } + + // Find where the minimum energy seam ends. + // We need to find the tail of the lowest energy seam to start + // traversing it from its tail to its head (from the bottom to the top). + let lastMinCoordinate: Coordinate | null = null; + let minSeamEnergy = Infinity; + for (let x = 0; x < w; x += 1) { + const y = h - 1; + if (seamsEnergies[y][x].energy < minSeamEnergy) { + minSeamEnergy = seamsEnergies[y][x].energy; + lastMinCoordinate = { x, y }; + } + } + + // Find the lowest energy energy seam. + // Once we know where the tail is we may traverse and assemble the lowest + // energy seam based on the "previous" value of the seam pixel metadata. + const seam: Seam = []; + if (!lastMinCoordinate) { + return seam; + } + + const { x: lastMinX, y: lastMinY } = lastMinCoordinate; + + // Adding new pixel to the seam path one by one until we reach the top. + let currentSeam = seamsEnergies[lastMinY][lastMinX]; + while (currentSeam) { + seam.push(currentSeam.coordinate); + const prevMinCoordinates = currentSeam.previous; + if (!prevMinCoordinates) { + currentSeam = null; + } else { + const { x: prevMinX, y: prevMinY } = prevMinCoordinates; + currentSeam = seamsEnergies[prevMinY][prevMinX]; + } + } + + return seam; +}; +``` + +### Removing the seam with the lowest energy + +Once we found the lowest energy seam, we need to remove (to carve) the pixels that form it from the image. The removal is happening by shifting the pixels to the right of the seam by `1px` to the left. For performance reasons, we don't actually delete the last columns. Instead, the rendering component will just ignore the part of the image that lays beyond the resized image width. + +![Deleting the seam](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/60-deleting-example.png) + +```typescript +// Deletes the seam from the image data. +// We delete the pixel in each row and then shift the rest of the row pixels to the left. +const deleteSeam = (img: ImageData, seam: Seam, { w }: ImageSize): void => { + seam.forEach(({ x: seamX, y: seamY }: Coordinate) => { + for (let x = seamX; x < (w - 1); x += 1) { + const nextPixel = getPixel(img, { x: x + 1, y: seamY }); + setPixel(img, { x, y: seamY }, nextPixel); + } + }); +}; +``` + +## Objects removal + +The Seam Carving algorithm tries to remove the seams which consist of low energy pixels first. We could leverage this fact and by assigning low energy to some pixels manually (i.e. by drawing on the image and masking out some areas of it) we could make the Seam Carving algorithm to do *objects removal* for us for free. + +Currently, in `getPixelEnergy()` function we were using only the `R`, `G`, `B` color channels to calculate the pixel's energy. But there is also the `A` (alpha, transparency) parameter of the color that we didn't use yet. We may use the transparency channel to tell the algorithm that transparent pixels are the pixels we want to remove. You may check the [source-code of the energy function](https://github.com/trekhleb/js-image-carver/blob/main/src/utils/contentAwareResizer.ts#L54) that takes transparency into account. + +Here is how the algorithm works for object removal. + +![JS IMAGE CARVER OBJECT REMOVAL DEMO](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/10-demo-02.gif) + +## Issues and what's next + +The [JS IMAGE CARVER](https://github.com/trekhleb/js-image-carver) web app is far from being a production ready resizer of course. Its main purpose was to experiment with the Seam Carving algorithm interactively. So the plan for the future is to continue experimentation. + +The [original paper](https://perso.crans.org/frenoy/matlab2012/seamcarving.pdf) describes how the Seam Carving algorithm might be used not only for the downscaling but also for the **upscaling of the images**. The upscaling, in turn, might be used to **upscale the image back to its original width after the objects' removal**. + +Another interesting area of experimentation might be to make the algorithm work in a **real-time**. + +> Those are the plans for the future, but for now, I hope that the example with image downsizing was interesting and useful for you. I also hope that you've got the idea of using dynamic programming to implement it. +> +> So, good luck with your own experiments! diff --git a/src/algorithms/image-processing/seam-carving/README.ru-RU.md b/src/algorithms/image-processing/seam-carving/README.ru-RU.md new file mode 100644 index 0000000000..444ce6df61 --- /dev/null +++ b/src/algorithms/image-processing/seam-carving/README.ru-RU.md @@ -0,0 +1,509 @@ +# Изменение размеров изображения с учетом его содержимого в JavaScript + +![Content-aware image resizing in JavaScript](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/01-cover-02.png) + +> Доступна [английская интерактивная версия этой статьи](https://trekhleb.dev/blog/2021/content-aware-image-resizing-in-javascript/) в которой вы можете загрузить свои собственные изображения и посмотреть, как алгоритм "справляется" с ними. + +## TL;DR + +Написано много замечательных статей об алгоритме *Seam Carving* ("Вырезание швов"), но я не смог устоять перед соблазном самостоятельно исследовать этот элегантный, мощный и в то же время простой алгоритм и написать о своем личном опыте работы с ним. Мое внимание также привлек тот факт, что для его имплементации мы можем применить *динамическое программирование (DP)*. И, если вы, как и я, все еще находитесь на пути изучения алгоритмов, то это решение может обогатить ваш личный арсенал DP. + +Итак, в этой статье я хочу сделать три вещи: + +1. Предоставить вам возможность "поиграться" с алгоритмом самостоятельно при помощи **интерактивного ресайзера**. +2. Объяснить **идею алгоритма Seam Carving**. +3. Объяснить как можно **применить динамическое программирование** для имплементации алгоритма (мы будем писать на TypeScript). + +### Изменение размеров изображений с учетом их содержимого + +*Изменение размера изображения с учетом содержимого* (content-aware image resizing) может быть применено, когда дело доходит до изменения пропорций изображения (например, уменьшения ширины при сохранении высоты), а также когда потеря некоторых частей изображения нежелательна. Простое масштабирование изображения в этом случае исказит находящиеся в нем объекты. Для сохранения пропорций объектов при изменении пропорций изображения можно использовать [алгоритм Seam Carving](https://perso.crans.org/frenoy/matlab2012/seamcarving.pdf), который был описан *Shai Avidan* и *Ariel Shamir*. + +В приведенном ниже примере показано, как ширина исходного изображения была уменьшена на 50% *с учетом содержимого изображения* (слева) и *без учета содержимого изображения* (справа, простой скейлинг). В данном случае левое изображение выглядит более естественным, так как пропорции воздушных шаров в нем были сохранены. + +![Content-aware image resizing](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/01-resizing-options.png) + +Идея алгоритма Seam Carving заключается в том, чтобы найти *шов* (seam, непрерывную последовательность пикселей) с наименьшим влиянием на содержание изображения, а затем его *вырезать* (carve). Этот процесс повторяется снова и снова, пока мы не получим требуемую ширину или высоту изображения. В примере ниже интуитивно видно, что пиксели воздушных шаров вносят больший "вклад" в содержание и смысл изображения, чем пиксели неба. Таким образом, сначала удаляются пиксели неба. + +![JS IMAGE CARVER DEMO](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/10-demo-01.gif) + +Поиск шва с наименьшей энергией (с наименьшим вкладом в содержимое изображения) является вычислительно дорогостоящей операцией (особенно для больших изображений). Для ускорения поиска шва может быть применено *динамическое программирование* (мы рассмотрим детали реализации ниже). + +### Удаление объектов + +Важность каждого пикселя (так называемая энергия пикселя) вычисляется исходя из его цветовой разницы (`R`, `G`, `B`, `A`) между двумя соседними пикселями. Если же мы вручную зададим некоторым пикселям низкий уровень энергии (например нарисовав маску поверх них), то алгоритм Seam Carving выполнит для нас **удаление помеченного объекта**, как говорится, "забесплатно". + +![JS IMAGE CARVER OBJECT REMOVAL DEMO](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/10-demo-02.gif) + +### Интерактивный ресзайзер + +Для этой статьи я создал приложение [JS IMAGE CARVER](https://trekhleb.dev/js-image-carver/) (доступен также и [исходный код на GitHub](https://github.com/trekhleb/js-image-carver)), которым вы можете воспользоваться для ресайза своих изображений и увидеть в реальном времени, как работает алгоритм. + +### Другие примеры ресайза + +Вот еще несколько примеров того, как алгоритм справляется с более сложным фоном. + +Горы на заднем плане плавно сжимаются, без видимых швов. + +![Resizing demo with more complex backgrounds](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/11-demo-01.png) + +То же самое и с океанскими волнами. Алгоритм сохранил волновую структуру, не искажая серферов. + +![Resizing demo with more complex backgrounds](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/11-demo-02.png) + +Нужно помнить, что алгоритм Seam Carving не является "волшебной таблеткой", и может не сохранить пропорции важных частей изображения в том случае, когда *большая часть пикселей выглядят как края, ребра или границы* (почти все пиксели выглядят одинаково важными с точки зрения алгоритма). В приведенном ниже примере изменение размера изображения с учетом содержимого похоже на простое масштабирование, т.к. для алгоритма все пиксели выглядят важными, и ему трудно отличить лицо Ван Гога от фона. + +![Example when the algorithm does not work as expected](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/12-demo-01.png) + +## Как работает алгоритм Seam Carving + +Представим, что у нас есть картинка размером `1000 x 500 px`, и мы хотим уменьшить ее до `500 x 500 px` (допустим, квадратное изображение больше подходит для Instagram). В этом случае мы, возможно, захотим задать несколько **требований к процессу изменения размера**: + +- *Важные части изображения должны быть сохранены* (если до ресайза на фото было 5 деревьев, то и после ресайза мы хотим увидеть все те же 5 деревьев). +- *Пропорции важных частей изображения должны быть сохранены* (круглые колеса автомобиля не должны стать овальными после ресайза). + +Чтобы избежать изменения важных частей изображения можно найти **непрерывную последовательность пикселей (шов)**, которая будет идти от верхней границы к нижней и иметь *наименьший вклад в содержимое* изображения (шов, который не проходит через важные части изображения), а затем удалить его. Удаление шва сожмет изображение на один пиксель. Далее надо повторять этот шаг до тех пор, пока изображение не станет нужной ширины. + +Вопрос в том, как определить *важность пикселя* и его вклад в содержание изображения (в оригинальной статье авторы используют термин **энергия пикселя**). Один из способов это сделать — рассматривать все пиксели, образующие края (границы, ребра), как важные. В случае, если пиксель является частью ребра, его цвет будет отличаться от соседей (левого и правого пикселей). + +![Pixels color difference](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/30-pixel-energy-comparison.png) + +Предполагая, что цвет пикселя представлен *4-мя* числами (`R` - красный, `G` - зеленый, `B` - синий, `A` - альфа, прозрачность), мы можем использовать следующую формулу для вычисления разницы в цвете (энергии пикселя): + +![Pixel energy formula](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/20-energy-formula.png) + +Где: + +- `mEnergy` - *Энергия* (важность) *среднего* пикселя (`[0..626]` если округлить) +- `lR` - *Красный* цветовой канал *левого* пикселя (`[0..255]`) +- `mR` - *Красный* цветовой канал *среднего* пикселя (`[0..255]`) +- `rR` - *Красный* цветовой канал *правого* пикселя (`[0..255]`) +- `lG` - *Зеленый* цветовой канал *левого* пикселя (`[0..255]`) +- и так далее... + +В приведенной выше формуле мы пока не используем альфа-канал (прозрачность), предполагая, что изображение не содержит прозрачные пиксели. Позже мы будем использовать альфа-канал для маскировки и удаления объектов. + +![Example of pixel energy calculation](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/30-pixel-energy-calculation-example.png) + +Поскольку мы знаем, как найти энергию одного пикселя, мы можем вычислить так называемую **энергетическую карту**, которая будет содержать энергии каждого пикселя изображения. На каждом шаге изменения размера изображения карту энергий необходимо пересчитывать (по крайней мере частично, подробнее об этом ниже), и она будет иметь тот же размер, что и изображение. + +Например, на 1-м шаге у нас будет изображение размером `1000 x 500` и энергетическая карта размером `1000 x 500`. На 2-м шаге изменения размера мы удалим шов с изображения и пересчитаем карту энергий на основе нового уменьшенного изображения. Таким образом, мы получим изображение размером `999 x 500` и карту энергий размером `999 x 500`. + +Чем выше энергия пикселя, тем больше вероятность того, что он является частью ребра, важен для содержимого изображения и тем меньше вероятность того, что нам потребуется его удалить. + +Для визуализации карты энергий мы можем присвоить более яркий цвет пикселям с большей энергией и более темные цвета пикселям с меньшей энергией. Вот как может выглядеть часть карты энергий. Вы можете увидеть светлую линию, которая представляет край и которую мы хотим сохранить при изменении размера. + +![Energy map sketch](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/30-energy-map-padding.png) + +Вот реальный пример энергетической карты для изображения, которое вы видели выше (с воздушными шарами). + +![Energy map example](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/40-energy-map.png) + +Вы можете загрузить свое изображение и посмотреть, как будет выглядеть энергетическая карта в [интерактивной версии статьи](https://trekhleb.dev/blog/2021/content-aware-image-resizing-in-javascript/). + +Мы можем использовать энергетическую карту, чтобы найти швы (один за другим) с наименьшей энергией и тем самым решить, какие пиксели в конечном итоге должны быть удалены. + +![Searching the seam](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/41-seam-search.png) + +Поиск шва с наименьшими затратами энергии не является тривиальной задачей и требует перебора множества возможных комбинаций пикселей. Мы применим динамическое программирование для оптимизации поиска шва. + +В примере ниже вы можете увидеть карту энергий с первым найденным для нее швом с наименьшей энергией. + +![Energy map example with seam](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/40-energy-map-with-seam.png) + +В приведенных выше примерах мы уменьшали ширину изображения. Аналогичный подход может быть использован для уменьшения высоты изображения. Для этого нам нужно: + +- начать использовать соседей *сверху* и *снизу*, а не *слева* и *справа*, для вычисления энергии пикселя +- при поиске шва нам нужно двигаться *слева* *направо*, а не *сверху* *вниз*. + +## Реализация алгоритма на TypeScript + +> Исходный код и функции, упомянутые ниже, можно найти в репозитории [js-image-carver](https://github.com/trekhleb/js-image-carver). + +Для реализации алгоритма мы будем использовать TypeScript. Если вам нужна версия на JavaScript, вы можете игнорировать (удалить) определения типов и их использование. + +Для простоты примеров мы напишем код только для уменьшения *ширины* изображения. + +### Уменьшение ширины с учетом содержимого изображения (исходная функция) + +Для начала определим некоторые общие типы, которые мы будем использовать при реализации алгоритма. + +```typescript +// Type that describes the image size (width and height). +type ImageSize = { w: number, h: number }; + +// The coordinate of the pixel. +type Coordinate = { x: number, y: number }; + +// The seam is a sequence of pixels (coordinates). +type Seam = Coordinate[]; + +// Energy map is a 2D array that has the same width and height +// as the image the map is being calculated for. +type EnergyMap = number[][]; + +// Type that describes the image pixel's RGBA color. +type Color = [ + r: number, // Red + g: number, // Green + b: number, // Blue + a: number, // Alpha (transparency) +] | Uint8ClampedArray; +``` + +Для имплементации алгоритма нам необходимо выполнить следующие шаги: + +1. Рассчитать **карту энергии** для текущей версии изображения. +2. Найти **шов** с наименьшей энергией на основе карты энергий (здесь мы применим динамическое программирование). +3. **Удалить шов** с наименьшей энергией из изображения. +4. **Повторять** до тех пор, пока ширина изображения не будет уменьшена до нужного значения. + +```typescript +type ResizeImageWidthArgs = { + img: ImageData, // Image data we want to resize. + toWidth: number, // Final image width we want the image to shrink to. +}; + +type ResizeImageWidthResult = { + img: ImageData, // Resized image data. + size: ImageSize, // Resized image size (w x h). +}; + +// Performs the content-aware image width resizing using the seam carving method. +export const resizeImageWidth = ( + { img, toWidth }: ResizeImageWidthArgs, +): ResizeImageWidthResult => { + // For performance reasons we want to avoid changing the img data array size. + // Instead we'll just keep the record of the resized image width and height separately. + const size: ImageSize = { w: img.width, h: img.height }; + + // Calculating the number of pixels to remove. + const pxToRemove = img.width - toWidth; + if (pxToRemove < 0) { + throw new Error('Upsizing is not supported for now'); + } + + let energyMap: EnergyMap | null = null; + let seam: Seam | null = null; + + // Removing the lowest energy seams one by one. + for (let i = 0; i < pxToRemove; i += 1) { + // 1. Calculate the energy map for the current version of the image. + energyMap = calculateEnergyMap(img, size); + + // 2. Find the seam with the lowest energy based on the energy map. + seam = findLowEnergySeam(energyMap, size); + + // 3. Delete the seam with the lowest energy seam from the image. + deleteSeam(img, seam, size); + + // Reduce the image width, and continue iterations. + size.w -= 1; + } + + // Returning the resized image and its final size. + // The img is actually a reference to the ImageData, so technically + // the caller of the function already has this pointer. But let's + // still return it for better code readability. + return { img, size }; +}; +``` + +Изображение, которому необходимо изменить размер, передается в функцию в формате [ImageData](https://developer.mozilla.org/en-US/docs/Web/API/ImageData). Вы можете отобразить изображение на canvas-е, а затем извлечь ImageData из того же canvas-а следующим образом: + +```javascript +const ctx = canvas.getContext('2d'); +const imgData = ctx.getImageData(0, 0, imgWidth, imgHeight); +``` + +> Загрузка и отрисовка изображений в JavaScript выходит за рамки данной статьи, но вы можете найти полный исходный код того, как это можно сделать с помощью React в репозитории [js-image-carver](https://github.com/trekhleb/js-image-carver). + +Теперь, пошагово реализуем функции `calculateEnergyMap()`, `findLowEnergySeam()` и `deleteSeam()`. + +### Расчет энергии пикселя + +Для расчета воспользуемся формулой разницы цветов, описанной выше. Для левой и правой краев изображения (когда нет левого или правого соседей) мы игнорируем соседей и не учитываем их при расчете энергии. + +```typescript +// Calculates the energy of a pixel. +const getPixelEnergy = (left: Color | null, middle: Color, right: Color | null): number => { + // Middle pixel is the pixel we're calculating the energy for. + const [mR, mG, mB] = middle; + + // Energy from the left pixel (if it exists). + let lEnergy = 0; + if (left) { + const [lR, lG, lB] = left; + lEnergy = (lR - mR) ** 2 + (lG - mG) ** 2 + (lB - mB) ** 2; + } + + // Energy from the right pixel (if it exists). + let