chore: Add PowLogarithmic in Math (TheAlgorithms#836)

* Add PowLogarithmic in Math * add description

Author: Yatin-kathuria

Maths/PowLogarithmic.js

@@ -0,0 +1,26 @@
+import { isEven } from './IsEven'
+
+/**
+ * This algorithm is divide the n by 2 every time and pass this to recursive call to find the result of smaller result.
+ * why? Because
+ * x^n => [if n is even] x^(n / 2) * x^(n / 2) (example : 7^4 => 7^2 * 7^2)
+ * [if n is odd] x^(n / 2) * x^(n / 2) * x (example : 7^5 => 7^2 * 7^2 * 7)
+ * and repeat the above step until we reach to the base case.
+ *
+ * @function PowLogarithmic
+ * @description Given two integers x and n, return x^n in logarithmic complexity.
+ * @param {Integer} x - The input integer
+ * @param {Integer} n - The input integer
+ * @return {Integer} - Returns x^n.
+ * @see [Pow-Logarithmic](https://www.geeksforgeeks.org/write-a-c-program-to-calculate-powxn/)
+ */
+const powLogarithmic = (x, n) => {
+ if (n === 0) return 1
+ const result = powLogarithmic(x, Math.floor(n / 2))
+ if (isEven(n)) {
+ return result * result
+ }
+ return result * result * x
+}
+
+export { powLogarithmic }

Maths/test/PowLogarithmic.test.js

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+import { powLogarithmic } from '../PowLogarithmic'
+
+describe('PowLogarithmic', () => {
+ it('should return 1 for numbers with exponent 0', () => {
+ expect(powLogarithmic(2, 0)).toBe(1)
+ })
+
+ it('should return 0 for numbers with base 0', () => {
+ expect(powLogarithmic(0, 23)).toBe(0)
+ })
+
+ it('should return the base to the exponent power', () => {
+ expect(powLogarithmic(24, 4)).toBe(331776)
+ })
+})