merge: Added bisection method (#827)

* feat: Added bisection method

* Auto-update DIRECTORY.md

Co-authored-by: ggkogkou <[email protected]>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

Author: 3 people

DIRECTORY.md

@@ -145,6 +145,7 @@
   * [BinaryConvert](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/BinaryConvert.js)
   * [BinaryExponentiationIterative](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/BinaryExponentiationIterative.js)
   * [BinaryExponentiationRecursive](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/BinaryExponentiationRecursive.js)
+  * [BisectionMethod](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/BisectionMethod.js)
   * [CheckKishnamurthyNumber](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/CheckKishnamurthyNumber.js)
   * [Coordinate](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/Coordinate.js)
   * [CoPrimeCheck](https://github.com/TheAlgorithms/Javascript/blob/master/Maths/CoPrimeCheck.js)

Maths/BisectionMethod.js

@@ -0,0 +1,46 @@
+/**
+ *
+ * @file
+ * @brief Find real roots of a function in a specified interval [a, b], where f(a)*f(b) < 0
+ *
+ * @details Given a function f(x) and an interval [a, b], where f(a) * f(b) < 0, find an approximation of the root
+ * by calculating the middle m = (a + b) / 2, checking f(m) * f(a) and f(m) * f(b) and then by choosing the
+ * negative product that means Bolzano's theorem is applied,, define the new interval with these points. Repeat until
+ * we get the precision we want [Wikipedia](https://en.wikipedia.org/wiki/Bisection_method)
+ *
+ * @author [ggkogkou](https://github.com/ggkogkou)
+ *
+ */
+
+const findRoot = (a, b, func, numberOfIterations) => {
+  // Check if a given  real value belongs to the function's domain
+  const belongsToDomain = (x, f) => {
+    const res = f(x)
+    return !Number.isNaN(res)
+  }
+  if (!belongsToDomain(a, func) || !belongsToDomain(b, func)) throw Error("Given interval is not a valid subset of function's domain")
+
+  // Bolzano theorem
+  const hasRoot = (a, b, func) => {
+    return func(a) * func(b) < 0
+  }
+  if (hasRoot(a, b, func) === false) { throw Error('Product f(a)*f(b) has to be negative so that Bolzano theorem is applied') }
+
+  // Declare m
+  const m = (a + b) / 2
+
+  // Recursion terminal condition
+  if (numberOfIterations === 0) { return m }
+
+  // Find the products of f(m) and f(a), f(b)
+  const fm = func(m)
+  const prod1 = fm * func(a)
+  const prod2 = fm * func(b)
+
+  // Depending on the sign of the products above, decide which position will m fill (a's or b's)
+  if (prod1 > 0 && prod2 < 0) return findRoot(m, b, func, --numberOfIterations)
+  else if (prod1 < 0 && prod2 > 0) return findRoot(a, m, func, --numberOfIterations)
+  else throw Error('Unexpected behavior')
+}
+
+export { findRoot }

Maths/test/BisectionMethod.test.js

@@ -0,0 +1,16 @@
+import { findRoot } from '../BisectionMethod'
+
+test('Equation f(x) = x^2 - 3*x + 2 = 0, has root x = 1 in [a, b] = [0, 1.5]', () => {
+  const root = findRoot(0, 1.5, (x) => { return Math.pow(x, 2) - 3 * x + 2 }, 8)
+  expect(root).toBe(0.9990234375)
+})
+
+test('Equation f(x) = ln(x) + sqrt(x) + π*x^2 = 0, has root x = 0.36247037 in [a, b] = [0, 10]', () => {
+  const root = findRoot(0, 10, (x) => { return Math.log(x) + Math.sqrt(x) + Math.PI * Math.pow(x, 2) }, 32)
+  expect(Number(Number(root).toPrecision(8))).toBe(0.36247037)
+})
+
+test('Equation f(x) = sqrt(x) + e^(2*x) - 8*x = 0, has root x = 0.93945851 in [a, b] = [0.5, 100]', () => {
+  const root = findRoot(0.5, 100, (x) => { return Math.exp(2 * x) + Math.sqrt(x) - 8 * x }, 32)
+  expect(Number(Number(root).toPrecision(8))).toBe(0.93945851)
+})