rEnergy = 0; + if (right) { + const [rR, rG, rB] = right; + rEnergy = (rR - mR) ** 2 + (rG - mG) ** 2 + (rB - mB) ** 2; + } + + // Resulting pixel energy. + return Math.sqrt(lEnergy + rEnergy); +}; +``` + +### Расчет энергетической карты + +Изображение, с которым мы работаем, имеет формат [ImageData](https://developer.mozilla.org/en-US/docs/Web/API/ImageData). Это означает, что все пиксели (и их цвета) хранятся в одномерном массиве [Uint8ClampedArray](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Uint8ClampedArray). Для удобства чтения введем пару вспомогательных функций, которые позволят работать с массивом Uint8ClampedArray как с *2D* матрицей. + +```typescript +// Helper function that returns the color of the pixel. +const getPixel = (img: ImageData, { x, y }: Coordinate): Color => { + // The ImageData data array is a flat 1D array. + // Thus we need to convert x and y coordinates to the linear index. + const i = y * img.width + x; + const cellsPerColor = 4; // RGBA + // For better efficiency, instead of creating a new sub-array we return + // a pointer to the part of the ImageData array. + return img.data.subarray(i * cellsPerColor, i * cellsPerColor + cellsPerColor); +}; + +// Helper function that sets the color of the pixel. +const setPixel = (img: ImageData, { x, y }: Coordinate, color: Color): void => { + // The ImageData data array is a flat 1D array. + // Thus we need to convert x and y coordinates to the linear index. + const i = y * img.width + x; + const cellsPerColor = 4; // RGBA + img.data.set(color, i * cellsPerColor); +}; +``` + +Для вычисления карты энергии мы проходим через каждый пиксель изображения и вызываем для него описанную ранее функцию `getPixelEnergy()`. + +```typescript +// Helper function that creates a matrix (2D array) of specific +// size (w x h) and fills it with specified value. +const matrix = (w: number, h: number, filler: T): T[][] => { + return new Array(h) + .fill(null) + .map(() => { + return new Array(w).fill(filler); + }); +}; + +// Calculates the energy of each pixel of the image. +const calculateEnergyMap = (img: ImageData, { w, h }: ImageSize): EnergyMap => { + // Create an empty energy map where each pixel has infinitely high energy. + // We will update the energy of each pixel. + const energyMap: number[][] = matrix(w, h, Infinity); + for (let y = 0; y < h; y += 1) { + for (let x = 0; x < w; x += 1) { + // Left pixel might not exist if we're on the very left edge of the image. + const left = (x - 1) >= 0 ? getPixel(img, { x: x - 1, y }) : null; + // The color of the middle pixel that we're calculating the energy for. + const middle = getPixel(img, { x, y }); + // Right pixel might not exist if we're on the very right edge of the image. + const right = (x + 1) < w ? getPixel(img, { x: x + 1, y }) : null; + energyMap[y][x] = getPixelEnergy(left, middle, right); + } + } + return energyMap; +}; +``` + +> Карта энергии будет пересчитываться при каждой итерации изменения размера. Это значит, что она будет пересчитываться, скажем, 500 раз, если нам нужно будет уменьшить изображение на 500 пикселей, что выглядит неоптимально. Чтобы ускорить вычисление карты энергии на 2-м, 3-м и последующих этапах, мы можем пересчитать энергию только для тех пикселей, которые расположены вокруг шва, который будет удален. Для простоты эта оптимизация здесь пропущена, но пример с исходным кодом можно найти в репозитории [js-image-carver](https://github.com/trekhleb/js-image-carver). + +### Нахождение шва с минимальной энергией (применяем динамическое программирование) + +> В статье [Dynamic Programming vs Divide-and-Conquer](https://trekhleb.dev/blog/2018/dynamic-programming-vs-divide-and-conquer/) я описывал некоторые аспекты динамического программирования на примере нахождения "расстояния Левенштейна" (преобразование одной строки в другую). Возможно она будет полезна для ознакомления. + +Проблема, которую нам необходимо решить заключается в нахождении пути (шва) на энергетической карте, который идет от верхней границы изображения к нижней и имеет минимальную энергию (сумма энергий пикселей, составляющих шов должна быть минимальной). + +#### "Наивный" подход (naive) + +Прямолинейный ("наивный") подход — перебрать все возможные пути один за другим. + +![The naive approach](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/50-naive-approach.png) + +Двигаясь сверху вниз, для каждого пикселя у нас есть 3 варианта (↙︎ идти вниз-влево, ↓ вниз, ↘︎ идти вниз-вправо). Это дает нам временную сложность `O (w * 3 ^ h)` или просто `O (3 ^ h)`, где `w` и` h` - ширина и высота изображения. Такой подход выглядит неоптимальным. + +#### "Жадный" подход (greedy) + +Жадный подход — выбирать следующий пиксель как пиксель с наименьшей энергией, надеясь, что результирующая энергия шва будет наименьшей. + +![The greedy approach](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/51-greedy-approach.png) + +Жадный подход приведет нас к не самому худшему решению, но он не сможет гарантировать, что мы найдем наилучшее доступное решение. На картинке выше видно, как мы выбрали `5` вместо `10` и пропустили цепочку оптимальных пикселей. + +Плюс этого подхода в том, что он быстрый и имеет временную сложность `O(w + h)`, где `w` и `h` - это ширина и высота изображения. В этом случае плата за скорость — низкое качество ресайза (много искажений). Временная сложность обусловлена тем, что нужно найти минимальное значение в первом ряду (обход `w` ячеек), а затем исследовать только 3 соседних пикселя для каждого ряда (обход `h` рядов). + +#### Используем динамическое программирование + +Вы, наверное, заметили, что в наивном подходе мы снова и снова суммировали одни и те же энергии пикселей, вычисляя энергию образовавшихся швов. + +![Repeated problems](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/52-dp-repeated-problems.png) + +В примере выше видно, что для первых двух швов мы повторно используем энергию более короткого шва (который имеет энергию `235`). Вместо одной операции `235 + 70` для вычисления энергии 2-го шва мы делаем четыре операции `(5 + 0 + 80 + 150) + 70`. + +> Тот факт, что мы повторно используем энергию предыдущего шва для вычисления энергии текущего шва, может быть применен рекурсивно ко всем более коротким швам до самого верхнего 1-го ряда. Когда у нас есть такие перекрывающиеся под-проблемы, [это признак](https://trekhleb.dev/blog/2018/dynamic-programming-vs-divide-and-conquer/), что общая задача *может* быть оптимизирована с использованием динамического программирования. + +Таким образом, мы можем **сохранить энергию текущего шва** для конкретного пикселя в дополнительной таблице `samsEnergies`, чтобы повторно использовать ее при расчете энергии следующих швов (таблица `samsEnergies` будет иметь тот же размер, что и энергетическая карта и само изображение). + +Обратите также внимание, что для большинства пикселей в изображении (например, для левого нижнего) мы можем иметь *несколько* значений энергий предыдущих швов. + +![What seam to choose](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/53-dp-what-to-choose.png) + +Так как мы ищем шов с наименьшей результирующей энергией, имеет смысл выбирать и предыдущий шов с наименьшей результирующей энергией. + +![Seams energies example](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/56-dp-seams-energies-example.png) + +Как правило, у нас есть три возможных предыдущих шва, которые текущий пиксель продолжает: + +![Three options to choose from](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/55-dp-three-options.png) + +Можем посмотреть на это с такой стороны: + +- Ячейка `[1][x]`: содержит наименьшую возможную энергию шва, который начинается где-то в ряду `[0][?] ` и заканчивается в ячейке `[1][x]`. +- **Текущая ячейка** `[2][3]`: содержит наименьшую возможную энергию шва, который начинается где-то в ряду `[0][?] ` и заканчивается в ячейке `[2][3]`. Для вычисления нужно суммировать энергию текущего пикселя `[2][3]` (из энергетической карты) с `min(seam_energy_1_2, seam_energy_1_3, seam_energy_1_4)`. + +Если мы заполним таблицу `ShesamsEnergies` полностью, то минимальное число в нижнем ряду будет наименьшей возможной энергией шва. + +Попробуем заполнить несколько ячеек этой таблицы, чтобы посмотреть, как это работает. + +![Seams energies map traversal](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/57-dp-seams-energies-traversal.png) + +После заполнения таблицы `ShesamsEnergies` видно, что в нижнем ряду пиксель с самой низкой энергией имеет значение `50`. Для удобства во время генерации `samsEnergies` для каждого пикселя мы можем сохранить не только энергию шва, но и координаты предыдущего шва с наименьшей энергией. Это даст нам возможность легко восстанавливать траекторию шва снизу вверх. + +Временная сложность DP подхода составит `O(w * h)`, где `w` и `h` - это ширина и высота изображения. Обусловлена она тем, что нужно вычислить энергии для *всех* пикселей изображения. + +Вот пример того, как эта логика может быть реализована: + +```typescript +// The metadata for the pixels in the seam. +type SeamPixelMeta = { + energy: number, // The energy of the pixel. + coordinate: Coordinate, // The coordinate of the pixel. + previous: Coordinate | null, // The previous pixel in a seam. +}; + +// Finds the seam (the sequence of pixels from top to bottom) that has the +// lowest resulting energy using the Dynamic Programming approach. +const findLowEnergySeam = (energyMap: EnergyMap, { w, h }: ImageSize): Seam => { + // The 2D array of the size of w and h, where each pixel contains the + // seam metadata (pixel energy, pixel coordinate and previous pixel from + // the lowest energy seam at this point). + const seamsEnergies: (SeamPixelMeta | null)[][] = matrix(w, h, null); + + // Populate the first row of the map by just copying the energies + // from the energy map. + for (let x = 0; x < w; x += 1) { + const y = 0; + seamsEnergies[y][x] = { + energy: energyMap[y][x], + coordinate: { x, y }, + previous: null, + }; + } + + // Populate the rest of the rows. + for (let y = 1; y < h; y += 1) { + for (let x = 0; x < w; x += 1) { + // Find the top adjacent cell with minimum energy. + // This cell would be the tail of a seam with lowest energy at this point. + // It doesn't mean that this seam (path) has lowest energy globally. + // Instead, it means that we found a path with the lowest energy that may lead + // us to the current pixel with the coordinates x and y. + let minPrevEnergy = Infinity; + let minPrevX: number = x; + for (let i = (x - 1); i <= (x + 1); i += 1) { + if (i >= 0 && i < w && seamsEnergies[y - 1][i].energy < minPrevEnergy) { + minPrevEnergy = seamsEnergies[y - 1][i].energy; + minPrevX = i; + } + } + + // Update the current cell. + seamsEnergies[y][x] = { + energy: minPrevEnergy + energyMap[y][x], + coordinate: { x, y }, + previous: { x: minPrevX, y: y - 1 }, + }; + } + } + + // Find where the minimum energy seam ends. + // We need to find the tail of the lowest energy seam to start + // traversing it from its tail to its head (from the bottom to the top). + let lastMinCoordinate: Coordinate | null = null; + let minSeamEnergy = Infinity; + for (let x = 0; x < w; x += 1) { + const y = h - 1; + if (seamsEnergies[y][x].energy < minSeamEnergy) { + minSeamEnergy = seamsEnergies[y][x].energy; + lastMinCoordinate = { x, y }; + } + } + + // Find the lowest energy energy seam. + // Once we know where the tail is we may traverse and assemble the lowest + // energy seam based on the "previous" value of the seam pixel metadata. + const seam: Seam = []; + if (!lastMinCoordinate) { + return seam; + } + + const { x: lastMinX, y: lastMinY } = lastMinCoordinate; + + // Adding new pixel to the seam path one by one until we reach the top. + let currentSeam = seamsEnergies[lastMinY][lastMinX]; + while (currentSeam) { + seam.push(currentSeam.coordinate); + const prevMinCoordinates = currentSeam.previous; + if (!prevMinCoordinates) { + currentSeam = null; + } else { + const { x: prevMinX, y: prevMinY } = prevMinCoordinates; + currentSeam = seamsEnergies[prevMinY][prevMinX]; + } + } + + return seam; +}; +``` + +### Удаление шва с минимальной энергией + +Как только мы нашли шов с наименьшей суммарной энергией, нам нужно удалить (вырезать) пиксели, которые образуют его из изображения. Удаление происходит путем смещения пикселей справа от шва на `1px` влево. Из соображений производительности мы не будем удалять крайний столбик пикселей. Вместо этого, компонент, отвечающий за отрисовку уменьшенного изображения просто проигнорирует ту часть изображения, которая лежит за пределами обрезанной ширины. + +![Deleting the seam](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/60-deleting-example.png) + +```typescript +// Deletes the seam from the image data. +// We delete the pixel in each row and then shift the rest of the row pixels to the left. +const deleteSeam = (img: ImageData, seam: Seam, { w }: ImageSize): void => { + seam.forEach(({ x: seamX, y: seamY }: Coordinate) => { + for (let x = seamX; x < (w - 1); x += 1) { + const nextPixel = getPixel(img, { x: x + 1, y: seamY }); + setPixel(img, { x, y: seamY }, nextPixel); + } + }); +}; +``` + +## Удаление объектов с изображения + +Seam Carving алгоритм пытается сначала удалить швы, состоящие из низкоэнергетических пикселей. Мы могли бы использовать этот факт и, присвоив низкую энергию некоторым пикселям вручную (например, нарисовав на изображении маску), мы могли бы заставить алгоритм удалить отмеченные пиксели (*объекты*). + +В настоящее время в функции `getPixelEnergy()` мы используем только каналы цветов `R`, `G`, `B` для вычисления энергии пикселей. Но есть еще и параметр `A` (альфа, прозрачность), который мы не использовали. Мы можем использовать канал прозрачности, чтобы "сказать" алгоритму, что прозрачные пиксели — это те пиксели, которые мы хотим удалить. Вы можете ознакомиться с [исходным кодом функции getPixelEnergy()](https://github.com/trekhleb/js-image-carver/blob/main/src/utils/contentAwareResizer.ts#L54), которая учитывает прозрачность. + +Вот как при этом будет выглядеть удаление объектов: + +![JS IMAGE CARVER OBJECT REMOVAL DEMO](https://raw.githubusercontent.com/trekhleb/trekhleb.github.io/master/src/posts/2021/content-aware-image-resizing-in-javascript/assets/10-demo-02.gif) + +## Проблемы алгоритма и дальнейшие планы + +Приложение [JS IMAGE CARVER](https://github.com/trekhleb/js-image-carver) далеко от идеала и не является приложением production-ready качества. Основной его целью была возможность интерактивного экспериментирования с алгоритмом. Поэтому в дальнейших планах — использовать его именно для экспериментов. + +В [оригинальной статье](https://perso.crans.org/frenoy/matlab2012/seamcarving.pdf) описывается, как алгоритм может быть использован не только для уменьшения, но и для **увеличения изображения**. Увеличение (расширение) изображения, в свою очередь, может быть использовано для **автоматического расширения изображения до его исходной ширины после удаления объектов**. + +Еще одной интересной областью экспериментов может быть попытка ускорить алгоритм, чтобы он работал в режиме **реального времени**. + +> Таковы планы на будущее, но пока, надеюсь, пример с уменьшением изображения был интересен и полезен для вас. Также надеюсь, что вам было интересно увидеть применение динамического программирования в задачах, приближенных к реальности. +> +> Удачи с вашими собственными экспериментами! diff --git a/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js b/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js new file mode 100644 index 0000000000..b6400a3522 --- /dev/null +++ b/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js @@ -0,0 +1,51 @@ +import { createCanvas, loadImage } from 'canvas'; +import resizeImageWidth from '../resizeImageWidth'; + +const testImageBeforePath = './src/algorithms/image-processing/seam-carving/__tests__/test-image-before.jpg'; +const testImageAfterPath = './src/algorithms/image-processing/seam-carving/__tests__/test-image-after.jpg'; + +describe('resizeImageWidth', () => { + it('should perform content-aware image width reduction', () => { + // @see: https://jestjs.io/docs/asynchronous + return Promise.all([ + loadImage(testImageBeforePath), + loadImage(testImageAfterPath), + ]).then(([imgBefore, imgAfter]) => { + // Original image. + const canvasBefore = createCanvas(imgBefore.width, imgBefore.height); + const ctxBefore = canvasBefore.getContext('2d'); + ctxBefore.drawImage(imgBefore, 0, 0, imgBefore.width, imgBefore.height); + const imgDataBefore = ctxBefore.getImageData(0, 0, imgBefore.width, imgBefore.height); + + // Resized image saved. + const canvasAfter = createCanvas(imgAfter.width, imgAfter.height); + const ctxAfter = canvasAfter.getContext('2d'); + ctxAfter.drawImage(imgAfter, 0, 0, imgAfter.width, imgAfter.height); + + const toWidth = Math.floor(imgBefore.width / 2); + + const { + img: resizedImg, + size: resizedSize, + } = resizeImageWidth({ img: imgDataBefore, toWidth }); + + expect(resizedImg).toBeDefined(); + expect(resizedSize).toBeDefined(); + + // Resized image generated. + const canvasTest = createCanvas(resizedSize.w, resizedSize.h); + const ctxTest = canvasTest.getContext('2d'); + ctxTest.putImageData(resizedImg, 0, 0, 0, 0, resizedSize.w, resizedSize.h); + const imgDataTest = ctxTest.getImageData(0, 0, resizedSize.w, resizedSize.h); + + expect(resizedSize).toEqual({ w: toWidth, h: imgBefore.height }); + expect(imgDataTest.width).toBe(toWidth); + expect(imgDataTest.height).toBe(imgBefore.height); + expect(imgDataTest.width).toBe(imgAfter.width); + expect(imgDataTest.height).toBe(imgAfter.height); + + // @TODO: Check that images are identical. + // expect(canvasTest.toDataURL()).toEqual(canvasAfter.toDataURL()); + }); + }); +}); diff --git a/src/algorithms/image-processing/seam-carving/__tests__/test-image-after.jpg b/src/algorithms/image-processing/seam-carving/__tests__/test-image-after.jpg new file mode 100644 index 0000000000000000000000000000000000000000..9af094e3ea2fc4e5cb70b1291c4a71a33c580ce5 GIT binary patch literal 6088 zcmV;(7dPmMP)-6Q>;pY&ZH;Xi*Z6Gsp#kPb@+;_*r#_Av@_H^WGWcaS83(nuGP zXh^C+iy@_s>>>n56%sS0F{+`6Ee!))wnXXZR0N|zX~+$z29-ejk{l}{Ek;?q8KeCG z8#KXA&?e9|8f)k1RHTTJRtw~oJ{5-KAZK(Iq5`kM#6IL1I%^0WVhxqG^n7CGGo3An zDk7?d2#JW*f)|ZsMQbA_Bmxi$1s-N<2BIJtbO%Z@-dIqYlp{$SOb9qr(dIE2P0Wg< zgsg;+G-XlI$b^!T&XtfND8YM=G0CBF28l#%PEO?z0vaJGp%5?!`z*AP$_&|UGvi^8 zgA@^KAVfkA^J0cdGhRG4mB$A4d97qc)lTo06 zP?E(!>PWdIB?YE{oN3h<6GfpibS{Bvkfg{ORMZ3$n2U*p<30ZJ#Z}DRo4oR^|IWgx zi`+Z4MmW37xX={d(&~&WOLVL8QZjQhBv;h4Kw~pePBv4fOg1nT&?3~cKp8!v6~}2t zECdlv4ho2V z6HP)3ARfs*lu}?LXaOG}wqOmusOTldqfN*2I&x}yhjjaOHk&>8#y2^B^BQwi30E9<;e7u>TIknz1CVKzm_mZpgGeMjB;lRJaL&t^2vvO5^k zRs|{w!yH&C4B8~toT5PCH!iR>X-Q(iCM5SsML<+!u^scpOIP^#T*uvZOwsM~)n9pz zy*T4LlLL&inSOK3dYG}I61T<^KIo4)a&s*DWA<&y!O}Ut{{A+X9tM8!&V=(HzQ`MC z#6f?El8zK0tBPO)ND2O!=aS*lcEjthy~XW&cW9hu>Ekal*;pqQmiODpeJz|>JIB)- zkMi0p*Emiki)YVqD|D1`N*E1EA>))nx*2_&DF>G2ZcMpzz;n@Y7t32tqwCLo{>vXR z4Zl7tn1A~%e)7kELOs`~TA9bMoFjHEN4}-qxWx9^%k0lD z9ZT(mf4=!7mw)mu(>u2*kB^9l$1Dx|$e?0xXxVZwK04y)t!vzQ^E%&p`#SZfKSO%z z3X{U%e4v=jD7B`rn(U_xY{C_a8!uf&lHuQe?T_#ud4Zqw=P~`*@R@Ti@(5*)AZY8E-1L*4Ey6f z-Ww;>!W{qMoohUN;xRUx0srON+kE@-vuvE&;6^=%v0}J+?;%f@6<2THqCEE)qiV=l zRZK((rp3*GEQDe}mp#rwk3f==gry=wvyKXIQwx2XJMZy>H{PYPJsuXCgXQ!5!3X<%z8>=Z z`DOOL@Hn&cn{>vZSAP2+efj48E^cuFU)9_aP4C4|us6TJl!QrPA?k+Dd8T6^e(u;~FYvlAA zUF9IPd}e-ue|+u?=kC7F?A}i}*nXGsjSrX)ef(gRdvl8n)CB#=Cf%uJqP4i@2vf9) z?X`8jak$Usho2#zA9MfIh<#VEG@Y_rC_40F8^Y5 zzHE47dY{v=raM07&<6@@+3PEk%FJa*?HI}mB{tEs71Cc~r(QsrVZnJJNRMEcPTV)0YYqdxtM04~!p1|&+%aes?=1EyO<>~?j!nsTKK=^~XGa*T$v!bl16;7o6POiyOiiCTZ)tVI zLbt`6G{b?2opP@?rO5i6e(l7NYWKngq77(ymIFz2WdvySR>RH69U>~g3~Aw6hc;+ zEQ*}K7^N^-Av&Xd;zZUbVvHN01WAZV zsO(TiV?#;OWBSRXydoBsiRqJ3WS^;Z0ufRctP%tOMamh2!iWeacP!34k|9-=tf7xV zR6TaEZLcpfm4T5n&=&v6Vph_1cXdRl{)iS zbetOtM}PJz>D{|5D1+qz-dgs`nov2k);uhSe6tbWzx*_3Uibud7Af@twe}p(rd-{h zvFK-n=?)Z$VpyU=z;%g21(dEaqA8>vE(V9eB?6dLIV@!;pBw=*o z%u$04HnrQ&4U`?