feat: Function to check a number is Square free (TheAlgorithms#94)

* Update DIRECTORY.md

* feat: Function to check a number is Square free

* Update DIRECTORY.md

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

Author: MohdFaisalBidda

DIRECTORY.md

@@ -29,6 +29,7 @@
   * [Is Even](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/is_even.ts)
   * [Is Leap Year](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/is_leap_year.ts)
   * [Is Odd](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/is_odd.ts)
+  * [Is Square Free](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/is_square_free.ts)
   * [Lowest Common Multiple](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/lowest_common_multiple.ts)
   * [Perfect Square](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/perfect_square.ts)
   * [Pronic Number](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/pronic_number.ts)

maths/is_square_free.ts

@@ -0,0 +1,24 @@
+/**
+ * @function isSquareFree
+ * @description A number is said to be square-free if no prime factor divides it more than once, i.e., the largest power of a prime factor that divides n is one.
+ * @param {number} n - A number.
+ * @return {boolean} - True if given number is a square free.
+ * @see https://www.geeksforgeeks.org/square-free-number/
+ * @example isSquareFree(10) = true
+ * @example isSquareFree(20) = false
+ */
+
+export const isSquareFree = (n: number): boolean => {
+
+    if (n < 0) throw new Error("number must be a natural number > 0");
+    if (n % 2 === 0) n = n / 2;
+    if (n % 2 === 0) return false;
+
+    for (let i: number = 3; i < Math.sqrt(n); i = i + 2) {
+        if (n % i === 0) {
+            n = n / i;
+            if (n % i === 0) return false;
+        }
+    }
+    return true;
+}

maths/test/is_square_free.test.ts

@@ -0,0 +1,11 @@
+import { isSquareFree } from '../is_square_free';
+
+describe('isSquareFree', () => {
+    test('should return correct boolean value', () => {
+        expect(isSquareFree(1)).toBe(true);
+        expect(isSquareFree(10)).toBe(true);
+        expect(isSquareFree(20)).toBe(false);
+        expect(isSquareFree(26)).toBe(true);
+        expect(isSquareFree(48)).toBe(false);
+    });
+});