Quick Select Search (#131)

* HeapSort algorithm

* Create QuickSelect.js

* Algorithm to reverse a string.

* Update ReverseString.js

* Update Heapsort.js

* Update QuickSelect.js

Co-authored-by: vinayak <[email protected]>

Author: NourBc

QuickSelect.js

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+/**
+ * QuickSelect is an algorithm to find the kth smallest number
+ *
+ * Notes:
+ * -QuickSelect is related to QuickSort, thus has optimal best and average
+ *  case (O(n)) but unlikely poor worst case (O(n^2))
+ * -This implementation uses randomly selected pivots for better performance
+ *
+ * @complexity: O(n) (on average )
+ * @complexity: O(n^2) (worst case)
+ * @flow
+ */
+
+function QuickSelect (items, kth) {
+  return RandomizedSelect(items, 0, items.length - 1, kth)
+}
+
+function RandomizedSelect (
+  items,
+  left,
+  right,
+  i
+) {
+  if (left === right) return items[left]
+
+  const pivotIndex = RandomizedPartition(items, left, right)
+  const k = pivotIndex - left + 1
+
+  if (i === k) return items[pivotIndex]
+  if (i < k) return RandomizedSelect(items, left, pivotIndex - 1, i)
+
+  return RandomizedSelect(items, pivotIndex + 1, right, i - k)
+}
+
+function RandomizedPartition (items, left, right) {
+  const rand = getRandomInt(left, right)
+  Swap(items, rand, right)
+  return Partition(items, left, right)
+}
+
+function Partition (items, left, right) {
+  const x = items[right]
+  let pivotIndex = left - 1
+
+  for (let j = left; j < right; j++) {
+    if (items[j] <= x) {
+      pivotIndex++
+      Swap(items, pivotIndex, j)
+    }
+  }
+
+  Swap(items, pivotIndex + 1, right)
+
+  return pivotIndex + 1
+}
+
+function getRandomInt (min, max) {
+  return Math.floor(Math.random() * (max - min + 1)) + min
+}
+
+function Swap (arr, x, y) {
+  const temp = arr[x]
+  arr[x] = arr[y]
+  arr[y] = temp
+}
+
+// testing
+console.log(QuickSelect([1, 4, 2, -2, 4, 5]))

Sorts/Heapsort.js

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+let arrayLength = 0
+
+/* to create MAX  array */
+
+function heapRoot (input, i) {
+  const left = 2 * i + 1
+  const right = 2 * i + 2
+  let max = i
+
+  if (left < arrayLength && input[left] > input[max]) {
+    max = left
+  }
+
+  if (right < arrayLength && input[right] > input[max]) {
+    max = right
+  }
+
+  if (max !== i) {
+    swap(input, i, max)
+    heapRoot(input, max)
+  }
+}
+
+function swap (input, indexA, indexB) {
+  const temp = input[indexA]
+
+  input[indexA] = input[indexB]
+  input[indexB] = temp
+}
+
+function heapSort (input) {
+  arrayLength = input.length
+
+  for (let i = Math.floor(arrayLength / 2); i >= 0; i -= 1) {
+    heapRoot(input, i)
+  }
+
+  for (let i = input.length - 1; i > 0; i--) {
+    swap(input, 0, i)
+    arrayLength--
+
+    heapRoot(input, 0)
+  }
+}
+
+const arr = [3, 0, 2, 5, -1, 4, 1]
+heapSort(arr)
+console.log(arr)

maths/ReverseString.js

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+/**
+ * A short example showing how to reverse a string
+ * @flow
+ */
+
+/**
+ * Create a new string and append
+ * @complexity O(n)
+ */
+
+function ReverseStringIterative (string) {
+  let reversedString = ''
+  let index
+
+  for (index = string.length - 1; index >= 0; index--) {
+    reversedString += string[index]
+  }
+
+  return reversedString
+}
+
+/**
+ * JS disallows string mutation so we're actually a bit slower.
+ *
+ * @complexity: O(n)
+ *
+ * 'some' -> 'eoms' -> 'emos'
+ */
+
+function ReverseStringIterativeInplace (string) {
+  const _string = string.split('')
+
+  for (let i = 0; i < Math.floor(_string.length / 2); i++) {
+    const first = _string[i]
+    const second = _string[_string.length - 1 - i]
+    _string[i] = second
+    _string[_string.length - 1 - i] = first
+  }
+
+  return _string.join('')
+}
+
+// testing
+console.log(ReverseStringIterative('Javascript'))
+console.log(ReverseStringIterativeInplace('Javascript'))