*kd>glvxq2 z`w?rJBYy6mlZtyQCl{l(RTyWD$&j{5)wfz9=~?BjdAu zp7{rVgX6g#-e{7*VspsHssTUz?)SOxYF0k>0(*XfC?Tta(uovj)Jkw&U=&+^|Hd`q z$||$@5mQyr*j=7?id7l#;O1@itV4|!*jE}c78@*Dx0qB?#*EDhuOaD#4Fx^r@oh!n zP7pQfj1@)Fnh*k+h|wBjQ=rv`xH2Th%tSP`7nY8<`P>s%Sh{hCfAy8Gu=(OA>77}n zJbxN;$5IC0MGmVz53*rd;QFn1dF9q^9$#H&V0xhY)H?Dj=a$ghd)!Nr-LfJAV;?X& zqe6+(ib5=O4bddL%gl15UmIv5HUQD#NMzm8{oFxot52vSXHZQD>;2Q?%g*_~TpfkfQe=Kh5r`L%R&=OgyEWM5M99qpFYP>#43*X!w^Vq3X{CUkjmgA5y zm8EJE-gK0mh8XcqGn@%e%ZRvtpC7#UCiB1eJiEP2kzn98V$?}8>RX%u2$K{sP8*u! zab%ju#|%ohD{m${f}qF{)$w!?*h zl@k@N5mHJ->o5kPKv8K;@Es{6Mx|rVD#k_TXA=3|jrV!#(xY@M8#v{NF`(w=n8bk2 z2Gv9aLvWfw=gCIVN}>)5Z-lb$(RQBLs|i0hVk1`&eLBgPEhwkats*1f&K@VTljKon; 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+ }); +}; + +/** + * Calculates the energy of a pixel. + * @param {?PixelColor} left + * @param {PixelColor} middle + * @param {?PixelColor} right + * @returns {number} + */ +const getPixelEnergy = (left, middle, right) => { + // Middle pixel is the pixel we're calculating the energy for. + const [mR, mG, mB] = middle; + + // Energy from the left pixel (if it exists). + let lEnergy = 0; + if (left) { + const [lR, lG, lB] = left; + lEnergy = (lR - mR) ** 2 + (lG - mG) ** 2 + (lB - mB) ** 2; + } + + // Energy from the right pixel (if it exists). + let rEnergy = 0; + if (right) { + const [rR, rG, rB] = right; + rEnergy = (rR - mR) ** 2 + (rG - mG) ** 2 + (rB - mB) ** 2; + } + + // Resulting pixel energy. + return Math.sqrt(lEnergy + rEnergy); +}; + +/** + * Calculates the energy of each pixel of the image. + * @param {ImageData} img + * @param {ImageSize} size + * @returns {EnergyMap} + */ +const calculateEnergyMap = (img, { w, h }) => { + // Create an empty energy map where each pixel has infinitely high energy. + // We will update the energy of each pixel. + const energyMap = matrix(w, h, Infinity); + for (let y = 0; y < h; y += 1) { + for (let x = 0; x < w; x += 1) { + // Left pixel might not exist if we're on the very left edge of the image. + const left = (x - 1) >= 0 ? getPixel(img, { x: x - 1, y }) : null; + // The color of the middle pixel that we're calculating the energy for. + const middle = getPixel(img, { x, y }); + // Right pixel might not exist if we're on the very right edge of the image. + const right = (x + 1) < w ? getPixel(img, { x: x + 1, y }) : null; + energyMap[y][x] = getPixelEnergy(left, middle, right); + } + } + return energyMap; +}; + +/** + * Finds the seam (the sequence of pixels from top to bottom) that has the + * lowest resulting energy using the Dynamic Programming approach. + * @param {EnergyMap} energyMap + * @param {ImageSize} size + * @returns {Seam} + */ +const findLowEnergySeam = (energyMap, { w, h }) => { + // The 2D array of the size of w and h, where each pixel contains the + // seam metadata (pixel energy, pixel coordinate and previous pixel from + // the lowest energy seam at this point). + const seamPixelsMap = matrix(w, h, null); + + // Populate the first row of the map by just copying the energies + // from the energy map. + for (let x = 0; x < w; x += 1) { + const y = 0; + seamPixelsMap[y][x] = { + energy: energyMap[y][x], + coordinate: { x, y }, + previous: null, + }; + } + + // Populate the rest of the rows. + for (let y = 1; y < h; y += 1) { + for (let x = 0; x < w; x += 1) { + // Find the top adjacent cell with minimum energy. + // This cell would be the tail of a seam with lowest energy at this point. + // It doesn't mean that this seam (path) has lowest energy globally. + // Instead, it means that we found a path with the lowest energy that may lead + // us to the current pixel with the coordinates x and y. + let minPrevEnergy = Infinity; + let minPrevX = x; + for (let i = (x - 1); i <= (x + 1); i += 1) { + if (i >= 0 && i < w && seamPixelsMap[y - 1][i].energy < minPrevEnergy) { + minPrevEnergy = seamPixelsMap[y - 1][i].energy; + minPrevX = i; + } + } + + // Update the current cell. + seamPixelsMap[y][x] = { + energy: minPrevEnergy + energyMap[y][x], + coordinate: { x, y }, + previous: { x: minPrevX, y: y - 1 }, + }; + } + } + + // Find where the minimum energy seam ends. + // We need to find the tail of the lowest energy seam to start + // traversing it from its tail to its head (from the bottom to the top). + let lastMinCoordinate = null; + let minSeamEnergy = Infinity; + for (let x = 0; x < w; x += 1) { + const y = h - 1; + if (seamPixelsMap[y][x].energy < minSeamEnergy) { + minSeamEnergy = seamPixelsMap[y][x].energy; + lastMinCoordinate = { x, y }; + } + } + + // Find the lowest energy energy seam. + // Once we know where the tail is we may traverse and assemble the lowest + // energy seam based on the "previous" value of the seam pixel metadata. + const seam = []; + + const { x: lastMinX, y: lastMinY } = lastMinCoordinate; + + // Adding new pixel to the seam path one by one until we reach the top. + let currentSeam = seamPixelsMap[lastMinY][lastMinX]; + while (currentSeam) { + seam.push(currentSeam.coordinate); + const prevMinCoordinates = currentSeam.previous; + if (!prevMinCoordinates) { + currentSeam = null; + } else { + const { x: prevMinX, y: prevMinY } = prevMinCoordinates; + currentSeam = seamPixelsMap[prevMinY][prevMinX]; + } + } + + return seam; +}; + +/** + * Deletes the seam from the image data. + * We delete the pixel in each row and then shift the rest of the row pixels to the left. + * @param {ImageData} img + * @param {Seam} seam + * @param {ImageSize} size + */ +const deleteSeam = (img, seam, { w }) => { + seam.forEach(({ x: seamX, y: seamY }) => { + for (let x = seamX; x < (w - 1); x += 1) { + const nextPixel = getPixel(img, { x: x + 1, y: seamY }); + setPixel(img, { x, y: seamY }, nextPixel); + } + }); +}; + +/** + * Performs the content-aware image width resizing using the seam carving method. + * @param {ResizeImageWidthArgs} args + * @returns {ResizeImageWidthResult} + */ +const resizeImageWidth = ({ img, toWidth }) => { + /** + * For performance reasons we want to avoid changing the img data array size. + * Instead we'll just keep the record of the resized image width and height separately. + * @type {ImageSize} + */ + const size = { w: img.width, h: img.height }; + + // Calculating the number of pixels to remove. + const pxToRemove = img.width - toWidth; + + let energyMap = null; + let seam = null; + + // Removing the lowest energy seams one by one. + for (let i = 0; i < pxToRemove; i += 1) { + // 1. Calculate the energy map for the current version of the image. + energyMap = calculateEnergyMap(img, size); + + // 2. Find the seam with the lowest energy based on the energy map. + seam = findLowEnergySeam(energyMap, size); + + // 3. Delete the seam with the lowest energy seam from the image. + deleteSeam(img, seam, size); + + // Reduce the image width, and continue iterations. + size.w -= 1; + } + + // Returning the resized image and its final size. + // The img is actually a reference to the ImageData, so technically + // the caller of the function already has this pointer. But let's + // still return it for better code readability. + return { img, size }; +}; + +export default resizeImageWidth; diff --git a/src/algorithms/image-processing/utils/imageData.js b/src/algorithms/image-processing/utils/imageData.js new file mode 100644 index 0000000000..de397b8ead --- /dev/null +++ b/src/algorithms/image-processing/utils/imageData.js @@ -0,0 +1,39 @@ +/** + * @typedef {ArrayLike | Uint8ClampedArray} PixelColor + */ + +/** + * @typedef {Object} PixelCoordinate + * @property {number} x - horizontal coordinate. + * @property {number} y - vertical coordinate. + */ + +/** + * Helper function that returns the color of the pixel. + * @param {ImageData} img + * @param {PixelCoordinate} coordinate + * @returns {PixelColor} + */ +export const getPixel = (img, { x, y }) => { + // The ImageData data array is a flat 1D array. + // Thus we need to convert x and y coordinates to the linear index. + const i = y * img.width + x; + const cellsPerColor = 4; // RGBA + // For better efficiency, instead of creating a new sub-array we return + // a pointer to the part of the ImageData array. + return img.data.subarray(i * cellsPerColor, i * cellsPerColor + cellsPerColor); +}; + +/** + * Helper function that sets the color of the pixel. + * @param {ImageData} img + * @param {PixelCoordinate} coordinate + * @param {PixelColor} color + */ +export const setPixel = (img, { x, y }, color) => { + // The ImageData data array is a flat 1D array. + // Thus we need to convert x and y coordinates to the linear index. + const i = y * img.width + x; + const cellsPerColor = 4; // RGBA + img.data.set(color, i * cellsPerColor); +}; From cfd9a630ff8cacd17880b16b27f32781eaac6bb7 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Wed, 21 Apr 2021 07:39:58 +0200 Subject: [PATCH 003/186] Test that two images are identical for the Seam Carving algorithm. (#694) * Test that two images are identical for the Seam Carving algorithm. * Tune the Seam Carving tests. * Tune the Seam Carving tests. * Tune the Seam Carving tests. * Tune the Seam Carving tests. --- .husky/pre-commit | 1 + .../__tests__/resizeImageWidth.test.js | 44 ++++++++++++++++++- 2 files changed, 43 insertions(+), 2 deletions(-) diff --git a/.husky/pre-commit b/.husky/pre-commit index bec1c08a1a..a29a4166ea 100755 --- a/.husky/pre-commit +++ b/.husky/pre-commit @@ -1,5 +1,6 @@ #!/bin/sh . "$(dirname "$0")/_/husky.sh" +# @TODO: Implement the pre-commit checks. # npm run lint # npm run test diff --git a/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js b/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js index b6400a3522..9afed97123 100644 --- a/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js +++ b/src/algorithms/image-processing/seam-carving/__tests__/resizeImageWidth.test.js @@ -4,6 +4,40 @@ import resizeImageWidth from '../resizeImageWidth'; const testImageBeforePath = './src/algorithms/image-processing/seam-carving/__tests__/test-image-before.jpg'; const testImageAfterPath = './src/algorithms/image-processing/seam-carving/__tests__/test-image-after.jpg'; +/** + * Compares two images and finds the number of different pixels. + * + * @param {ImageData} imgA - ImageData for the first image. + * @param {ImageData} imgB - ImageData for the second image. + * @param {number} threshold - Color difference threshold [0..255]. Smaller - stricter. + * @returns {number} - Number of different pixels. + */ +function pixelsDiff(imgA, imgB, threshold = 0) { + if (imgA.width !== imgB.width || imgA.height !== imgB.height) { + throw new Error('Images must have the same size'); + } + + let differentPixels = 0; + const numColorParams = 4; // RGBA + + for (let pixelIndex = 0; pixelIndex < imgA.data.length; pixelIndex += numColorParams) { + // Get pixel's color for each image. + const [aR, aG, aB] = imgA.data.subarray(pixelIndex, pixelIndex + numColorParams); + const [bR, bG, bB] = imgB.data.subarray(pixelIndex, pixelIndex + numColorParams); + + // Get average pixel's color for each image (make them greyscale). + const aAvgColor = Math.floor((aR + aG + aB) / 3); + const bAvgColor = Math.floor((bR + bG + bB) / 3); + + // Compare pixel colors. + if (Math.abs(aAvgColor - bAvgColor) > threshold) { + differentPixels += 1; + } + } + + return differentPixels; +} + describe('resizeImageWidth', () => { it('should perform content-aware image width reduction', () => { // @see: https://jestjs.io/docs/asynchronous @@ -21,6 +55,7 @@ describe('resizeImageWidth', () => { const canvasAfter = createCanvas(imgAfter.width, imgAfter.height); const ctxAfter = canvasAfter.getContext('2d'); ctxAfter.drawImage(imgAfter, 0, 0, imgAfter.width, imgAfter.height); + const imgDataAfter = ctxAfter.getImageData(0, 0, imgAfter.width, imgAfter.height); const toWidth = Math.floor(imgBefore.width / 2); @@ -44,8 +79,13 @@ describe('resizeImageWidth', () => { expect(imgDataTest.width).toBe(imgAfter.width); expect(imgDataTest.height).toBe(imgAfter.height); - // @TODO: Check that images are identical. - // expect(canvasTest.toDataURL()).toEqual(canvasAfter.toDataURL()); + const colorThreshold = 50; + const differentPixels = pixelsDiff(imgDataTest, imgDataAfter, colorThreshold); + + // Allow 10% of pixels to be different + const pixelsThreshold = Math.floor((imgAfter.width * imgAfter.height) / 10); + + expect(differentPixels).toBeLessThanOrEqual(pixelsThreshold); }); }); }); From 144b6867761a064bfe766c0c1994ebd1be676e74 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Wed, 21 Apr 2021 16:55:26 +0200 Subject: [PATCH 004/186] Testing Husky integration --- .husky/pre-commit | 5 ++--- .npmrc | 1 + package.json | 5 ++++- 3 files changed, 7 insertions(+), 4 deletions(-) create mode 100644 .npmrc diff --git a/.husky/pre-commit b/.husky/pre-commit index a29a4166ea..660b820968 100755 --- a/.husky/pre-commit +++ b/.husky/pre-commit @@ -1,6 +1,5 @@ #!/bin/sh . "$(dirname "$0")/_/husky.sh" -# @TODO: Implement the pre-commit checks. -# npm run lint -# npm run test +npm run lint +npm run test diff --git a/.npmrc b/.npmrc new file mode 100644 index 0000000000..c0c80ba447 --- /dev/null +++ b/.npmrc @@ -0,0 +1 @@ +engine-strict=false diff --git a/package.json b/package.json index c4ae69b6fd..f77d87ff50 100644 --- a/package.json +++ b/package.json @@ -48,5 +48,8 @@ "husky": "6.0.0", "jest": "26.6.3" }, - "dependencies": {} + "engines": { + "node": ">=12.0.0", + "npm": ">=6.9.0" + } } From f7d07ae66d0fbd2c9b093bb074c8cb02de7be4b8 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Wed, 21 Apr 2021 17:09:59 +0200 Subject: [PATCH 005/186] Testing Husky integration --- .husky/pre-commit | 1 + 1 file changed, 1 insertion(+) diff --git a/.husky/pre-commit b/.husky/pre-commit index 660b820968..4c19307277 100755 --- a/.husky/pre-commit +++ b/.husky/pre-commit @@ -1,5 +1,6 @@ #!/bin/sh . "$(dirname "$0")/_/husky.sh" +# Testing Husky. npm run lint npm run test From 4ca41ea83b8fdbfe2eb056c8b89852466a840a29 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Wed, 21 Apr 2021 17:12:53 +0200 Subject: [PATCH 006/186] Testing Husky integration --- .husky/pre-commit | 1 - 1 file changed, 1 deletion(-) diff --git a/.husky/pre-commit b/.husky/pre-commit index 4c19307277..660b820968 100755 --- a/.husky/pre-commit +++ b/.husky/pre-commit @@ -1,6 +1,5 @@ #!/bin/sh . "$(dirname "$0")/_/husky.sh" -# Testing Husky. npm run lint npm run test From 912941be1d42d19a0a8b5ded73b35deee8e05718 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Wed, 21 Apr 2021 17:30:49 +0200 Subject: [PATCH 007/186] Add troubleshooting instructions. --- README.md | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/README.md b/README.md index 71b0798fbe..a9fc7b5ea0 100644 --- a/README.md +++ b/README.md @@ -236,6 +236,7 @@ tree is being used. ## How to use this repository **Install all dependencies** + ``` npm install ``` @@ -249,15 +250,26 @@ npm run lint ``` **Run all tests** + ``` npm test ``` **Run tests by name** + ``` npm test -- 'LinkedList' ``` +**Troubleshooting** + +In case if linting or testing is failing try to delete the `node_modules` folder and re-install npm packages: + +``` +rm -rf ./node_modules +npm i +``` + **Playground** You may play with data-structures and algorithms in `./src/playground/playground.js` file and write From 7ad3fbc0f9eebfc4e86623be94e7c3dfbe9e611d Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Wed, 21 Apr 2021 18:09:48 +0200 Subject: [PATCH 008/186] Disabling tests in pre-commit to speed up the commits. --- .husky/pre-commit | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/.husky/pre-commit b/.husky/pre-commit index 660b820968..598a5dceaa 100755 --- a/.husky/pre-commit +++ b/.husky/pre-commit @@ -2,4 +2,4 @@ . "$(dirname "$0")/_/husky.sh" npm run lint -npm run test +# npm run test From d38cecd2e79d64efba1dd0b37cdd9acd60bc42ba Mon Sep 17 00:00:00 2001 From: Coco Guerra Date: Wed, 5 May 2021 22:43:28 -0600 Subject: [PATCH 009/186] Update README.es-ES.md (#704) * Update README.es-ES.md * Update README.es-ES.md --- .../linked-list/README.es-ES.md | 41 +++++++++---------- 1 file changed, 20 insertions(+), 21 deletions(-) diff --git a/src/data-structures/linked-list/README.es-ES.md b/src/data-structures/linked-list/README.es-ES.md index 978e234ddf..58eb2b860d 100644 --- a/src/data-structures/linked-list/README.es-ES.md +++ b/src/data-structures/linked-list/README.es-ES.md @@ -7,27 +7,26 @@ _Lee esto en otros idiomas:_ [_Português_](README.pt-BR.md) [_English_](README.md) -En ciencias de la computaciòn una **lista enlazada** es una coleccion linear +En ciencias de la computación una **lista enlazada** es una colección linear de elemntos de datos, en los cuales el orden linear no es dado por -su posciòn fisica en memoria. En cambio, cada -elemento señala al siguiente. Es una estructura de datos +su posción física en memoria. En cambio, cada +elemento señala al siguiente. Es una estructura de datos que consiste en un grupo de nodos los cuales juntos representan -una secuencia. Bajo la forma mas simple, cada nodo es -compuesto de datos y una referencia (en otras palabras, +una secuencia. Bajo la forma más simple, cada nodo es +compuesto de datos y una referencia (en otras palabras, un lazo) al siguiente nodo en la secuencia. Esta estructura -permite la insercion o remocion de elementos -desde cualquier posicion en la secuencia durante la iteracion. -Variantes mas complejas agregan lazos adicionales, permitiendo -una eficiente insercion o remocion desde referencias arbitrarias +permite la inserción o remoción de elementos +desde cualquier posición en la secuencia durante la iteración. +Variantes más complejas agregan lazos adicionales, permitiendo +una eficiente inserción o remoción desde referencias arbitrarias del elemento. Una desventaja de las listas lazadas es que el tiempo de -acceso es linear (y dificil de canalizar) Un acceso -mas rapido, como un acceso aleatorio, no es factible. Los arreglos +acceso es linear (y difícil de canalizar). Un acceso +más rápido, como un acceso aleatorio, no es factible. Los arreglos tienen una mejor locazion comparados con las listas lazadas. - ![Linked List](https://upload.wikimedia.org/wikipedia/commons/6/6d/Singly-linked-list.svg) -## Pseudocodigo para operacones basicas +## Pseudocódigo para operacones básicas ### Insertar @@ -76,7 +75,7 @@ Contains(head, value) return true end Contains ``` - + ### Borrar ```text @@ -146,19 +145,19 @@ ReverseTraversal(head, tail) end ReverseTraversal ``` -## Complexities +## Complejidades -### Time Complexity +### Complejidad del Tiempo -| Access | Search | Insertion | Deletion | -| :-------: | :-------: | :-------: | :-------: | -| O(n) | O(n) | O(1) | O(n) | +| Access | Search | Insertion | Deletion | +| :----: | :----: | :-------: | :------: | +| O(n) | O(n) | O(1) | O(n) | -### Space Complexity +### Complejidad Espacial O(n) -## References +## Referencias - [Wikipedia](https://en.wikipedia.org/wiki/Linked_list) - [YouTube](https://www.youtube.com/watch?v=njTh_OwMljA&index=2&t=1s&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) From 64abcf12f28e02580b28cc8b64bab5ff0ac9c037 Mon Sep 17 00:00:00 2001 From: Deniz Binay <69312106+denizbinay@users.noreply.github.com> Date: Thu, 6 May 2021 06:46:04 +0200 Subject: [PATCH 010/186] add german translation for main readme (#703) --- README.ar-AR.md | 3 +- README.de-DE.md | 333 ++++++++++++++++++++++++++++++++++++++++++++++++ README.es-ES.md | 3 +- README.fr-FR.md | 3 +- README.id-ID.md | 3 +- README.it-IT.md | 3 +- README.ja-JP.md | 3 +- README.ko-KR.md | 3 +- README.md | 3 +- README.pl-PL.md | 3 +- README.pt-BR.md | 3 +- README.ru-RU.md | 3 +- README.tr-TR.md | 3 +- README.uk-UA.md | 3 +- README.zh-CN.md | 3 +- README.zh-TW.md | 3 +- 16 files changed, 363 insertions(+), 15 deletions(-) create mode 100644 README.de-DE.md diff --git a/README.ar-AR.md b/README.ar-AR.md index 378334fab0..797006b6ef 100644 --- a/README.ar-AR.md +++ b/README.ar-AR.md @@ -21,7 +21,8 @@ _اقرأ هذا في لغات أخرى:_ [_Português_](README.pt-BR.md), [_Русский_](README.ru-RU.md), [_Türk_](README.tr-TR.md), -[_Italiana_](README.it-IT.md) +[_Italiana_](README.it-IT.md), +[_Deutsch_](README.de-DE.md) ☝ ملاحضة هذا المشروع مخصص للاستخدام لأغراض التعلم والبحث فقط ، و ** ليست ** معدة للاستخدام في **الإنتاج** diff --git a/README.de-DE.md b/README.de-DE.md new file mode 100644 index 0000000000..3e127c3ea0 --- /dev/null +++ b/README.de-DE.md @@ -0,0 +1,333 @@ +# JavaScript-Algorithmen und Datenstrukturen + +[![CI](https://github.com/trekhleb/javascript-algorithms/workflows/CI/badge.svg)](https://github.com/trekhleb/javascript-algorithms/actions?query=workflow%3ACI+branch%3Amaster) +[![codecov](https://codecov.io/gh/trekhleb/javascript-algorithms/branch/master/graph/badge.svg)](https://codecov.io/gh/trekhleb/javascript-algorithms) + +Dieses Repository enthält JavaScript Beispiele für viele +gängige Algorithmen und Datenstrukturen. + +Jeder Algorithmus und jede Datenstruktur hat eine eigene README +mit zugehörigen Erklärungen und weiterführenden Links (einschließlich zu YouTube-Videos). + +_Lies dies in anderen Sprachen:_ +[_English_](https://github.com/trekhleb/javascript-algorithms/) +[_简体中文_](README.zh-CN.md), +[_繁體中文_](README.zh-TW.md), +[_한국어_](README.ko-KR.md), +[_日本語_](README.ja-JP.md), +[_Polski_](README.pl-PL.md), +[_Français_](README.fr-FR.md), +[_Español_](README.es-ES.md), +[_Português_](README.pt-BR.md), +[_Русский_](README.ru-RU.md), +[_Türk_](README.tr-TR.md), +[_Italiana_](README.it-IT.md), +[_Bahasa Indonesia_](README.id-ID.md), +[_Українська_](README.uk-UA.md), +[_Arabic_](README.ar-AR.md) + +_☝ Beachte, dass dieses Projekt nur für Lern- und Forschungszwecke gedacht ist und **nicht** für den produktiven Einsatz verwendet werden soll_ + +## Datenstrukturen + +Eine Datenstruktur ist eine bestimmte Art und Weise, Daten in einem Computer so zu organisieren und zu speichern, dass sie +effizient erreicht und verändert werden können. Genauer gesagt, ist eine Datenstruktur eine Sammlung von Werten, +den Beziehungen zwischen ihnen und den Funktionen oder Operationen, die auf die Daten angewendet werden können. + +`B` - Anfänger:innen, `A` - Fortgeschrittene + +* `B` [Verkettete Liste (Linked List)](src/data-structures/linked-list) +* `B` [Doppelt verkettete Liste (Doubly Linked List)](src/data-structures/doubly-linked-list) +* `B` [Warteschlange (Queue)](src/data-structures/queue) +* `B` [Stapelspeicher (Stack)](src/data-structures/stack) +* `B` [Hashtabelle (Hash Table)](src/data-structures/hash-table) +* `B` [Heap-Algorithmus (Heap)](src/data-structures/heap) - max und min Heap-Versionen +* `B` [Vorrangwarteschlange (Priority Queue)](src/data-structures/priority-queue) +* `A` [Trie (Trie)](src/data-structures/trie) +* `A` [Baum (Tree)](src/data-structures/tree) + * `A` [Binärer Suchbaum (Binary Search Tree)](src/data-structures/tree/binary-search-tree) + * `A` [AVL-Baum (AVL Tree)](src/data-structures/tree/avl-tree) + * `A` [Rot-Schwarz-Baum (Red-Black Tree)](src/data-structures/tree/red-black-tree) + * `A` [Segment-Baum (Segment Tree)](src/data-structures/tree/segment-tree) - mit Min/Max/Summenbereich-Abfrage Beispiel + * `A` [Fenwick Baum (Fenwick Tree)](src/data-structures/tree/fenwick-tree) (Binär indizierter Baum / Binary Indexed Tree) +* `A` [Graph (Graph)](src/data-structures/graph) (sowohl gerichtet als auch ungerichtet) +* `A` [Union-Find-Struktur (Disjoint Set)](src/data-structures/disjoint-set) +* `A` [Bloomfilter (Bloom Filter)](src/data-structures/bloom-filter) + +## Algorithmen + +Ein Algorithmus ist eine eindeutige Spezifikation, wie eine Klasse von Problemen zu lösen ist. Er besteht +aus einem Satz von Regeln, die eine Abfolge von Operationen genau definieren. + +`B` - Anfänger:innen, `A` - Fortgeschrittene + +### Algorithmen nach Thema + +* **Mathe** + * `B` [Bitmanipulation (Bit Manipulation)](src/algorithms/math/bits) - Bits setzen/lesen/aktualisieren/löschen, Multiplikation/Division durch zwei negieren usw.. + * `B` [Faktoriell (Factorial)](src/algorithms/math/factorial) + * `B` [Fibonacci-Zahl (Fibonacci Number)](src/algorithms/math/fibonacci) - Klassische und geschlossene Version + * `B` [Primfaktoren (Prime Factors)](src/algorithms/math/prime-factors) - Auffinden von Primfaktoren und deren Zählung mit Hilfe des Satz von Hardy-Ramanujan (Hardy-Ramanujan's theorem) + * `B` [Primzahl-Test (Primality Test)](src/algorithms/math/primality-test) (Probedivision / trial division method) + * `B` [Euklidischer Algorithmus (Euclidean Algorithm)](src/algorithms/math/euclidean-algorithm) - Berechnen des größten gemeinsamen Teilers (ggT) + * `B` [Kleinstes gemeinsames Vielfaches (Least Common Multiple)](src/algorithms/math/least-common-multiple) (kgV) + * `B` [Sieb des Eratosthenes (Sieve of Eratosthenes)](src/algorithms/math/sieve-of-eratosthenes) - Finden aller Primzahlen bis zu einer bestimmten Grenze + * `B` [Power of two (Is Power of Two)](src/algorithms/math/is-power-of-two) - Prüft, ob die Zahl eine Zweierpotenz ist (naive und bitweise Algorithmen) + * `B` [Pascalsches Dreieck (Pascal's Triangle)](src/algorithms/math/pascal-triangle) + * `B` [Komplexe Zahlen (Complex Number)](src/algorithms/math/complex-number) - Komplexe Zahlen und Grundoperationen mit ihnen + * `B` [Bogenmaß & Grad (Radian & Degree)](src/algorithms/math/radian) - Umrechnung von Bogenmaß in Grad und zurück + * `B` [Fast Powering Algorithmus (Fast Powering)](src/algorithms/math/fast-powering) + * `B` [Horner-Schema (Horner's method)](src/algorithms/math/horner-method) - Polynomauswertung + * `B` [Matrizen (Matrices)](src/algorithms/math/matrix) - Matrizen und grundlegende Matrixoperationen (Multiplikation, Transposition usw.) + * `B` [Euklidischer Abstand (Euclidean Distance)](src/algorithms/math/euclidean-distance) - Abstand zwischen zwei Punkten/Vektoren/Matrizen + * `A` [Ganzzahlige Partitionierung (Integer Partition)](src/algorithms/math/integer-partition) + * `A` [Quadratwurzel (Square Root)](src/algorithms/math/square-root) - Newtonverfahren (Newton's method) + * `A` [Liu Hui π Algorithmus (Liu Hui π Algorithm)](src/algorithms/math/liu-hui) - Näherungsweise π-Berechnungen auf Basis von N-gons + * `A` [Diskrete Fourier-Transformation (Discrete Fourier Transform)](src/algorithms/math/fourier-transform) - Eine Funktion der Zeit (ein Signal) in die Frequenzen zerlegen, aus denen sie sich zusammensetzt +* **Sets** + * `B` [Kartesisches Produkt (Cartesian Product)](src/algorithms/sets/cartesian-product) - Produkt aus mehreren Mengen + * `B` [Fisher-Yates-Verfahren (Fisher–Yates Shuffle)](src/algorithms/sets/fisher-yates) - Zufällige Permutation einer endlichen Folge + * `A` [Potenzmenge (Power Set)](src/algorithms/sets/power-set) - Alle Teilmengen einer Menge (Bitweise und Rücksetzverfahren Lösungen(backtracking solutions)) + * `A` [Permutation (Permutations)](src/algorithms/sets/permutations) (mit und ohne Wiederholungen) + * `A` [Kombination (Combinations)](src/algorithms/sets/combinations) (mit und ohne Wiederholungen) + * `A` [Problem der längsten gemeinsamen Teilsequenz (Longest Common Subsequence)](src/algorithms/sets/longest-common-subsequence) (LCS) + * `A` [Längste gemeinsame Teilsequenz (Longest Increasing Subsequence)](src/algorithms/sets/longest-increasing-subsequence) + * `A` [Der kürzeste gemeinsame String (Shortest Common Supersequence)](src/algorithms/sets/shortest-common-supersequence) (SCS) + * `A` [Rucksackproblem (Knapsack Problem)](src/algorithms/sets/knapsack-problem) - "0/1" und "Ungebunden" + * `A` [Das Maximum-Subarray Problem (Maximum Subarray)](src/algorithms/sets/maximum-subarray) - "Brute-Force-Methode" und "Dynamische Programmierung" (Kadane' Algorithmus) + * `A` [Kombinationssumme (Combination Sum)](src/algorithms/sets/combination-sum) - Alle Kombinationen finden, die eine bestimmte Summe bilden +* **Zeichenketten (Strings)** + * `B` [Hamming-Abstand (Hamming Distance)](src/algorithms/string/hamming-distance) - Anzahl der Positionen, an denen die Symbole unterschiedlich sind + * `A` [Levenshtein-Distanz (Levenshtein Distance)](src/algorithms/string/levenshtein-distance) - Minimaler Editierabstand zwischen zwei Sequenzen + * `A` [Knuth-Morris-Pratt-Algorithmus (Knuth–Morris–Pratt Algorithm)](src/algorithms/string/knuth-morris-pratt) (KMP Algorithmus) - Teilstringsuche (Mustervergleich / Pattern Matching) + * `A` [Z-Algorithmus (Z Algorithm)](src/algorithms/string/z-algorithm) - Teilstringsuche (Mustervergleich / Pattern Matching) + * `A` [Rabin-Karp-Algorithmus (Rabin Karp Algorithm)](src/algorithms/string/rabin-karp) - Teilstringsuche + * `A` [Längstes häufiges Teilzeichenfolgenproblem (Longest Common Substring)](src/algorithms/string/longest-common-substring) + * `A` [Regulärer Ausdruck (Regular Expression Matching)](src/algorithms/string/regular-expression-matching) +* **Suchen** + * `B` [Lineare Suche (Linear Search)](src/algorithms/search/linear-search) + * `B` [Sprungsuche (Jump Search)](src/algorithms/search/jump-search) (oder Blocksuche) - Suche im sortierten Array + * `B` [Binäre Suche (Binary Search)](src/algorithms/search/binary-search) - Suche in einem sortierten Array + * `B` [Interpolationssuche (Interpolation Search)](src/algorithms/search/interpolation-search) - Suche in gleichmäßig verteilt sortiertem Array +* **Sortieren** + * `B` [Bubblesort (Bubble Sort)](src/algorithms/sorting/bubble-sort) + * `B` [Selectionsort (Selection Sort)](src/algorithms/sorting/selection-sort) + * `B` [Einfügesortierenmethode (Insertion Sort)](src/algorithms/sorting/insertion-sort) + * `B` [Haldensortierung (Heap Sort)](src/algorithms/sorting/heap-sort) + * `B` [Mergesort (Merge Sort)](src/algorithms/sorting/merge-sort) + * `B` [Quicksort (Quicksort)](src/algorithms/sorting/quick-sort) - in-place und non-in-place Implementierungen + * `B` [Shellsort (Shellsort)](src/algorithms/sorting/shell-sort) + * `B` [Countingsort (Counting Sort)](src/algorithms/sorting/counting-sort) + * `B` [Fachverteilen (Radix Sort)](src/algorithms/sorting/radix-sort) +* **Verkettete Liste (Linked List)** + * `B` [Gerade Traversierung (Straight Traversal)](src/algorithms/linked-list/traversal) + * `B` [Umgekehrte Traversierung (Reverse Traversal)](src/algorithms/linked-list/reverse-traversal) +* **Bäume** + * `B` [Tiefensuche (Depth-First Search)](src/algorithms/tree/depth-first-search) (DFS) + * `B` [Breitensuche (Breadth-First Search)](src/algorithms/tree/breadth-first-search) (BFS) +* **Graphen** + * `B` [Tiefensuche (Depth-First Search)](src/algorithms/graph/depth-first-search) (DFS) + * `B` [Breitensuche (Breadth-First Search)](src/algorithms/graph/breadth-first-search) (BFS) + * `B` [Algorithmus von Kruskal (Kruskal’s Algorithm)](src/algorithms/graph/kruskal) - Finden des Spannbaum (Minimum Spanning Tree / MST) für einen gewichteten ungerichteten Graphen + * `A` [Dijkstra-Algorithmus (Dijkstra Algorithm)](src/algorithms/graph/dijkstra) - Finden der kürzesten Wege zu allen Knoten des Graphen von einem einzelnen Knotenpunkt aus + * `A` [Bellman-Ford-Algorithmus (Bellman-Ford Algorithm)](src/algorithms/graph/bellman-ford) - Finden der kürzesten Wege zu allen Knoten des Graphen von einem einzelnen Knotenpunkt aus + * `A` [Algorithmus von Floyd und Warshall (Floyd-Warshall Algorithm)](src/algorithms/graph/floyd-warshall) - Die kürzesten Wege zwischen allen Knotenpaaren finden + * `A` [Zykluserkennung (Detect Cycle)](src/algorithms/graph/detect-cycle) - Sowohl für gerichtete als auch für ungerichtete Graphen (DFS- und Disjoint-Set-basierte Versionen) + * `A` [Algorithmus von Prim (Prim’s Algorithm)](src/algorithms/graph/prim) - Finden des Spannbaums (Minimum Spanning Tree / MST) für einen gewichteten ungerichteten Graphen + * `A` [Topologische Sortierung (Topological Sorting)](src/algorithms/graph/topological-sorting) - DFS-Verfahren + * `A` [Artikulationspunkte (Articulation Points)](src/algorithms/graph/articulation-points) - Algorithmus von Tarjan (Tarjan's algorithm) (DFS basiert) + * `A` [Brücke (Bridges)](src/algorithms/graph/bridges) - DFS-basierter Algorithmus + * `A` [Eulerkreisproblem (Eulerian Path and Eulerian Circuit)](src/algorithms/graph/eulerian-path) - Algorithmus von Fleury (Fleury's algorithm) - Jede Kante genau einmal durchlaufen. + * `A` [Hamiltonkreisproblem (Hamiltonian Cycle)](src/algorithms/graph/hamiltonian-cycle) - Jeden Eckpunkt genau einmal durchlaufen. + * `A` [Starke Zusammenhangskomponente (Strongly Connected Components)](src/algorithms/graph/strongly-connected-components) - Kosarajus Algorithmus + * `A` [Problem des Handlungsreisenden (Travelling Salesman Problem)](src/algorithms/graph/travelling-salesman) - Kürzestmögliche Route, die jede Stadt besucht und zur Ausgangsstadt zurückkehrt +* **Kryptographie** + * `B` [Polynomiale Streuwertfunktion(Polynomial Hash)](src/algorithms/cryptography/polynomial-hash) - Rollierende Streuwert-Funktion basierend auf Polynom + * `B` [Schienenzaun Chiffre (Rail Fence Cipher)](src/algorithms/cryptography/rail-fence-cipher) - Ein Transpositionsalgorithmus zur Verschlüsselung von Nachrichten + * `B` [Caesar-Verschlüsselung (Caesar Cipher)](src/algorithms/cryptography/caesar-cipher) - Einfache Substitutions-Chiffre + * `B` [Hill-Chiffre (Hill Cipher)](src/algorithms/cryptography/hill-cipher) - Substitutionschiffre basierend auf linearer Algebra +* **Maschinelles Lernen** + * `B` [Künstliches Neuron (NanoNeuron)](https://github.com/trekhleb/nano-neuron) - 7 einfache JS-Funktionen, die veranschaulichen, wie Maschinen tatsächlich lernen können (Vorwärts-/Rückwärtspropagation) + * `B` [Nächste-Nachbarn-Klassifikation (k-NN)](src/algorithms/ml/knn) - k-nächste-Nachbarn-Algorithmus + * `B` [k-Means (k-Means)](src/algorithms/ml/k-means) - k-Means-Algorithmus +* **Image Processing** + * `B` [Inhaltsabhängige Bildverzerrung (Seam Carving)](src/algorithms/image-processing/seam-carving) - Algorithmus zur inhaltsabhängigen Bildgrößenänderung +* **Unkategorisiert** + * `B` [Türme von Hanoi (Tower of Hanoi)](src/algorithms/uncategorized/hanoi-tower) + * `B` [Rotationsmatrix (Square Matrix Rotation)](src/algorithms/uncategorized/square-matrix-rotation) - In-Place-Algorithmus + * `B` [Jump Game (Jump Game)](src/algorithms/uncategorized/jump-game) - Backtracking, dynamische Programmierung (Top-down + Bottom-up) und gierige Beispiele + * `B` [Eindeutige Pfade (Unique Paths)](src/algorithms/uncategorized/unique-paths) - Backtracking, dynamische Programmierung und Pascalsches Dreieck basierte Beispiele + * `B` [Regenterrassen (Rain Terraces)](src/algorithms/uncategorized/rain-terraces) - Auffangproblem für Regenwasser (trapping rain water problem) (dynamische Programmierung und Brute-Force-Versionen) + * `B` [Rekursive Treppe (Recursive Staircase)](src/algorithms/uncategorized/recursive-staircase) - Zählen der Anzahl der Wege, die nach oben führen (4 Lösungen) + * `B` [Beste Zeit zum Kaufen/Verkaufen von Aktien (Best Time To Buy Sell Stocks)](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - Beispiele für "Teile und Herrsche" und Beispiele für den One-Pass-Algorithmus + * `A` [Damenproblem (N-Queens Problem)](src/algorithms/uncategorized/n-queens) + * `A` [Springerproblem (Knight's Tour)](src/algorithms/uncategorized/knight-tour) + +### Algorithmen nach Paradigma + +Ein algorithmisches Paradigma ist eine generische Methode oder ein Ansatz, der dem Entwurf einer Klasse von Algorithmen zugrunde liegt. Es ist eine Abstraktion, die höher ist als der Begriff des Algorithmus. Genauso wie ein Algorithmus eine Abstraktion ist, die höher ist als ein Computerprogramm. + +* **Brachiale Gewalt (Brute Force)** - schaut sich alle Möglichkeiten an und wählt die beste Lösung aus + * `B` [Lineare Suche (Linear Search)](src/algorithms/search/linear-search) + * `B` [Regenterrassen (Rain Terraces)](src/algorithms/uncategorized/rain-terraces) - Auffangproblem für Regenwasser (trapping rain water problem) (dynamische Programmierung und Brute-Force-Versionen) + * `B` [Rekursive Treppe (Recursive Staircase)](src/algorithms/uncategorized/recursive-staircase) - Zählen der Anzahl der Wege, die nach oben führen (4 Lösungen) + * `A` [Das Maximum-Subarray Problem (Maximum Subarray)](src/algorithms/sets/maximum-subarray) + * `A` [Problem des Handlungsreisenden (Travelling Salesman Problem)](src/algorithms/graph/travelling-salesman) - Kürzestmögliche Route, die jede Stadt besucht und zur Ausgangsstadt zurückkehrt + * `A` [Diskrete Fourier-Transformation (Discrete Fourier Transform)](src/algorithms/math/fourier-transform) - Eine Funktion der Zeit (ein Signal) in die Frequenzen zerlegen, aus denen sie sich zusammensetzt +* **Gierig (Greedy)** - Wählt die beste Option zum aktuellen Zeitpunkt, ohne Rücksicht auf die Zukunft + * `B` [Jump Game (Jump Game)](src/algorithms/uncategorized/jump-game) + * `A` [Rucksackproblem (Unbound Knapsack Problem)](src/algorithms/sets/knapsack-problem) + * `A` [Dijkstra-Algorithmus (Dijkstra Algorithm)](src/algorithms/graph/dijkstra) - Finden der kürzesten Wege zu allen Knoten des Graphen von einem einzelnen Knotenpunkt aus + * `A` [Algorithmus von Prim (Prim’s Algorithm)](src/algorithms/graph/prim) - Finden des Spannbaums (Minimum Spanning Tree / MST) für einen gewichteten ungerichteten Graphen + * `B` [Algorithmus von Kruskal (Kruskal’s Algorithm)](src/algorithms/graph/kruskal) - Finden des Spannbaum (Minimum Spanning Tree / MST) für einen gewichteten ungerichteten Graphen +* **Teile und herrsche** - Das Problem in kleinere Teile aufteilen und diese Teile dann lösen + * `B` [Binäre Suche (Binary Search)](src/algorithms/search/binary-search) + * `B` [Türme von Hanoi (Tower of Hanoi)](src/algorithms/uncategorized/hanoi-tower) + * `B` [Pascalsches Dreieck (Pascal's Triangle)](src/algorithms/math/pascal-triangle) + * `B` [Euklidischer Algorithmus (Euclidean Algorithm)](src/algorithms/math/euclidean-algorithm) - calculate the Greatest Common Divisor (GCD) + * `B` [Mergesort (Merge Sort)](src/algorithms/sorting/merge-sort) + * `B` [Quicksort (Quicksort)](src/algorithms/sorting/quick-sort) + * `B` [Tiefensuche (Depth-First Search)](src/algorithms/tree/depth-first-search) (DFS) + * `B` [Breitensuche (Breadth-First Search)](src/algorithms/graph/depth-first-search) (DFS) + * `B` [Matrizen (Matrices)](src/algorithms/math/matrix) - Matrizen und grundlegende Matrixoperationen (Multiplikation, Transposition usw.) + * `B` [Jump Game (Jump Game)](src/algorithms/uncategorized/jump-game) + * `B` [Fast Powering Algorithmus (Fast Powering)](src/algorithms/math/fast-powering) + * `B` [Beste Zeit zum Kaufen/Verkaufen von Aktien (Best Time To Buy Sell Stocks)](src/algorithms/uncategorized/best-time-to-buy-sell-stocks) - Beispiele für "Teile und Herrsche" und Beispiele für den One-Pass-Algorithmus + * `A` [Permutation (Permutations)](src/algorithms/sets/permutations) (mit und ohne Wiederholungen) + * `A` [Kombination (Combinations)](src/algorithms/sets/combinations) (mit und ohne Wiederholungen) +* **Dynamische Programmierung** - Eine Lösung aus zuvor gefundenen Teillösungen aufbauen + * `B` [Fibonacci-Zahl (Fibonacci Number)](src/algorithms/math/fibonacci) + * `B` [Jump Game (Jump Game)](src/algorithms/uncategorized/jump-game) + * `B` [Eindeutige Pfade (Unique Paths)](src/algorithms/uncategorized/unique-paths) + * `B` [Regenterrassen (Rain Terraces)](src/algorithms/uncategorized/rain-terraces) - Auffangproblem für Regenwasser (trapping rain water problem) (dynamische Programmierung und Brute-Force-Versionen) + * `B` [Rekursive Treppe (Recursive Staircase)](src/algorithms/uncategorized/recursive-staircase) - Zählen der Anzahl der Wege, die nach oben führen (4 Lösungen) + * `B` [Inhaltsabhängige Bildverzerrung (Seam Carving)](src/algorithms/image-processing/seam-carving) - Algorithmus zur inhaltsabhängigen Bildgrößenänderung + * `A` [Levenshtein-Distanz (Levenshtein Distance)](src/algorithms/string/levenshtein-distance) - Minimaler Editierabstand zwischen zwei Sequenzen + * `A` [Problem der längsten gemeinsamen Teilsequenz (Longest