From c1c895bebd532a5943b85460cc498d656bec2fcd Mon Sep 17 00:00:00 2001
From: YATIN KATHURIA <47096348+Yatin-kathuria@users.noreply.github.com>
Date: Fri, 19 Nov 2021 10:40:51 +0530
Subject: [PATCH] chore: Add PowLogarithmic in Math (#836)

* Add PowLogarithmic in Math

* add description
---
 Maths/PowLogarithmic.js           | 26 ++++++++++++++++++++++++++
 Maths/test/PowLogarithmic.test.js | 15 +++++++++++++++
 2 files changed, 41 insertions(+)
 create mode 100644 Maths/PowLogarithmic.js
 create mode 100644 Maths/test/PowLogarithmic.test.js

diff --git a/Maths/PowLogarithmic.js b/Maths/PowLogarithmic.js
new file mode 100644
index 000000000..ff57d14ef
--- /dev/null
+++ b/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 }
diff --git a/Maths/test/PowLogarithmic.test.js b/Maths/test/PowLogarithmic.test.js
new file mode 100644
index 000000000..e432213f6
--- /dev/null
+++ b/Maths/test/PowLogarithmic.test.js
@@ -0,0 +1,15 @@
+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)
+  })
+})