fix: hadnle zeros at the endpoints in BisectionMethod (TheAlgorithms#1640)

* fix: hadnle zeros at the endpoints

* style: use simpler syntax express polynomials

Co-authored-by: appgurueu <34514239+appgurueu@users.noreply.github.com>

---------

Co-authored-by: appgurueu <34514239+appgurueu@users.noreply.github.com>

Author: vil02

Maths/BisectionMethod.js

@@ -23,7 +23,7 @@ const findRoot = (a, b, func, numberOfIterations) => {
 
   // Bolzano theorem
   const hasRoot = (a, b, func) => {
-    return func(a) * func(b) < 0
+    return func(a) * func(b) <= 0
   }
   if (hasRoot(a, b, func) === false) {
     throw Error(
@@ -45,10 +45,9 @@ const findRoot = (a, b, func, numberOfIterations) => {
   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')
+  if (prod2 <= 0) return findRoot(m, b, func, --numberOfIterations)
+
+  return findRoot(a, m, func, --numberOfIterations)
 }
 
 export { findRoot }

Maths/test/BisectionMethod.test.js

@@ -1,14 +1,7 @@
 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
-  )
+  const root = findRoot(0, 1.5, (x) => x ** 2 - 3 * x + 2, 8)
   expect(root).toBe(0.9990234375)
 })
 
@@ -35,3 +28,12 @@ test('Equation f(x) = sqrt(x) + e^(2*x) - 8*x = 0, has root x = 0.93945851 in [a
   )
   expect(Number(Number(root).toPrecision(8))).toBe(0.93945851)
 })
+
+test('Equation f(x) = x^3 = 0, has root x = 0.0 in [a, b] = [-1.0, 1.0]', () => {
+  const root = findRoot(-1.0, 1.0, (x) => x ** 3, 32)
+  expect(root).toBeCloseTo(0.0, 5)
+})
+
+test('Throws an error when function does not change sign', () => {
+  expect(() => findRoot(-1.0, 1.0, (x) => x ** 2, 10)).toThrowError()
+})