Common Subsequence)](src/algorithms/sets/longest-common-subsequence) (LCS) + * `A` [Längstes häufiges Teilzeichenfolgenproblem (Longest Common Substring)](src/algorithms/string/longest-common-substring) + * `A` [Längste gemeinsame Teilsequenz (Longest Increasing Subsequence)](src/algorithms/sets/longest-increasing-subsequence) + * `A` [Der kürzeste gemeinsame String (Shortest Common Supersequence)](src/algorithms/sets/shortest-common-supersequence) + * `A` [Rucksackproblem (0/1 Knapsack Problem)](src/algorithms/sets/knapsack-problem) + * `A` [Ganzzahlige Partitionierung (Integer Partition)](src/algorithms/math/integer-partition) + * `A` [Das Maximum-Subarray Problem (Maximum Subarray)](src/algorithms/sets/maximum-subarray) + * `A` [Bellman-Ford-Algorithmus (Bellman-Ford Algorithm)](src/algorithms/graph/bellman-ford) - Finden der kürzesten Wege zu allen Knoten des Graphen von einem einzelnen Knotenpunkt aus + * `A` [Algorithmus von Floyd und Warshall (Floyd-Warshall Algorithm)](src/algorithms/graph/floyd-warshall) - Die kürzesten Wege zwischen allen Knotenpaaren finden + * `A` [Regulärer Ausdruck (Regular Expression Matching)](src/algorithms/string/regular-expression-matching) +* **Zurückverfolgung** - Ähnlich wie bei Brute-Force versuchen Sie, alle möglichen Lösungen zu generieren, aber jedes Mal, wenn Sie die nächste Lösung generieren, testen Sie, ob sie alle Bedingungen erfüllt, und fahren erst dann mit der Generierung weiterer Lösungen fort. Andernfalls gehen Sie zurück und nehmen einen anderen Weg, um eine Lösung zu finden. Normalerweise wird das DFS-Traversal des Zustandsraums verwendet. + * `B` [Jump Game (Jump Game)](src/algorithms/uncategorized/jump-game) + * `B` [Eindeutige Pfade (Unique Paths)](src/algorithms/uncategorized/unique-paths) + * `A` [Potenzmenge (Power Set)](src/algorithms/sets/power-set) - Alle Teilmengen einer Menge + * `A` [Hamiltonkreisproblem (Hamiltonian Cycle)](src/algorithms/graph/hamiltonian-cycle) - Jeden Eckpunkt genau einmal durchlaufen. + * `A` [Damenproblem (N-Queens Problem)](src/algorithms/uncategorized/n-queens) + * `A` [Springerproblem (Knight's Tour)](src/algorithms/uncategorized/knight-tour) + * `A` [Kombinationssumme (Combination Sum)](src/algorithms/sets/combination-sum) - Alle Kombinationen finden, die eine bestimmte Summe bilden +* **Verzweigung & Bindung** - Merkt sich die Lösung mit den niedrigsten Kosten, die in jeder Phase der Backtracking-Suche gefunden wurde, und verwendet die Kosten der bisher gefundenen Lösung mit den niedrigsten Kosten als untere Schranke für die Kosten einer Lösung des Problems mit den geringsten Kosten, um Teillösungen zu verwerfen, deren Kosten größer sind als die der bisher gefundenen Lösung mit den niedrigsten Kosten. Normalerweise wird das BFS-Traversal in Kombination mit dem DFS-Traversal des Zustandsraumbaums verwendet. + +## So verwendest du dieses Repository + +**Alle Abhängigkeiten installieren** + +``` +npm install +``` + +**ESLint ausführen** + +You may want to run it to check code quality. + +``` +npm run lint +``` + +**Alle Tests ausführen** + +``` +npm test +``` + +**Tests nach Namen ausführen** + +``` +npm test -- 'LinkedList' +``` + +**Fehlerbehebung** + +Falls das Linting oder Testen fehlschlägt, versuche, den Ordner "node_modules" zu löschen und die npm-Pakete neu zu installieren: + +``` +rm -rf ./node_modules +npm i +``` + +**Spielwiese** + +Du kannst mit Datenstrukturen und Algorithmen in der Datei `./src/playground/playground.js` herumspielen und +dir in dieser Datei Tests schreiben `./src/playground/__test__/playground.test.js`. + +Dann führe einfach folgenden Befehl aus, um zu testen, ob dein Spielwiesencode wie erwartet funktioniert: + +``` +npm test -- 'playground' +``` + +## Nützliche Informationen + +### Referenzen + +[▶ Datenstrukturen und Algorithmen auf YouTube(Englisch)](https://www.youtube.com/playlist?list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) + +### O-Notation (_Big O Notation_) + +Die O-Notation wird verwendet, um Algorithmen danach zu klassifizieren, wie ihre Laufzeit oder ihr Platzbedarf mit zunehmender Eingabegröße wächst. In der folgenden Tabelle finden Sie die häufigsten Wachstumsordnungen von Algorithmen, die in Big-O-Notation angegeben sind. + +![O-Notation Graphen](./assets/big-o-graph.png) + +Quelle: [Big O Cheat Sheet](http://bigocheatsheet.com/). + +Nachfolgend finden Sie eine Liste einiger der am häufigsten verwendeten Big O-Notationen und deren Leistungsvergleiche für unterschiedliche Größen der Eingabedaten. + +| Big O Notation | Berechnungen für 10 Elemente | Berechnungen für 100 Elemente | Berechnungen für 1000 Elemente | +| -------------- | ---------------------------- | ----------------------------- | ------------------------------ | +| **O(1)** | 1 | 1 | 1 | +| **O(log N)** | 3 | 6 | 9 | +| **O(N)** | 10 | 100 | 1000 | +| **O(N log N)** | 30 | 600 | 9000 | +| **O(N^2)** | 100 | 10000 | 1000000 | +| **O(2^N)** | 1024 | 1.26e+29 | 1.07e+301 | +| **O(N!)** | 3628800 | 9.3e+157 | 4.02e+2567 | + +### Komplexität von Datenstrukturoperationen + +| Datenstruktur | Zugriff auf | Suche | Einfügen | Löschung | Kommentare | +| ---------------------- | :---------: | :----: | :------: | :------: | :-------------------------------------------------------------- | +| **Array** | 1 | n | n | n | | +| **Stack** | n | n | 1 | 1 | | +| **Queue** | n | n | 1 | 1 | | +| **Linked List** | n | n | 1 | n | | +| **Hash Table** | - | n | n | n | Im Falle einer perfekten Hash-Funktion wären die Kosten O(1) | +| **Binary Search Tree** | n | n | n | n | Im Falle eines ausgeglichenen Baumes wären die Kosten O(log(n)) | +| **B-Tree** | log(n) | log(n) | log(n) | log(n) | | +| **Red-Black Tree** | log(n) | log(n) | log(n) | log(n) | | +| **AVL Tree** | log(n) | log(n) | log(n) | log(n) | | +| **Bloom Filter** | - | 1 | 1 | - | Falschpostive sind bei der Suche möglichen | + +### Komplexität von Array-Sortieralgorithmen + +| Name | Bester | Durchschnitt | Schlechtester | Speicher | Stabil | Kommentar | +| ------------------ | :-----------: | :---------------------: | :-------------------------: | :------: | :----: | :------------------------------------------------------------------------- | +| **Bubble sort** | n | n2 | n2 | 1 | JA | | +| **Insertion sort** | n | n2 | n2 | 1 | Ja | | +| **Selection sort** | n2 | n2 | n2 | 1 | Nein | | +| **Heap sort** | n log(n) | n log(n) | n log(n) | 1 | Nein | | +| **Merge sort** | n log(n) | n log(n) | n log(n) | n | Ja | | +| **Quick sort** | n log(n) | n log(n) | n2 | log(n) | Nein | Quicksort wird normalerweise in-place mit O(log(n)) Stapelplatz ausgeführt | +| **Shell sort** | n log(n) | abhängig von Spaltfolge | n (log(n))2 | 1 | Nein | | +| **Counting sort** | n + r | n + r | n + r | n + r | Ja | r - größte Zahl im Array | +| **Radix sort** | n \* k | n \* k | n \* k | n + k | Ja | k - Länge des längsten Schlüssels | + +## Projekt-Unterstützer + +> Du kannst dieses Projekt unterstützen über ❤️️ [GitHub](https://github.com/sponsors/trekhleb) or ❤️️ [Patreon](https://www.patreon.com/trekhleb). + +[Leute, die dieses Projekt unterstützen](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0` diff --git a/README.es-ES.md b/README.es-ES.md index fa1fd340c6..f350ee059e 100644 --- a/README.es-ES.md +++ b/README.es-ES.md @@ -23,7 +23,8 @@ _Léelo en otros idiomas:_ [_Italiana_](README.it-IT.md), [_Bahasa Indonesia_](README.id-ID.md), [_Українська_](README.uk-UA.md), -[_Arabic_](README.ar-AR.md) +[_Arabic_](README.ar-AR.md), +[_Deutsch_](README.de-DE.md) *☝ Nótese que este proyecto está pensado con fines de aprendizaje e investigación, y **no** para ser usado en producción.* diff --git a/README.fr-FR.md b/README.fr-FR.md index 024a3b1904..4508340aec 100644 --- a/README.fr-FR.md +++ b/README.fr-FR.md @@ -24,7 +24,8 @@ _Lisez ceci dans d'autres langues:_ [_Italiana_](README.it-IT.md), [_Bahasa Indonesia_](README.id-ID.md), [_Українська_](README.uk-UA.md), -[_Arabic_](README.ar-AR.md) +[_Arabic_](README.ar-AR.md), +[_Deutsch_](README.de-DE.md) ## Data Structures diff --git a/README.id-ID.md b/README.id-ID.md index 2a258f973c..2f5212ac64 100644 --- a/README.id-ID.md +++ b/README.id-ID.md @@ -21,7 +21,8 @@ _Baca ini dalam bahasa yang lain:_ [_Türk_](README.tr-TR.md), [_Italiana_](README.it-IT.md), [_Українська_](README.uk-UA.md), -[_Arabic_](README.ar-AR.md) +[_Arabic_](README.ar-AR.md), +[_Deutsch_](README.de-DE.md) _☝ Perhatikan bahwa proyek ini hanya dimaksudkan untuk tujuan pembelajaran dan riset, dan **tidak** dimaksudkan untuk digunakan sebagai produksi._ diff --git a/README.it-IT.md b/README.it-IT.md index 9d8c664f6a..d74befd683 100644 --- a/README.it-IT.md +++ b/README.it-IT.md @@ -20,7 +20,8 @@ _Leggilo in altre lingue:_ [_Türk_](README.tr-TR.md), [_Bahasa Indonesia_](README.id-ID.md), [_Українська_](README.uk-UA.md), -[_Arabic_](README.ar-AR.md) +[_Arabic_](README.ar-AR.md), +[_Deutsch_](README.de-DE.md) *☝ Si noti che questo progetto è destinato ad essere utilizzato solo per l'apprendimento e la ricerca e non è destinato ad essere utilizzato per il commercio.* diff --git a/README.ja-JP.md b/README.ja-JP.md index af2c887c2c..a1c13211a0 100644 --- a/README.ja-JP.md +++ b/README.ja-JP.md @@ -23,7 +23,8 @@ _Read this in other languages:_ [_Italiana_](README.it-IT.md), [_Bahasa Indonesia_](README.id-ID.md), [_Українська_](README.uk-UA.md), -[_Arabic_](README.ar-AR.md) +[_Arabic_](README.ar-AR.md), +[_Deutsch_](README.de-DE.md) ## データ構造 diff --git a/README.ko-KR.md b/README.ko-KR.md index 02f35d0250..e9b77dca27 100644 --- a/README.ko-KR.md +++ b/README.ko-KR.md @@ -22,7 +22,8 @@ _Read this in other languages:_ [_Italiana_](README.it-IT.md), [_Bahasa Indonesia_](README.id-ID.md), [_Українська_](README.uk-UA.md), -[_Arabic_](README.ar-AR.md) +[_Arabic_](README.ar-AR.md), +[_Deutsch_](README.de-DE.md) ## 자료 구조 diff --git a/README.md b/README.md index a9fc7b5ea0..d16c264d1e 100644 --- a/README.md +++ b/README.md @@ -24,7 +24,8 @@ _Read this in other languages:_ [_Italiana_](README.it-IT.md), [_Bahasa Indonesia_](README.id-ID.md), [_Українська_](README.uk-UA.md), -[_Arabic_](README.ar-AR.md) +[_Arabic_](README.ar-AR.md), +[_Deutsch_](README.de-DE.md) *☝ Note that this project is meant to be used for learning and researching purposes only, and it is **not** meant to be used for production.* diff --git a/README.pl-PL.md b/README.pl-PL.md index 08dc09b6aa..235d0d47d6 100644 --- a/README.pl-PL.md +++ b/README.pl-PL.md @@ -24,7 +24,8 @@ _Read this in other languages:_ [_Italiana_](README.it-IT.md), [_Bahasa Indonesia_](README.id-ID.md), [_Українська_](README.uk-UA.md), -[_Arabic_](README.ar-AR.md) +[_Arabic_](README.ar-AR.md), +[_Deutsch_](README.de-DE.md) ## Struktury Danych diff --git a/README.pt-BR.md b/README.pt-BR.md index baffbc3179..c410fda651 100644 --- a/README.pt-BR.md +++ b/README.pt-BR.md @@ -24,7 +24,8 @@ _Leia isto em outros idiomas:_ [_Italiana_](README.it-IT.md), [_Bahasa Indonesia_](README.id-ID.md), [_Українська_](README.uk-UA.md), -[_Arabic_](README.ar-AR.md) +[_Arabic_](README.ar-AR.md), +[_Deutsch_](README.de-DE.md) ## Estrutura de Dados diff --git a/README.ru-RU.md b/README.ru-RU.md index 32f4b2f526..ef9e9444a3 100644 --- a/README.ru-RU.md +++ b/README.ru-RU.md @@ -21,7 +21,8 @@ _Читать на других языках:_ [_Italiana_](README.it-IT.md), [_Bahasa Indonesia_](README.id-ID.md), [_Українська_](README.uk-UA.md), -[_Arabic_](README.ar-AR.md) +[_Arabic_](README.ar-AR.md), +[_Deutsch_](README.de-DE.md) *☝ Замечание: этот репозиторий предназначен для учебно-исследовательских целей (**не** для использования в продакшн-системах).* diff --git a/README.tr-TR.md b/README.tr-TR.md index f7ed57fc91..fff640c415 100644 --- a/README.tr-TR.md +++ b/README.tr-TR.md @@ -22,7 +22,8 @@ _Read this in other languages:_ [_Italiana_](README.it-IT.md), [_Bahasa Indonesia_](README.id-ID.md), [_Українська_](README.uk-UA.md), -[_Arabic_](README.ar-AR.md) +[_Arabic_](README.ar-AR.md), +[_Deutsch_](README.de-DE.md) *☝ Not, bu proje araştırma ve öğrenme amacı ile yapılmış olup üretim için **yaplılmamıştır**.* diff --git a/README.uk-UA.md b/README.uk-UA.md index 4391ed1992..6fdd7b4c13 100644 --- a/README.uk-UA.md +++ b/README.uk-UA.md @@ -21,7 +21,8 @@ _Вивчення матеріалу на інших мовах:_ [_Türk_](README.tr-TR.md), [_Italiana_](README.it-IT.md), [_Bahasa Indonesia_](README.id-ID.md), -[_Arabic_](README.ar-AR.md) +[_Arabic_](README.ar-AR.md), +[_Deutsch_](README.de-DE.md) *☝ Зверніть увагу! Даний проект призначений лише для навчальних та дослідницьких цілей, і він **не** призначений для виробництва (продакшн).* diff --git a/README.zh-CN.md b/README.zh-CN.md index 35a3733fc3..22b50d405c 100644 --- a/README.zh-CN.md +++ b/README.zh-CN.md @@ -21,7 +21,8 @@ _Read this in other languages:_ [_Italiana_](README.it-IT.md), [_Bahasa Indonesia_](README.id-ID.md), [_Українська_](README.uk-UA.md), -[_Arabic_](README.ar-AR.md) +[_Arabic_](README.ar-AR.md), +[_Deutsch_](README.de-DE.md) *注意：这个项目仅用于学习和研究，**不是**用于生产环境。* diff --git a/README.zh-TW.md b/README.zh-TW.md index 4a09b8433e..bf90fbbe62 100644 --- a/README.zh-TW.md +++ b/README.zh-TW.md @@ -20,7 +20,8 @@ _Read this in other languages:_ [_Italiana_](README.it-IT.md), [_Bahasa Indonesia_](README.id-ID.md), [_Українська_](README.uk-UA.md), -[_Arabic_](README.ar-AR.md) +[_Arabic_](README.ar-AR.md), +[_Deutsch_](README.de-DE.md) ## 資料結構 From 464a84bc7cb8fcc9c78ccb9fab0d77d978e8363c Mon Sep 17 00:00:00 2001 From: justforever Date: Thu, 6 May 2021 12:56:40 +0800 Subject: [PATCH 011/186] Update README.zh-TW.md (#690) --- README.zh-TW.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.zh-TW.md b/README.zh-TW.md index bf90fbbe62..ddf043d7af 100644 --- a/README.zh-TW.md +++ b/README.zh-TW.md @@ -215,7 +215,7 @@ npm test -- 'playground' | 名稱 | 最佳 | 平均 | 最差 | 記憶體 | 穩定 | | ---------------------- | :-------: | :-------: | :-----------: | :-------: | :-------: | -| **氣派排序** | n | n^2 | n^2 | 1 | Yes | +| **氣泡排序** | n | n^2 | n^2 | 1 | Yes | | **插入排序** | n | n^2 | n^2 | 1 | Yes | | **選擇排序** | n^2 | n^2 | n^2 | 1 | No | | **Heap 排序** | n log(n) | n log(n) | n log(n) | 1 | No | From 5ffab573ca4610c3ea6bd00709883b0a2ec5b898 Mon Sep 17 00:00:00 2001 From: Freivin Campbell Date: Wed, 5 May 2021 23:00:10 -0600 Subject: [PATCH 012/186] Create README.es-ES.md (#680) new translation added --- .../doubly-linked-list/README.es-ES.md | 102 ++++++++++++++++++ 1 file changed, 102 insertions(+) create mode 100644 src/data-structures/doubly-linked-list/README.es-ES.md diff --git a/src/data-structures/doubly-linked-list/README.es-ES.md b/src/data-structures/doubly-linked-list/README.es-ES.md new file mode 100644 index 0000000000..0736d499ac --- /dev/null +++ b/src/data-structures/doubly-linked-list/README.es-ES.md @@ -0,0 +1,102 @@ +# Lista doblemente enlazada + +_Lea esto en otros idiomas:_ +[_Русский_](README.ru-RU.md), +[_简体中文_](README.zh-CN.md), +[_日本語_](README.ja-JP.md), +[_Português_](README.pt-BR.md) +[_한국어_](README.ko-KR.md) + +En informática, una **lista doblemente enlazada** es una estructura de datos enlazados que consta de un conjunto de registros enlazados secuencialmente llamados nodos. Cada nodo contiene dos campos, llamados enlaces, que son referencias al nodo anterior y al siguiente en la secuencia de nodos. Los enlaces anterior y siguiente de los nodos inicial y final, respectivamente, apuntan a algún tipo de terminador, normalmente un nodo centinela o nulo, para facilitar el recorrido de la lista. Si solo hay un ganglio centinela, la lista se enlaza circularmente a través del ganglio centinela. Puede conceptualizarse como dos listas enlazadas individualmente formadas a partir de los mismos elementos de datos, pero en órdenes secuenciales opuestos. + +![Lista doblemente enlazada](https://upload.wikimedia.org/wikipedia/commons/5/5e/Doubly-linked-list.svg) + +Los dos enlaces de nodo permiten recorrer la lista en cualquier dirección. Si bien agregar o eliminar un nodo en una lista doblemente enlazada requiere cambiar más enlaces que las mismas operaciones en una lista enlazada individualmente, las operaciones son más simples y potencialmente más eficientes (para nodos que no sean los primeros) porque no hay necesidad de realizar un seguimiento de el nodo anterior durante el recorrido o no es necesario recorrer la lista para encontrar el nodo anterior, de modo que se pueda modificar su enlace. + +## Pseudocódigo para operaciones básicas + +### Insertar + +```text +Add(value) + Pre: value is the value to add to the list + Post: value has been placed at the tail of the list + n ← node(value) + if head = ø + head ← n + tail ← n + else + n.previous ← tail + tail.next ← n + tail ← n + end if +end Add +``` + +### Eliminar + +```text +Remove(head, value) + Pre: head is the head node in the list + value is the value to remove from the list + Post: value is removed from the list, true; otherwise false + if head = ø + return false + end if + if value = head.value + if head = tail + head ← ø + tail ← ø + else + head ← head.next + head.previous ← ø + end if + return true + end if + n ← head.next + while n != ø and value !== n.value + n ← n.next + end while + if n = tail + tail ← tail.previous + tail.next ← ø + return true + else if n != ø + n.previous.next ← n.next + n.next.previous ← n.previous + return true + end if + return false +end Remove +``` + +### Recorrido Inverso + +```text +ReverseTraversal(tail) + Pre: tail is the node of the list to traverse + Post: the list has been traversed in reverse order + n ← tail + while n != ø + yield n.value + n ← n.previous + end while +end Reverse Traversal +``` + +## Complejidades + +## Complejidad del Tiempo + +| Acceso | Busqueda | Inserción | Supresión | +| :-------: | :-------: | :-------: | :-------: | +| O(n) | O(n) | O(1) | O(n) | + +### Complejidad del Espacio + +O(n) + +## Referencias + +- [Wikipedia](https://en.wikipedia.org/wiki/Doubly_linked_list) +- [YouTube](https://www.youtube.com/watch?v=JdQeNxWCguQ&t=7s&index=72&list=PLLXdhg_r2hKA7DPDsunoDZ-Z769jWn4R8) From 22b323e6b112a85210369f48bf9044d9fa9c6371 Mon Sep 17 00:00:00 2001 From: CodingInvoker <71058225+CodingInvoker@users.noreply.github.com> Date: Thu, 6 May 2021 13:02:52 +0800 Subject: [PATCH 013/186] update linkedlist comment (#687) Co-authored-by: Jiachen Zhou Co-authored-by: Oleksii Trekhleb --- src/data-structures/linked-list/LinkedList.js | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/data-structures/linked-list/LinkedList.js b/src/data-structures/linked-list/LinkedList.js index 1fb0b5eaf4..71c2b49755 100644 --- a/src/data-structures/linked-list/LinkedList.js +++ b/src/data-structures/linked-list/LinkedList.js @@ -65,7 +65,7 @@ export default class LinkedList { let deletedNode = null; - // If the head must be deleted then make next node that is differ + // If the head must be deleted then make next node that is different // from the head to be a new head. while (this.head && this.compare.equal(this.head.value, value)) { deletedNode = this.head; From cb50e4e9f394ebaf8172f71bc31dd2f68b1417d4 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Thu, 6 May 2021 07:05:27 +0200 Subject: [PATCH 014/186] Add link to Spanish translation in Doubly-Linked list README. --- .../doubly-linked-list/README.md | 39 ++++++++++--------- 1 file changed, 20 insertions(+), 19 deletions(-) diff --git a/src/data-structures/doubly-linked-list/README.md b/src/data-structures/doubly-linked-list/README.md index c64b51262d..703520aaf4 100644 --- a/src/data-structures/doubly-linked-list/README.md +++ b/src/data-structures/doubly-linked-list/README.md @@ -4,26 +4,27 @@ _Read this in other languages:_ [_Русский_](README.ru-RU.md), [_简体中文_](README.zh-CN.md), [_日本語_](README.ja-JP.md), -[_Português_](README.pt-BR.md) -[_한국어_](README.ko-KR.md) - -In computer science, a **doubly linked list** is a linked data structure that -consists of a set of sequentially linked records called nodes. Each node contains -two fields, called links, that are references to the previous and to the next -node in the sequence of nodes. The beginning and ending nodes' previous and next -links, respectively, point to some kind of terminator, typically a sentinel -node or null, to facilitate the traversal of the list. If there is only one -sentinel node, then the list is circularly linked via the sentinel node. It can -be conceptualized as two singly linked lists formed from the same data items, +[_Português_](README.pt-BR.md), +[_한국어_](README.ko-KR.md), +[_Español_](README.es-ES.md), + +In computer science, a **doubly linked list** is a linked data structure that +consists of a set of sequentially linked records called nodes. Each node contains +two fields, called links, that are references to the previous and to the next +node in the sequence of nodes. The beginning and ending nodes' previous and next +links, respectively, point to some kind of terminator, typically a sentinel +node or null, to facilitate the traversal of the list. If there is only one +sentinel node, then the list is circularly linked via the sentinel node. It can +be conceptualized as two singly linked lists formed from the same data items, but in opposite sequential orders. ![Doubly Linked List](https://upload.wikimedia.org/wikipedia/commons/5/5e/Doubly-linked-list.svg) -The two node links allow traversal of the list in either direction. While adding -or removing a node in a doubly linked list requires changing more links than the -same operations on a singly linked list, the operations are simpler and -potentially more efficient (for nodes other than first nodes) because there -is no need to keep track of the previous node during traversal or no need +The two node links allow traversal of the list in either direction. While adding +or removing a node in a doubly linked list requires changing more links than the +same operations on a singly linked list, the operations are simpler and +potentially more efficient (for nodes other than first nodes) because there +is no need to keep track of the previous node during traversal or no need to traverse the list to find the previous node, so that its link can be modified. ## Pseudocode for Basic Operations @@ -45,7 +46,7 @@ Add(value) end if end Add ``` - + ### Delete ```text @@ -82,7 +83,7 @@ Remove(head, value) return false end Remove ``` - + ### Reverse Traversal ```text @@ -96,7 +97,7 @@ ReverseTraversal(tail) end while end Reverse Traversal ``` - + ## Complexities ## Time Complexity From 8a24fbfac94dc5d446d51768eaa062637a6c1a16 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Fri, 14 May 2021 09:56:18 +0200 Subject: [PATCH 015/186] Adding more details on how to run the playground code to address the issue #705. --- src/playground/__test__/playground.test.js | 7 +++++-- src/playground/playground.js | 13 ++++++++++++- 2 files changed, 17 insertions(+), 3 deletions(-) diff --git a/src/playground/__test__/playground.test.js b/src/playground/__test__/playground.test.js index 501a87a728..84a3e8301f 100644 --- a/src/playground/__test__/playground.test.js +++ b/src/playground/__test__/playground.test.js @@ -1,5 +1,8 @@ +import playground from '../playground'; + describe('playground', () => { - it('should perform playground tasks', () => { - // Place your playground tests here. + it('should return correct results', () => { + // Replace the next dummy test with your playground function tests. + expect(playground()).toBe(120); }); }); diff --git a/src/playground/playground.js b/src/playground/playground.js index 7872c9e3b8..b8c5b210bc 100644 --- a/src/playground/playground.js +++ b/src/playground/playground.js @@ -1 +1,12 @@ -// Place your playground code here. +// Import any algorithmic dependencies you need for your playground code here. +import factorial from '../algorithms/math/factorial/factorial'; + +// Write your playground code inside the playground() function. +// Test your code from __tests__/playground.test.js +// Launch playground tests by running: npm test -- 'playground' +function playground() { + // Replace the next line with your playground code. + return factorial(5); +} + +export default playground; From 6d2d8c9379873d0da2b1262a14dd26d0f9779522 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Tue, 18 May 2021 08:44:13 +0200 Subject: [PATCH 016/186] Testing Codecov integration without web-hooks. --- src/utils/comparator/Comparator.js | 1 + 1 file changed, 1 insertion(+) diff --git a/src/utils/comparator/Comparator.js b/src/utils/comparator/Comparator.js index 12957d2d73..f5c41b5c18 100644 --- a/src/utils/comparator/Comparator.js +++ b/src/utils/comparator/Comparator.js @@ -1,5 +1,6 @@ export default class Comparator { /** + * Constructor. * @param {function(a: *, b: *)} [compareFunction] - It may be custom compare function that, let's * say may compare custom objects together. */ From ee35bd6240af55d3353934cb50261c9e256d1326 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Wed, 26 May 2021 10:29:05 +0200 Subject: [PATCH 017/186] Testing Codecov integration without web-hooks. --- README.ar-AR.md | 2 ++ README.de-DE.md | 3 +++ README.es-ES.md | 2 ++ README.fr-FR.md | 1 + README.id-ID.md | 2 ++ README.it-IT.md | 2 ++ README.ja-JP.md | 2 ++ README.ko-KR.md | 2 ++ README.md | 2 ++ README.pl-PL.md | 2 ++ README.pt-BR.md | 2 ++ README.ru-RU.md | 2 ++ README.tr-TR.md | 2 ++ README.uk-UA.md | 2 ++ README.zh-CN.md | 2 ++ README.zh-TW.md | 2 ++ 16 files changed, 32 insertions(+) diff --git a/README.ar-AR.md b/README.ar-AR.md index 797006b6ef..3514bce12f 100644 --- a/README.ar-AR.md +++ b/README.ar-AR.md @@ -321,3 +321,5 @@ npm test -- 'playground' > يمكنك دعم هذا المشروع عبر ❤️️ [GitHub](https://github.com/sponsors/trekhleb) أو ❤️️ [Patreon](https://www.patreon.com/trekhleb). [الناس الذين يدعمون هذا المشروع](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0` + +> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.de-DE.md b/README.de-DE.md index 3e127c3ea0..bd250ab3b0 100644 --- a/README.de-DE.md +++ b/README.de-DE.md @@ -331,3 +331,6 @@ Nachfolgend finden Sie eine Liste einiger der am häufigsten verwendeten Big O-N > Du kannst dieses Projekt unterstützen über ❤️️ [GitHub](https://github.com/sponsors/trekhleb) or ❤️️ [Patreon](https://www.patreon.com/trekhleb). [Leute, die dieses Projekt unterstützen](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0` + +> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) + diff --git a/README.es-ES.md b/README.es-ES.md index f350ee059e..b5246bd61d 100644 --- a/README.es-ES.md +++ b/README.es-ES.md @@ -299,3 +299,5 @@ frente a diferentes tamaños de los datos de entrada. | **Shellsort** | n log(n) | depende de la secuencia de huecos | n (log(n))2 | 1 | No | | | **Ordenamiento por cuentas** | n + r | n + r | n + r | n + r | Si | r - mayor número en el arreglo | | **Ordenamiento Radix** | n \* k | n \* k | n \* k | n + k | Si | k - largo de la llave más larga | + +> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.fr-FR.md b/README.fr-FR.md index 4508340aec..aa7a9007a3 100644 --- a/README.fr-FR.md +++ b/README.fr-FR.md @@ -293,3 +293,4 @@ comparaisons de performance suivant différentes tailles pour les données d'ent | **Tri Shell** | n log(n) | dépend du gap séquence | n (log(n))2 | 1 | Non | | | **Tri Comptage** | n + r | n + r | n + r | n + r | Oui | r - le plus grand nombre dans la liste | | **Tri Radix** | n \* k | n \* k | n \* k | n + k | Non | k - longueur du plus long index | +> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.id-ID.md b/README.id-ID.md index 2f5212ac64..f1ad648258 100644 --- a/README.id-ID.md +++ b/README.id-ID.md @@ -304,3 +304,5 @@ Di bawah ini adalah daftar dari beberapa notasi _Bog O_ yang sering digunakan da > Anda dapat mendukung proyek ini via ❤️️ [GitHub](https://github.com/sponsors/trekhleb) atau ❤️️ [Patreon](https://www.patreon.com/trekhleb). [Orang-orang yang mendukung proyek ini](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1` + +> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.it-IT.md b/README.it-IT.md index d74befd683..5947b92e75 100644 --- a/README.it-IT.md +++ b/README.it-IT.md @@ -297,3 +297,5 @@ Nella tabella qua sotto ci sono riportate la lista delle notazioni Big O più us | **Shell sort** | n log(n) | dipende dagli spazi vuoti nella sequenza | n (log(n))2 | 1 | No | | | **Counting sort** | n + r | n + r | n + r | n + r | Yes | r - numero più grande nell'array | | **Radix sort** | n * k | n * k | n * k | n + k | Yes | k - lunghezza della chiave più grande | + +> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.ja-JP.md b/README.ja-JP.md index a1c13211a0..30a9979908 100644 --- a/README.ja-JP.md +++ b/README.ja-JP.md @@ -296,3 +296,5 @@ npm test -- 'playground' | **Shell sort** | n log(n) | depends on gap sequence | n (log(n))2 | 1 | No | | | **Counting sort** | n + r | n + r | n + r | n + r | Yes | r - biggest number in array | | **Radix sort** | n * k | n * k | n * k | n + k | Yes | k - length of longest key | + +> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.ko-KR.md b/README.ko-KR.md index e9b77dca27..8bdb98b837 100644 --- a/README.ko-KR.md +++ b/README.ko-KR.md @@ -277,3 +277,5 @@ Source: [Big O Cheat Sheet](http://bigocheatsheet.com/). | **셸 정렬** | n log(n) | 간격 순서에 영향을 받습니다. | n (log(n))2 | 1 | No | | | **계수 정렬** | n + r | n + r | n + r | n + r | Yes | r - 배열내 가장 큰 수 | | **기수 정렬** | n * k | n * k | n * k | n + k | Yes | k - 키값의 최대 길이 | + +> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.md b/README.md index d16c264d1e..a589d710e1 100644 --- a/README.md +++ b/README.md @@ -343,3 +343,5 @@ Below is the list of some of the most used Big O notations and their performance > You may support this project via ❤️️ [GitHub](https://github.com/sponsors/trekhleb) or ❤️️ [Patreon](https://www.patreon.com/trekhleb). [Folks who are backing this project](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0` + +> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.pl-PL.md b/README.pl-PL.md index 235d0d47d6..cc20e947e7 100644 --- a/README.pl-PL.md +++ b/README.pl-PL.md @@ -289,3 +289,5 @@ Poniżej umieszczamy listę najbardziej używanych Big O notacji i ich porównan | **Sortowanie Shella** | n log(n) | zależy od luki w układzie | n (log(n))2 | 1 | No | | | **Sortowanie przez zliczanie** | n + r | n + r | n + r | n + r | Yes | r - największy numer w tablicy| | **Sortowanie Radix** | n * k | n * k | n * k | n + k | Yes | k -długość najdłuższego klucza | + +> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.pt-BR.md b/README.pt-BR.md index c410fda651..cc3b9f2191 100644 --- a/README.pt-BR.md +++ b/README.pt-BR.md @@ -290,3 +290,5 @@ Abaixo está a lista de algumas das notações Big O mais usadas e suas compara | **Shell sort** | n log(n) | depende da sequência de lacunas | n (log(n))2 | 1 | Não | | | **Counting sort** | n + r | n + r | n + r | n + r | Sim | r - maior número na matriz | | **Radix sort** | n * k | n * k | n * k | n + k | Sim | k - comprimento da chave mais longa | + +> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.ru-RU.md b/README.ru-RU.md index ef9e9444a3..d5c2c69c6f 100644 --- a/README.ru-RU.md +++ b/README.ru-RU.md @@ -295,3 +295,5 @@ npm test -- 'playground' | **Сортировка Шелла** | n log(n) | зависит от выбранных шагов | n (log(n))2 | 1 | Нет | | | **Сортировка подсчётом** | n + r | n + r | n + r | n + r | Да | r — наибольшее число в массиве | | **Поразрядная сортировка** | n * k | n * k | n * k | n + k | Да | k — длина самого длинного ключа | + +> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.tr-TR.md b/README.tr-TR.md index fff640c415..73f3077e1e 100644 --- a/README.tr-TR.md +++ b/README.tr-TR.md @@ -315,3 +315,5 @@ Altta Big O notations ve farklı input boyutlarına karşın yapılmış perform ## Projeyi Destekleme Bu projeyi buradan destekleyebilirsiniz ❤️️ [GitHub](https://github.com/sponsors/trekhleb) veya ❤️️ [Patreon](https://www.patreon.com/trekhleb). + +> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.uk-UA.md b/README.uk-UA.md index 6fdd7b4c13..be4d923b70 100644 --- a/README.uk-UA.md +++ b/README.uk-UA.md @@ -305,3 +305,5 @@ npm test -- 'playground' > Ви можете підтримати цей проект через ❤️️ [GitHub](https://github.com/sponsors/trekhleb) або ❤️️ [Patreon](https://www.patreon.com/trekhleb). [Люди, які підтримують цей проект](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1` + +> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.zh-CN.md b/README.zh-CN.md index 22b50d405c..1425f87993 100644 --- a/README.zh-CN.md +++ b/README.zh-CN.md @@ -292,3 +292,5 @@ npm test -- 'playground' | **希尔排序** | n log(n) | 取决于差距序列 | n (log(n))^2 | 1 | No | | | **计数排序** | n + r | n + r | n + r | n + r | Yes | r - 数组里最大的数 | | **基数排序** | n * k | n * k | n * k | n + k | Yes | k - 最长 key 的升序 | + +> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.zh-TW.md b/README.zh-TW.md index ddf043d7af..10b6e84f08 100644 --- a/README.zh-TW.md +++ b/README.zh-TW.md @@ -222,3 +222,5 @@ npm test -- 'playground' | **合併排序** | n log(n) | n log(n) | n log(n) | n | Yes | | **快速排序** | n log(n) | n log(n) | n^2 | log(n) | No | | **希爾排序** | n log(n) | 由gap sequence決定 | n (log(n))^2 | 1 | No | + +> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) From 433515f1b22a1a53443429b20f09f821a3325895 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Wed, 26 May 2021 10:55:57 +0200 Subject: [PATCH 018/186] Fix typo in READMEs. --- README.ar-AR.md | 2 +- README.de-DE.md | 2 +- README.es-ES.md | 2 +- README.fr-FR.md | 3 ++- README.id-ID.md | 2 +- README.it-IT.md | 2 +- README.ja-JP.md | 2 +- README.ko-KR.md | 2 +- README.md | 2 +- README.pl-PL.md | 2 +- README.pt-BR.md | 2 +- README.ru-RU.md | 2 +- README.tr-TR.md | 2 +- README.uk-UA.md | 2 +- README.zh-CN.md | 2 +- README.zh-TW.md | 2 +- 16 files changed, 17 insertions(+), 16 deletions(-) diff --git a/README.ar-AR.md b/README.ar-AR.md index 3514bce12f..07522e78a6 100644 --- a/README.ar-AR.md +++ b/README.ar-AR.md @@ -322,4 +322,4 @@ npm test -- 'playground' [الناس الذين يدعمون هذا المشروع](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0` -> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) +> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.de-DE.md b/README.de-DE.md index bd250ab3b0..b34ad3563f 100644 --- a/README.de-DE.md +++ b/README.de-DE.md @@ -332,5 +332,5 @@ Nachfolgend finden Sie eine Liste einiger der am häufigsten verwendeten Big O-N [Leute, die dieses Projekt unterstützen](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0` -> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) +> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.es-ES.md b/README.es-ES.md index b5246bd61d..6f5db59bb8 100644 --- a/README.es-ES.md +++ b/README.es-ES.md @@ -300,4 +300,4 @@ frente a diferentes tamaños de los datos de entrada. | **Ordenamiento por cuentas** | n + r | n + r | n + r | n + r | Si | r - mayor número en el arreglo | | **Ordenamiento Radix** | n \* k | n \* k | n \* k | n + k | Si | k - largo de la llave más larga | -> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) +> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.fr-FR.md b/README.fr-FR.md index aa7a9007a3..59087825ff 100644 --- a/README.fr-FR.md +++ b/README.fr-FR.md @@ -293,4 +293,5 @@ comparaisons de performance suivant différentes tailles pour les données d'ent | **Tri Shell** | n log(n) | dépend du gap séquence | n (log(n))2 | 1 | Non | | | **Tri Comptage** | n + r | n + r | n + r | n + r | Oui | r - le plus grand nombre dans la liste | | **Tri Radix** | n \* k | n \* k | n \* k | n + k | Non | k - longueur du plus long index | -> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) + +> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.id-ID.md b/README.id-ID.md index f1ad648258..01d539c5ef 100644 --- a/README.id-ID.md +++ b/README.id-ID.md @@ -305,4 +305,4 @@ Di bawah ini adalah daftar dari beberapa notasi _Bog O_ yang sering digunakan da [Orang-orang yang mendukung proyek ini](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1` -> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) +> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.it-IT.md b/README.it-IT.md index 5947b92e75..b459ac87d1 100644 --- a/README.it-IT.md +++ b/README.it-IT.md @@ -298,4 +298,4 @@ Nella tabella qua sotto ci sono riportate la lista delle notazioni Big O più us | **Counting sort** | n + r | n + r | n + r | n + r | Yes | r - numero più grande nell'array | | **Radix sort** | n * k | n * k | n * k | n + k | Yes | k - lunghezza della chiave più grande | -> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) +> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.ja-JP.md b/README.ja-JP.md index 30a9979908..44b6b6c13e 100644 --- a/README.ja-JP.md +++ b/README.ja-JP.md @@ -297,4 +297,4 @@ npm test -- 'playground' | **Counting sort** | n + r | n + r | n + r | n + r | Yes | r - biggest number in array | | **Radix sort** | n * k | n * k | n * k | n + k | Yes | k - length of longest key | -> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) +> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.ko-KR.md b/README.ko-KR.md index 8bdb98b837..040ac8a57d 100644 --- a/README.ko-KR.md +++ b/README.ko-KR.md @@ -278,4 +278,4 @@ Source: [Big O Cheat Sheet](http://bigocheatsheet.com/). | **계수 정렬** | n + r | n + r | n + r | n + r | Yes | r - 배열내 가장 큰 수 | | **기수 정렬** | n * k | n * k | n * k | n + k | Yes | k - 키값의 최대 길이 | -> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) +> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.md b/README.md index a589d710e1..b8e2be362a 100644 --- a/README.md +++ b/README.md @@ -344,4 +344,4 @@ Below is the list of some of the most used Big O notations and their performance [Folks who are backing this project](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 0` -> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) +> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.pl-PL.md b/README.pl-PL.md index cc20e947e7..51777b0da2 100644 --- a/README.pl-PL.md +++ b/README.pl-PL.md @@ -290,4 +290,4 @@ Poniżej umieszczamy listę najbardziej używanych Big O notacji i ich porównan | **Sortowanie przez zliczanie** | n + r | n + r | n + r | n + r | Yes | r - największy numer w tablicy| | **Sortowanie Radix** | n * k | n * k | n * k | n + k | Yes | k -długość najdłuższego klucza | -> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) +> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.pt-BR.md b/README.pt-BR.md index cc3b9f2191..68b7e1721f 100644 --- a/README.pt-BR.md +++ b/README.pt-BR.md @@ -291,4 +291,4 @@ Abaixo está a lista de algumas das notações Big O mais usadas e suas compara | **Counting sort** | n + r | n + r | n + r | n + r | Sim | r - maior número na matriz | | **Radix sort** | n * k | n * k | n * k | n + k | Sim | k - comprimento da chave mais longa | -> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) +> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.ru-RU.md b/README.ru-RU.md index d5c2c69c6f..6200aedd53 100644 --- a/README.ru-RU.md +++ b/README.ru-RU.md @@ -296,4 +296,4 @@ npm test -- 'playground' | **Сортировка подсчётом** | n + r | n + r | n + r | n + r | Да | r — наибольшее число в массиве | | **Поразрядная сортировка** | n * k | n * k | n * k | n + k | Да | k — длина самого длинного ключа | -> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) +> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.tr-TR.md b/README.tr-TR.md index 73f3077e1e..0dd0ee3bf2 100644 --- a/README.tr-TR.md +++ b/README.tr-TR.md @@ -316,4 +316,4 @@ Altta Big O notations ve farklı input boyutlarına karşın yapılmış perform Bu projeyi buradan destekleyebilirsiniz ❤️️ [GitHub](https://github.com/sponsors/trekhleb) veya ❤️️ [Patreon](https://www.patreon.com/trekhleb). -> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) +> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.uk-UA.md b/README.uk-UA.md index be4d923b70..b43da83ca6 100644 --- a/README.uk-UA.md +++ b/README.uk-UA.md @@ -306,4 +306,4 @@ npm test -- 'playground' [Люди, які підтримують цей проект](https://github.com/trekhleb/javascript-algorithms/blob/master/BACKERS.md) `∑ = 1` -> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) +> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.zh-CN.md b/README.zh-CN.md index 1425f87993..8bf216d6bd 100644 --- a/README.zh-CN.md +++ b/README.zh-CN.md @@ -293,4 +293,4 @@ npm test -- 'playground' | **计数排序** | n + r | n + r | n + r | n + r | Yes | r - 数组里最大的数 | | **基数排序** | n * k | n * k | n * k | n + k | Yes | k - 最长 key 的升序 | -> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) +> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) diff --git a/README.zh-TW.md b/README.zh-TW.md index 10b6e84f08..e42aba445d 100644 --- a/README.zh-TW.md +++ b/README.zh-TW.md @@ -223,4 +223,4 @@ npm test -- 'playground' | **快速排序** | n log(n) | n log(n) | n^2 | log(n) | No | | **希爾排序** | n log(n) | 由gap sequence決定 | n (log(n))^2 | 1 | No | -> ℹ️ Some more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) +> ℹ️ A few more [projects](https://trekhleb.dev/projects/) and [articles](https://trekhleb.dev/blog/) about JavaScript and algorithms on [trekhleb.dev](https://trekhleb.dev) From b2d1ec83f04a66d9d2d3f09150bcaf0cacb0f7ba Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Fri, 16 Jul 2021 11:51:53 +0200 Subject: [PATCH 019/186] Binary representation of floating-point numbers (#737) * Add "Binary representation of floating point numbers" section. * Adding a half-precision explanatory picture. * Binary representation of the floating-point numbers. --- README.md | 1 + .../math/binary-floating-point/README.md | 93 ++++++++++++++ .../__tests__/bitsToFloat.test.js | 32 +++++ .../__tests__/floatAsBinaryString.test.js | 20 +++ .../math/binary-floating-point/bitsToFloat.js | 119 ++++++++++++++++++ .../floatAsBinaryString.js | 61 +++++++++ ...cision-floating-point-number-explained.png | Bin 0 -> 352613 bytes .../images/03-scientific-notation.png | Bin 0 -> 76251 bytes .../math/binary-floating-point/testCases.js | 71 +++++++++++ 9 files changed, 397 insertions(+) create mode 100644 src/algorithms/math/binary-floating-point/README.md create mode 100644 src/algorithms/math/binary-floating-point/__tests__/bitsToFloat.test.js create mode 100644 src/algorithms/math/binary-floating-point/__tests__/floatAsBinaryString.test.js create mode 100644 src/algorithms/math/binary-floating-point/bitsToFloat.js create mode 100644 src/algorithms/math/binary-floating-point/floatAsBinaryString.js create mode 100644 src/algorithms/math/binary-floating-point/images/02-half-precision-floating-point-number-explained.png create mode 100644 src/algorithms/math/binary-floating-point/images/03-scientific-notation.png create mode 100644 src/algorithms/math/binary-floating-point/testCases.js diff --git a/README.md b/README.md index b8e2be362a..d00945e5a5 100644 --- a/README.md +++ b/README.md @@ -68,6 +68,7 @@ a set of rules that precisely define a sequence of operations. * **Math** * `B` [Bit Manipulation](src/algorithms/math/bits) - set/get/update/clear bits, multiplication/division by two, make negative etc. + * `B` [Binary Floating Point](src/algorithms/math/binary-floating-point) - binary representation of the floating-point numbers. * `B` [Factorial](src/algorithms/math/factorial) * `B` [Fibonacci Number](src/algorithms/math/fibonacci) - classic and closed-form versions * `B` [Prime Factors](src/algorithms/math/prime-factors) - finding prime factors and counting them using Hardy-Ramanujan's theorem diff --git a/src/algorithms/math/binary-floating-point/README.md b/src/algorithms/math/binary-floating-point/README.md new file mode 100644 index 0000000000..2851902845 --- /dev/null +++ b/src/algorithms/math/binary-floating-point/README.md @@ -0,0 +1,93 @@ +# Binary representation of floating-point numbers + +Have you ever wondered how computers store the floating-point numbers like `3.1415` (𝝿) or `9.109 × 10⁻³¹` (the mass of the electron in kg) in the memory which is limited by a finite number of ones and zeroes (aka bits)? + +It seems pretty straightforward for integers (i.e. `17`). Let's say we have 16 bits (2 bytes) to store the number. In 16 bits we may store the integers in a range of `[0, 65535]`: + +```text +(0000000000000000)₂ = (0)₁₀ + +(0000000000010001)₂ = + (1 × 2⁴) + + (0 × 2³) + + (0 × 2²) + + (0 × 2¹) + + (1 × 2⁰) = (17)₁₀ + +(1111111111111111)₂ = + (1 × 2¹⁵) + + (1 × 2¹⁴) + + (1 × 2¹³) + + (1 × 2¹²) + + (1 × 2¹¹) + + (1 × 2¹⁰) + + (1 × 2⁹) + + (1 × 2⁸) + + (1 × 2⁷) + + (1 × 2⁶) + + (1 × 2⁵) + + (1 × 2⁴) + + (1 × 2³) + + (1 × 2²) + + (1 × 2¹) + + (1 × 2⁰) = (65535)₁₀ +``` + +If we need a signed integer we may use [two's complement](https://en.wikipedia.org/wiki/Two%27s_complement) and shift the range of `[0, 65535]` towards the negative numbers. In this case, our 16 bits would represent the numbers in a range of `[-32768, +32767]`. + +As you might have noticed, this approach won't allow you to represent the numbers like `-27.15625` (numbers after the decimal point are just being ignored). + +We're not the first ones who have noticed this issue though. Around ≈36 years ago some smart folks overcame this limitation by introducing the [IEEE 754](https://en.wikipedia.org/wiki/IEEE_754) standard for floating-point arithmetic. + +The IEEE 754 standard describes the way (the framework) of using those 16 bits (or 32, or 64 bits) to store the numbers of wider range, including the small floating numbers (smaller than 1 and closer to 0). + +To get the idea behind the standard we might recall the [scientific notation](https://en.wikipedia.org/wiki/Scientific_notation) - a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. + +![Scientific number notation](images/03-scientific-notation.png) + +As you may see from the image, the number representation might be split into three parts: + +- **sign** +- **fraction (aka significand)** - the valuable digits (the meaning, the payload) of the number +- **exponent** - controls how far and in which direction to move the decimal point in the fraction + +The **base** part we may omit by just agreeing on what it will be equal to. In our case, we'll be using `2` as a base. + +Instead of using all 16 bits (or 32 bits, or 64 bits) to store the fraction of the number, we may share the bits and store a sign, exponent, and fraction at the same time. Depending on the number of bits that we're going to use to store the number we end up with the following splits: + +| Floating-point format | Total bits | Sign bits | Exponent bits | Fraction bits | Base | +| :-------------------- | :--------: | :-------: | :-----------: | :--------------: | :--: | +| [Half-precision](https://en.wikipedia.org/wiki/Half-precision_floating-point_format) | 16 | 1 | 5 | 10 | 2 | +| [Single-precision](https://en.wikipedia.org/wiki/Single-precision_floating-point_format) | 32 | 1 | 8 | 23 | 2 | +| [Double-precision](https://en.wikipedia.org/wiki/Double-precision_floating-point_format) | 64 | 1 | 11 | 52 | 2 | + +With this approach, the number of bits for the fraction has been reduced (i.e. for the 16-bits number it was reduced from 16 bits to 10 bits). It means that the fraction might take a narrower range of values now (losing some precision). However, since we also have an exponent part, it will actually increase the ultimate number range and also allow us to describe the numbers between 0 and 1 (if the exponent is negative). + +> For example, a signed 32-bit integer variable has a maximum value of 2³¹ − 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of ≈ 3.4028235 × 10³⁸. + +To make it possible to have a negative exponent, the IEEE 754 standard uses the [biased exponent](https://en.wikipedia.org/wiki/Exponent_bias). The idea is simple - subtract the bias from the exponent value to make it negative. For example, if the exponent has 5 bits, it might take the values from the range of `[0, 31]` (all values are positive here). But if we subtract the value of `15` from it, the range will be `[-15, 16]`. The number `15` is called bias, and it is being calculated by the following formula: + +``` +exponent_bias = 2 ^ (k−1) − 1 + +k - number of exponent bits +``` + +I've tried to describe the logic behind the converting of floating-point numbers from a binary format back to the decimal format on the image below. Hopefully, it will give you a better understanding of how the IEEE 754 standard works. The 16-bits number is being used here for simplicity, but the same approach works for 32-bits and 64-bits numbers as well. + +![Half-precision floating point number format explained in one picture](images/02-half-precision-floating-point-number-explained.png) + +> Checkout the [interactive version of this diagram](https://trekhleb.dev/blog/2021/binary-floating-point/) to play around with setting bits on and off, and seeing how it would influence the final result + +## Code examples + +- See the [bitsToFloat.js](bitsToFloat.js) for the example of how to convert array of bits to the floating point number (the example is a bit artificial but still it gives the overview of how the conversion is going on) +- See the [floatAsBinaryString.js](floatAsBinaryString.js) for the example of how to see the actual binary representation of the floating-point number in JavaScript + +## References + +You might also want to check out the following resources to get a deeper understanding of the binary representation of floating-point numbers: + +- [Here is what you need to know about JavaScript’s Number type](https://indepth.dev/posts/1139/here-is-what-you-need-to-know-about-javascripts-number-type) +- [Float Exposed](https://float.exposed/) +- [IEEE754 Visualization](https://bartaz.github.io/ieee754-visualization/) diff --git a/src/algorithms/math/binary-floating-point/__tests__/bitsToFloat.test.js b/src/algorithms/math/binary-floating-point/__tests__/bitsToFloat.test.js new file mode 100644 index 0000000000..53afe691a2 --- /dev/null +++ b/src/algorithms/math/binary-floating-point/__tests__/bitsToFloat.test.js @@ -0,0 +1,32 @@ +import { testCases16Bits, testCases32Bits, testCases64Bits } from '../testCases'; +import { bitsToFloat16, bitsToFloat32, bitsToFloat64 } from '../bitsToFloat'; + +describe('bitsToFloat16', () => { + it('should convert floating point binary bits to floating point decimal number', () => { + for (let testCaseIndex = 0; testCaseIndex < testCases16Bits.length; testCaseIndex += 1) { + const [decimal, binary] = testCases16Bits[testCaseIndex]; + const bits = binary.split('').map((bitString) => parseInt(bitString, 10)); + expect(bitsToFloat16(bits)).toBeCloseTo(decimal, 4); + } + }); +}); + +describe('bitsToFloat32', () => { + it('should convert floating point binary bits to floating point decimal number', () => { + for (let testCaseIndex = 0; testCaseIndex < testCases32Bits.length; testCaseIndex += 1) { + const [decimal, binary] = testCases32Bits[testCaseIndex]; + const bits = binary.split('').map((bitString) => parseInt(bitString, 10)); + expect(bitsToFloat32(bits)).toBeCloseTo(decimal, 7); + } + }); +}); + +describe('bitsToFloat64', () => { + it('should convert floating point binary bits to floating point decimal number', () => { + for (let testCaseIndex = 0; testCaseIndex < testCases64Bits.length; testCaseIndex += 1) { + const [decimal, binary] = testCases64Bits[testCaseIndex]; + const bits = binary.split('').map((bitString) => parseInt(bitString, 10)); + expect(bitsToFloat64(bits)).toBeCloseTo(decimal, 14); + } + }); +}); diff --git a/src/algorithms/math/binary-floating-point/__tests__/floatAsBinaryString.test.js b/src/algorithms/math/binary-floating-point/__tests__/floatAsBinaryString.test.js new file mode 100644 index 0000000000..efb8a2ba5e --- /dev/null +++ b/src/algorithms/math/binary-floating-point/__tests__/floatAsBinaryString.test.js @@ -0,0 +1,20 @@ +import { floatAs32BinaryString, floatAs64BinaryString } from '../floatAsBinaryString'; +import { testCases32Bits, testCases64Bits } from '../testCases'; + +describe('floatAs32Binary', () => { + it('should create a binary representation of the floating numbers', () => { + for (let testCaseIndex = 0; testCaseIndex < testCases32Bits.length; testCaseIndex += 1) { + const [decimal, binary] = testCases32Bits[testCaseIndex]; + expect(floatAs32BinaryString(decimal)).toBe(binary); + } + }); +}); + +describe('floatAs64Binary', () => { + it('should create a binary representation of the floating numbers', () => { + for (let testCaseIndex = 0; testCaseIndex < testCases64Bits.length; testCaseIndex += 1) { + const [decimal, binary] = testCases64Bits[testCaseIndex]; + expect(floatAs64BinaryString(decimal)).toBe(binary); + } + }); +}); diff --git a/src/algorithms/math/binary-floating-point/bitsToFloat.js b/src/algorithms/math/binary-floating-point/bitsToFloat.js new file mode 100644 index 0000000000..6d1ef0d851 --- /dev/null +++ b/src/algorithms/math/binary-floating-point/bitsToFloat.js @@ -0,0 +1,119 @@ +/** + * Sequence of 0s and 1s. + * @typedef {number[]} Bits + */ + +/** + * @typedef {{ + * signBitsCount: number, + * exponentBitsCount: number, + * fractionBitsCount: number, + * }} PrecisionConfig + */ + +/** + * @typedef {{ + * half: PrecisionConfig, + * single: PrecisionConfig, + * double: PrecisionConfig + * }} PrecisionConfigs + */ + +/** + * ┌───────────────── sign bit + * │ ┌───────────── exponent bits + * │ │ ┌───── fraction bits + * │ │ │ + * X XXXXX XXXXXXXXXX + * + * @type {PrecisionConfigs} + */ +const precisionConfigs = { + // @see: https://en.wikipedia.org/wiki/Half-precision_floating-point_format + half: { + signBitsCount: 1, + exponentBitsCount: 5, + fractionBitsCount: 10, + }, + // @see: https://en.wikipedia.org/wiki/Single-precision_floating-point_format + single: { + signBitsCount: 1, + exponentBitsCount: 8, + fractionBitsCount: 23, + }, + // @see: https://en.wikipedia.org/wiki/Double-precision_floating-point_format + double: { + signBitsCount: 1, + exponentBitsCount: 11, + fractionBitsCount: 52, + }, +}; + +/** + * Converts the binary representation of the floating point number to decimal float number. + * + * @param {Bits} bits - sequence of bits that represents the floating point number. + * @param {PrecisionConfig} precisionConfig - half/single/double precision config. + * @return {number} - floating point number decoded from its binary representation. + */ +function bitsToFloat(bits, precisionConfig) { + const { signBitsCount, exponentBitsCount } = precisionConfig; + + // Figuring out the sign. + const sign = (-1) ** bits[0]; // -1^1 = -1, -1^0 = 1 + + // Calculating the exponent value. + const exponentBias = 2 ** (exponentBitsCount - 1) - 1; + const exponentBits = bits.slice(signBitsCount, signBitsCount + exponentBitsCount); + const exponentUnbiased = exponentBits.reduce( + (exponentSoFar, currentBit, bitIndex) => { + const bitPowerOfTwo = 2 ** (exponentBitsCount - bitIndex - 1); + return exponentSoFar + currentBit * bitPowerOfTwo; + }, + 0, + ); + const exponent = exponentUnbiased - exponentBias; + + // Calculating the fraction value. + const fractionBits = bits.slice(signBitsCount + exponentBitsCount); + const fraction = fractionBits.reduce( + (fractionSoFar, currentBit, bitIndex) => { + const bitPowerOfTwo = 2 ** -(bitIndex + 1); + return fractionSoFar + currentBit * bitPowerOfTwo; + }, + 0, + ); + + // Putting all parts together to calculate the final number. + return sign * (2 ** exponent) * (1 + fraction); +} + +/** + * Converts the 16-bit binary representation of the floating point number to decimal float number. + * + * @param {Bits} bits - sequence of bits that represents the floating point number. + * @return {number} - floating point number decoded from its binary representation. + */ +export function bitsToFloat16(bits) { + return bitsToFloat(bits, precisionConfigs.half); +} + +/** + * Converts the 32-bit binary representation of the floating point number to decimal float number. + * + * @param {Bits} bits - sequence of bits that represents the floating point number. + * @return {number} - floating point number decoded from its binary representation. + */ +export function bitsToFloat32(bits) { + return bitsToFloat(bits, precisionConfigs.single); +} + +/** + * Converts the 64-bit binary representation of the floating point number to decimal float number. + * + * @param {Bits} bits - sequence of bits that represents the floating point number. + * @return {number} - floating point number decoded from its binary representation. + */ +export function bitsToFloat64(bits) { + return bitsToFloat(bits, precisionConfigs.double); +} diff --git a/src/algorithms/math/binary-floating-point/floatAsBinaryString.js b/src/algorithms/math/binary-floating-point/floatAsBinaryString.js new file mode 100644 index 0000000000..aa907ac049 --- /dev/null +++ b/src/algorithms/math/binary-floating-point/floatAsBinaryString.js @@ -0,0 +1,61 @@ +// @see: https://en.wikipedia.org/wiki/Single-precision_floating-point_format +const singlePrecisionBytesLength = 4; // 32 bits + +// @see: https://en.wikipedia.org/wiki/Double-precision_floating-point_format +const doublePrecisionBytesLength = 8; // 64 bits + +const bitsInByte = 8; + +/** + * Converts the float number into its IEEE 754 binary representation. + * @see: https://en.wikipedia.org/wiki/IEEE_754 + * + * @param {number} floatNumber - float number in decimal format. + * @param {number} byteLength - number of bytes to use to store the float number. + * @return {string} - binary string representation of the float number. + */ +function floatAsBinaryString(floatNumber, byteLength) { + let numberAsBinaryString = ''; + + const arrayBuffer = new ArrayBuffer(byteLength); + const dataView = new DataView(arrayBuffer); + + const byteOffset = 0; + const littleEndian = false; + + if (byteLength === singlePrecisionBytesLength) { + dataView.setFloat32(byteOffset, floatNumber, littleEndian); + } else { + dataView.setFloat64(byteOffset, floatNumber, littleEndian); + } + + for (let byteIndex = 0; byteIndex < byteLength; byteIndex += 1) { + let bits = dataView.getUint8(byteIndex).toString(2); + if (bits.length < bitsInByte) { + bits = new Array(bitsInByte - bits.length).fill('0').join('') + bits; + } + numberAsBinaryString += bits; + } + + return numberAsBinaryString; +} + +/** + * Converts the float number into its IEEE 754 64-bits binary representation. + * + * @param {number} floatNumber - float number in decimal format. + * @return {string} - 64 bits binary string representation of the float number. + */ +export function floatAs64BinaryString(floatNumber) { + return floatAsBinaryString(floatNumber, doublePrecisionBytesLength); +} + +/** + * Converts the float number into its IEEE 754 32-bits binary representation. + * + * @param {number} floatNumber - float number in decimal format. + * @return {string} - 32 bits binary string representation of the float number. + */ +export function floatAs32BinaryString(floatNumber) { + return floatAsBinaryString(floatNumber, singlePrecisionBytesLength); +} diff --git a/src/algorithms/math/binary-floating-point/images/02-half-precision-floating-point-number-explained.png b/src/algorithms/math/binary-floating-point/images/02-half-precision-floating-point-number-explained.png new file mode 100644 index 0000000000000000000000000000000000000000..1bc0a5b83596b9479525362d67af1dfb5168ef70 GIT binary patch literal 352613 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Subject: [PATCH 020/186] Binary representation of the floating-point numbers. --- src/algorithms/math/binary-floating-point/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/algorithms/math/binary-floating-point/README.md b/src/algorithms/math/binary-floating-point/README.md index 2851902845..32b41f642a 100644 --- a/src/algorithms/math/binary-floating-point/README.md +++ b/src/algorithms/math/binary-floating-point/README.md @@ -1,6 +1,6 @@ # Binary representation of floating-point numbers -Have you ever wondered how computers store the floating-point numbers like `3.1415` (𝝿) or `9.109 × 10⁻³¹` (the mass of the electron in kg) in the memory which is limited by a finite number of ones and zeroes (aka bits)? +Have you ever wondered how computers store the floating-point numbers like `3.1416` (𝝿) or `9.109 × 10⁻³¹` (the mass of the electron in kg) in the memory which is limited by a finite number of ones and zeroes (aka bits)? It seems pretty straightforward for integers (i.e. `17`). Let's say we have 16 bits (2 bytes) to store the number. In 16 bits we may store the integers in a range of `[0, 65535]`: From 71da6df63312096964eaaf8f538c174d1c39014b Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Mon, 26 Jul 2021 07:43:07 +0200 Subject: [PATCH 021/186] Binary representation of the floating-point numbers. --- src/algorithms/math/binary-floating-point/README.md | 2 ++ 1 file changed, 2 insertions(+) diff --git a/src/algorithms/math/binary-floating-point/README.md b/src/algorithms/math/binary-floating-point/README.md index 32b41f642a..c0c6fce046 100644 --- a/src/algorithms/math/binary-floating-point/README.md +++ b/src/algorithms/math/binary-floating-point/README.md @@ -79,6 +79,8 @@ I've tried to describe the logic behind the converting of floating-point numbers > Checkout the [interactive version of this diagram](https://trekhleb.dev/blog/2021/binary-floating-point/) to play around with setting bits on and off, and seeing how it would influence the final result +Be aware that this is by no means a complete and sufficient overview of the IEEE 754 standard. It is rather a simplified and basic overview. Several corner cases were omitted in the examples above for simplicity of presentation (i.e. `-0`, `-∞`, `+∞` and `NaN` (not a number) values) + ## Code examples - See the [bitsToFloat.js](bitsToFloat.js) for the example of how to convert array of bits to the floating point number (the example is a bit artificial but still it gives the overview of how the conversion is going on) From 2ad5617a4bcf05a59c650d91ab950fd054d0f69a Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Mon, 26 Jul 2021 07:44:21 +0200 Subject: [PATCH 022/186] Binary representation of the floating-point numbers. --- src/algorithms/math/binary-floating-point/README.md | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/src/algorithms/math/binary-floating-point/README.md b/src/algorithms/math/binary-floating-point/README.md index c0c6fce046..0952d99f5b 100644 --- a/src/algorithms/math/binary-floating-point/README.md +++ b/src/algorithms/math/binary-floating-point/README.md @@ -79,6 +79,13 @@ I've tried to describe the logic behind the converting of floating-point numbers > Checkout the [interactive version of this diagram](https://trekhleb.dev/blog/2021/binary-floating-point/) to play around with setting bits on and off, and seeing how it would influence the final result +Here is the number ranges that different floating-point formats support: + +| Floating-point format | Exp min | Exp max | Range | Min positive | +| :-------------------- | :------ | :------ | :--------------- | :----------- | +| Half-precision | −14 | +15 | ±65,504 | 6.10 × 10⁻⁵ | +| Single-precision | −126 | +127 | ±3.4028235 × 10³⁸| 1.18 × 10⁻³⁸ | + Be aware that this is by no means a complete and sufficient overview of the IEEE 754 standard. It is rather a simplified and basic overview. Several corner cases were omitted in the examples above for simplicity of presentation (i.e. `-0`, `-∞`, `+∞` and `NaN` (not a number) values) ## Code examples From 4548296affb227c29ead868309e48667f8280c55 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Mon, 26 Jul 2021 11:55:40 +0200 Subject: [PATCH 023/186] Binary representation of the floating-point numbers. --- src/algorithms/math/binary-floating-point/README.md | 1 + 1 file changed, 1 insertion(+) diff --git a/src/algorithms/math/binary-floating-point/README.md b/src/algorithms/math/binary-floating-point/README.md index 0952d99f5b..d1ae72731e 100644 --- a/src/algorithms/math/binary-floating-point/README.md +++ b/src/algorithms/math/binary-floating-point/README.md @@ -97,6 +97,7 @@ Be aware that this is by no means a complete and sufficient overview of the IEEE You might also want to check out the following resources to get a deeper understanding of the binary representation of floating-point numbers: +- [Interactive version of this article](https://trekhleb.dev/blog/2021/binary-floating-point/) (allows setting the bits manually and seeing the resulting floating number) - [Here is what you need to know about JavaScript’s Number type](https://indepth.dev/posts/1139/here-is-what-you-need-to-know-about-javascripts-number-type) - [Float Exposed](https://float.exposed/) - [IEEE754 Visualization](https://bartaz.github.io/ieee754-visualization/) From d0576a2594f843cae01abfdb9a2aa08663bdee54 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Mon, 18 Oct 2021 18:02:40 +0200 Subject: [PATCH 024/186] Upgrade dependencies. 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"@babel/cli": "7.12.10", - "@babel/preset-env": "7.12.11", - "@types/jest": "26.0.19", - "canvas": "^2.7.0", - "eslint": "7.16.0", + "@babel/cli": "7.15.7", + "@babel/preset-env": "7.15.8", + "@types/jest": "27.0.2", + "canvas": "2.8.0", + "eslint": "8.0.1", "eslint-config-airbnb": "18.2.1", - "eslint-plugin-import": "2.22.1", - "eslint-plugin-jest": "24.1.3", + "eslint-plugin-import": "2.25.2", + "eslint-plugin-jest": "25.2.2", "eslint-plugin-jsx-a11y": "6.4.1", - "eslint-plugin-react": "7.21.5", - "husky": "6.0.0", - "jest": "26.6.3" + "eslint-plugin-react": "7.26.1", + "husky": "7.0.2", + "jest": "27.3.0" }, "engines": { "node": ">=12.0.0", From 99945f30deba9fb0ec5077e07ed093d0a531f1c1 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Fri, 22 Oct 2021 09:56:44 +0200 Subject: [PATCH 025/186] Add the "Weighted Random" algorithm (#792) * Add the link to the Weighted Random algorithm to the main README. * Add Weighted Random implementation and tests. * Add Weighted Random README. * Add Weighted Random README. * Add Weighted Random README. --- README.md | 2 + .../statistics/weighted-random/README.md | 141 ++++++++++++++++++ .../__test__/weightedRandom.test.js | 64 ++++++++ .../weighted-random/weightedRandom.js | 52 +++++++ 4 files changed, 259 insertions(+) create mode 100644 src/algorithms/statistics/weighted-random/README.md create mode 100644 src/algorithms/statistics/weighted-random/__test__/weightedRandom.test.js create mode 100644 src/algorithms/statistics/weighted-random/weightedRandom.js diff --git a/README.md b/README.md index d00945e5a5..826a3a45b8 100644 --- a/README.md +++ b/README.md @@ -156,6 +156,8 @@ a set of rules that precisely define a sequence of operations. * `B` [k-Means](src/algorithms/ml/k-means) - k-Means clustering algorithm * **Image Processing** * `B` [Seam Carving](src/algorithms/image-processing/seam-carving) - content-aware image resizing algorithm +* **Statistics** + * `B` [Weighted Random](src/algorithms/statistics/weighted-random) - select the random item from the list based on items' weights * **Uncategorized** * `B` [Tower of Hanoi](src/algorithms/uncategorized/hanoi-tower) * `B` [Square Matrix Rotation](src/algorithms/uncategorized/square-matrix-rotation) - in-place algorithm diff --git a/src/algorithms/statistics/weighted-random/README.md b/src/algorithms/statistics/weighted-random/README.md new file mode 100644 index 0000000000..1c700d41d6 --- /dev/null +++ b/src/algorithms/statistics/weighted-random/README.md @@ -0,0 +1,141 @@ +# Weighted Random + +## What is "Weighted Random" + +Let's say you have a list of **items**. Item could be anything. For example, we may have a list of fruits and vegetables that you like to eat: `[ '🍌', '🍎', '🥕' ]`. + +The list of **weights** represent the weight (or probability, or importance) of each item. Weights are numbers. For example, the weights like `[3, 7, 1]` would say that: + +- you would like to eat `🍎 apples` more often (`7` out of `3 + 7 + 1 = 11` times), +- then you would like to eat `bananas 🍌` less often (only `3` out of `11` times), +- and the `carrots 🥕` you really don't like (want to eat it only `1` out of `11` times). + +> If we speak in terms of probabilities than the weights list might be an array of floats that sum up to `1` (i.e. `[0.1, 0.5, 0.2, 0.2]`). + +The **Weighted Random** in this case will be the function that will randomly return you the item from the list, and it will take each item's weight into account, so that items with the higher weight will be picked more often. + +Example of the function interface: + +```javascript +const items = [ '🍌', '🍎', '🥕' ]; +const weights = [ 3, 7, 1 ]; + +function weightedRandom(items, weights) { + // implementation goes here ... +} + +const nextSnackToEat = weightedRandom(items, weights); // Could be '🍎' +``` + +## Applications of Weighted Random + +- In [Genetic Algorithm](https://en.wikipedia.org/wiki/Genetic_algorithm) the weighted random is used during the "Selection" phase, when we need to select the fittest/strongest individuums based on their fitness score for mating and for producing the next stronger generation. You may find an **example** in the [Self-Parking Car in 500 Lines of Code](https://trekhleb.dev/blog/2021/self-parking-car-evolution/) article. +- In [Recurrent Neural Networks (RNN)](https://en.wikipedia.org/wiki/Recurrent_neural_network) when trying to decide what letter to choose next (to form the sentence) based on the next letter probability. You may find an **example** in the [Recipe Generation using Recurrent Neural Network (RNN)](https://nbviewer.org/github/trekhleb/machine-learning-experiments/blob/master/experiments/recipe_generation_rnn/recipe_generation_rnn.ipynb) Jupyter notebook. +- In [Nginx Load Balancing](https://docs.nginx.com/nginx/admin-guide/load-balancer/http-load-balancer/) to send HTTP requests more often to the servers with the higher weights. +- And more... + +## The Algorithm + +The **straightforward approach** would be to: + +1. Repeat each item in the list according to its weight. +2. Pick the random item from the list. + +For example in our case with fruits and vegetables we could generate the following list of size `3 + 7 + 1 = 11`: + +```javascript +const items = [ '🍌', '🍎', '🥕' ]; +const weights = [ 3, 7, 1 ]; + +// Repeating the items based on weights. +const weightedItems = [ + '🍌', '🍌', '🍌', + '🍎', '🍎', '🍎', '🍎', '🍎', '🍎', '🍎', + '🥕', +]; + +// And now just pick the random item from weightedItems array. +``` + +However, as you may see, this approach may require a lot of memory, in case if the objects are heavy, and in case if we have a lot of them to repeat in `weightedItems` list. + +The **more efficient approach** would be to: + +1. Prepare the list of cumulative weights for each item (i.e. the `cumulativeWeights` list which will have the same number of elements as the original `weights` list). In our case it will look like this: `cumulativeWeights = [3, 3 + 7, 3 + 7 + 1] = [3, 10, 11]` +2. Generate the random number `randomNumber` from `0` to the highest cumulative weight value. In our case the random number will be in a range of `[0..11]`. Let's say that we have `randomNumber = 8`. +3. Go through the `cumulativeWeights` list from left to right and pick the first element which is higher or equal to the `randomNumber`. The index of such element we will use to pick the item from the `items` array. + +The idea behind this approach is that the higher weights will "occupy" more numeric space. Therefore, there is a higher chance that the random number will fall into the "higher weight numeric bucket". + +```javascript +const weights = [3, 7, 1 ]; +const cumulativeWeights = [3, 10, 11]; + +// In a pseudo-representation we may think about the cumulativeWeights array like this. +const pseudoCumulativeWeights = [ + 1, 2, 3, // <-- [3] numbers + 4, 5, 6, 7, 8, 9, 10, // <-- [7] numbers + 11, // <-- [1] number +]; +``` + +Here is an example of how the `weightedRandom` function might be implemented: + +```javascript +/** + * Picks the random item based on its weight. + * The items with higher weight will be picked more often (with a higher probability). + * + * For example: + * - items = ['banana', 'orange', 'apple'] + * - weights = [0, 0.2, 0.8] + * - weightedRandom(items, weights) in 80% of cases will return 'apple', in 20% of cases will return + * 'orange' and it will never return 'banana' (because probability of picking the banana is 0%) + * + * @param {any[]} items + * @param {number[]} weights + * @returns {{item: any, index: number}} + */ +export default function weightedRandom(items, weights) { + if (items.length !== weights.length) { + throw new Error('Items and weights must be of the same size'); + } + + if (!items.length) { + throw new Error('Items must not be empty'); + } + + // Preparing the cumulative weights array. + // For example: + // - weights = [1, 4, 3] + // - cumulativeWeights = [1, 5, 8] + const cumulativeWeights = []; + for (let i = 0; i < weights.length; i += 1) { + cumulativeWeights[i] = weights[i] + (cumulativeWeights[i - 1] || 0); + } + + // Getting the random number in a range of [0...sum(weights)] + // For example: + // - weights = [1, 4, 3] + // - maxCumulativeWeight = 8 + // - range for the random number is [0...8] + const maxCumulativeWeight = cumulativeWeights[cumulativeWeights.length - 1]; + const randomNumber = maxCumulativeWeight * Math.random(); + + // Picking the random item based on its weight. + // The items with higher weight will be picked more often. + for (let itemIndex = 0; itemIndex < items.length; itemIndex += 1) { + if (cumulativeWeights[itemIndex] >= randomNumber) { + return { + item: items[itemIndex], + index: itemIndex, + }; + } + } +} +``` + +## Implementation + +- Check the [weightedRandom.js](weightedRandom.js) file for the implementation of the `weightedRandom()` function. +- Check the [weightedRandom.test.js](__test__/weightedRandom.test.js) file for the tests-cases. diff --git a/src/algorithms/statistics/weighted-random/__test__/weightedRandom.test.js b/src/algorithms/statistics/weighted-random/__test__/weightedRandom.test.js new file mode 100644 index 0000000000..1b0b267627 --- /dev/null +++ b/src/algorithms/statistics/weighted-random/__test__/weightedRandom.test.js @@ -0,0 +1,64 @@ +import weightedRandom from '../weightedRandom'; + +describe('weightedRandom', () => { + it('should throw an error when the number of weights does not match the number of items', () => { + const getWeightedRandomWithInvalidInputs = () => { + weightedRandom(['a', 'b', 'c'], [10, 0]); + }; + expect(getWeightedRandomWithInvalidInputs).toThrow('Items and weights must be of the same size'); + }); + + it('should throw an error when the number of weights or items are empty', () => { + const getWeightedRandomWithInvalidInputs = () => { + weightedRandom([], []); + }; + expect(getWeightedRandomWithInvalidInputs).toThrow('Items must not be empty'); + }); + + it('should correctly do random selection based on wights in straightforward cases', () => { + expect(weightedRandom(['a', 'b', 'c'], [1, 0, 0])).toEqual({ index: 0, item: 'a' }); + expect(weightedRandom(['a', 'b', 'c'], [0, 1, 0])).toEqual({ index: 1, item: 'b' }); + expect(weightedRandom(['a', 'b', 'c'], [0, 0, 1])).toEqual({ index: 2, item: 'c' }); + expect(weightedRandom(['a', 'b', 'c'], [0, 1, 1])).not.toEqual({ index: 0, item: 'a' }); + expect(weightedRandom(['a', 'b', 'c'], [1, 0, 1])).not.toEqual({ index: 1, item: 'b' }); + expect(weightedRandom(['a', 'b', 'c'], [1, 1, 0])).not.toEqual({ index: 2, item: 'c' }); + }); + + it('should correctly do random selection based on wights', () => { + // Number of times we're going to select the random items based on their weights. + const ATTEMPTS_NUM = 1000; + // The +/- delta in the number of times each item has been actually selected. + // I.e. if we want the item 'a' to be selected 300 times out of 1000 cases (30%) + // then 267 times is acceptable since it is bigger that 250 (which is 300 - 50) + // ans smaller than 350 (which is 300 + 50) + const THRESHOLD = 50; + + const items = ['a', 'b', 'c']; // The actual items values don't matter. + const weights = [0.1, 0.3, 0.6]; + + const counter = []; + for (let i = 0; i < ATTEMPTS_NUM; i += 1) { + const randomItem = weightedRandom(items, weights); + if (!counter[randomItem.index]) { + counter[randomItem.index] = 1; + } else { + counter[randomItem.index] += 1; + } + } + + for (let itemIndex = 0; itemIndex < items.length; itemIndex += 1) { + /* + i.e. item with the index of 0 must be selected 100 times (ideally) + or with the threshold of [100 - 50, 100 + 50] times. + + i.e. item with the index of 1 must be selected 300 times (ideally) + or with the threshold of [300 - 50, 300 + 50] times. + + i.e. item with the index of 2 must be selected 600 times (ideally) + or with the threshold of [600 - 50, 600 + 50] times. + */ + expect(counter[itemIndex]).toBeGreaterThan(ATTEMPTS_NUM * weights[itemIndex] - THRESHOLD); + expect(counter[itemIndex]).toBeLessThan(ATTEMPTS_NUM * weights[itemIndex] + THRESHOLD); + } + }); +}); diff --git a/src/algorithms/statistics/weighted-random/weightedRandom.js b/src/algorithms/statistics/weighted-random/weightedRandom.js new file mode 100644 index 0000000000..0d58a504f8 --- /dev/null +++ b/src/algorithms/statistics/weighted-random/weightedRandom.js @@ -0,0 +1,52 @@ +/** + * Picks the random item based on its weight. + * The items with higher weight will be picked more often (with a higher probability). + * + * For example: + * - items = ['banana', 'orange', 'apple'] + * - weights = [0, 0.2, 0.8] + * - weightedRandom(items, weights) in 80% of cases will return 'apple', in 20% of cases will return + * 'orange' and it will never return 'banana' (because probability of picking the banana is 0%) + * + * @param {any[]} items + * @param {number[]} weights + * @returns {{item: any, index: number}} + */ +/* eslint-disable consistent-return */ +export default function weightedRandom(items, weights) { + if (items.length !== weights.length) { + throw new Error('Items and weights must be of the same size'); + } + + if (!items.length) { + throw new Error('Items must not be empty'); + } + + // Preparing the cumulative weights array. + // For example: + // - weights = [1, 4, 3] + // - cumulativeWeights = [1, 5, 8] + const cumulativeWeights = []; + for (let i = 0; i < weights.length; i += 1) { + cumulativeWeights[i] = weights[i] + (cumulativeWeights[i - 1] || 0); + } + + // Getting the random number in a range of [0...sum(weights)] + // For example: + // - weights = [1, 4, 3] + // - maxCumulativeWeight = 8 + // - range for the random number is [0...8] + const maxCumulativeWeight = cumulativeWeights[cumulativeWeights.length - 1]; + const randomNumber = maxCumulativeWeight * Math.random(); + + // Picking the random item based on its weight. + // The items with higher weight will be picked more often. + for (let itemIndex = 0; itemIndex < items.length; itemIndex += 1) { + if (cumulativeWeights[itemIndex] >= randomNumber) { + return { + item: items[itemIndex], + index: itemIndex, + }; + } + } +} From 17bfb551c0d1d38de5ff3ec4ef9c587678ce6ea9 Mon Sep 17 00:00:00 2001 From: Oleksii Trekhleb Date: Fri, 22 Oct 2021 10:16:37 +0200 Subject: [PATCH 026/186] Add Weighted Random cover. --- .../statistics/weighted-random/README.md | 2 ++ .../weighted-random/images/cover.png | Bin 0 -> 303430 bytes 2 files changed, 2 insertions(+) create mode 100644 src/algorithms/statistics/weighted-random/images/cover.png diff --git a/src/algorithms/statistics/weighted-random/README.md b/src/algorithms/statistics/weighted-random/README.md index 1c700d41d6..8b9c8890d7 100644 --- a/src/algorithms/statistics/weighted-random/README.md +++ b/src/algorithms/statistics/weighted-random/README.md @@ -1,5 +1,7 @@ # Weighted Random +![Weighted Random](images/cover.png) + ## What is "Weighted Random" Let's say you have a list of **items**. Item could be anything. 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