feat: add square root

DIRECTORY.md

@@ -124,6 +124,7 @@
       * [Hexagonal Numbers.Test](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/series/test/hexagonal_numbers.test.ts)
   * [Sieve Of Eratosthenes](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/sieve_of_eratosthenes.ts)
   * [Signum](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/signum.ts)
+  * [Square Root](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/square_root.ts)
   * [Ugly Numbers](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/ugly_numbers.ts)
   * [Zellers Congruence](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/zellers_congruence.ts)
 

maths/square_root.ts

@@ -0,0 +1,26 @@
+/**
+ * @function squareRoot
+ * @description Finding the square root of a number using Newton's method.
+ * @param {number} num - A number.
+ * @param {number} precision - Precision of square root, 1e-15 by default.
+ * @returns {number} - Square root of the given number.
+ * @see https://www.geeksforgeeks.org/find-root-of-a-number-using-newtons-method/
+ * @example SquareRoot(36) = 6
+ * @example SquareRoot(50) = 7.0710678118654755
+ */
+
+export const squareRoot = (num: number, precision: number = 1e-15): number => {
+  if (num < 0) throw new Error("number must be non-negative number");
+  if (num === 0) return 0;
+
+  let sqrt: number = num;
+  let curr: number;
+
+  while (true) {
+    curr = 0.5 * (sqrt + num / sqrt);
+    if (Math.abs(curr - sqrt) < precision) {
+      return sqrt;
+    }
+    sqrt = curr;
+  }
+};

maths/test/square_root.test.ts

@@ -0,0 +1,28 @@
+import { squareRoot } from "../square_root";
+
+describe("squareRoot", () => {
+  test.each([-1, -10, -2.4])(
+    "should throw an error for negative numbers",
+    (n: number) => {
+      expect(() => squareRoot(n)).toThrow("number must be non-negative number");
+    }
+  );
+
+  test.each([0, 1, 4, 9, 16, 25])(
+    "should return correct rational square root value",
+    () => {
+      (n: number) => {
+        expect(() => squareRoot(n)).toBeCloseTo(Math.sqrt(n));
+      };
+    }
+  );
+
+  test.each([2, 15, 20, 40, 99, 10032])(
+    "should return correct irrational square root value",
+    () => {
+      (n: number) => {
+        expect(() => squareRoot(n)).toBeCloseTo(Math.sqrt(n));
+      };
+    }
+  );
+});

maths/test/ugly_numbers.test.ts

@@ -1,6 +1,10 @@
-import { UglyNumbers } from '../ugly_numbers';
+import { uglyNumbers } from "../ugly_numbers";
 
-test('Ugly Numbers', () => {
-  const uglyNumbers = UglyNumbers();
-  expect(Array(11).fill(undefined).map(() => uglyNumbers.next().value)).toEqual([1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15]);
-})
+test("Ugly Numbers", () => {
+  const uglyNums = uglyNumbers();
+  expect(
+    Array(11)
+      .fill(undefined)
+      .map(() => uglyNums.next().value)
+  ).toEqual([1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15]);
+});

maths/ugly_numbers.ts

@@ -5,32 +5,34 @@
  * They can be represented in the form 2^a * 3^b * 5*c. By convention, 1 is also considered to be
  * an ugly number.
  * The first few terms of the sequence are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20...
- * 
+ *
  * For the provided n, the nth ugly number shall be computed.
  * @see [GeeksForGeeks](https://www.geeksforgeeks.org/ugly-numbers/)
  */
-function* UglyNumbers() {
-  yield 1
+function* uglyNumbers() {
+  yield 1;
 
-  let idx2 = 0, idx3 = 0, idx5 = 0
-  const uglyNumbers = [1]
+  let idx2 = 0,
+    idx3 = 0,
+    idx5 = 0;
+  const uglyNums: number[] = [1];
 
-  let nextx2: number, nextx3: number, nextx5: number, nextUglyNum: number
+  let nextx2: number, nextx3: number, nextx5: number, nextUglyNum: number;
 
-  while(true) {
-    nextx2 = uglyNumbers[idx2] * 2
-    nextx3 = uglyNumbers[idx3] * 3
-    nextx5 = uglyNumbers[idx5] * 5
+  while (true) {
+    nextx2 = uglyNums[idx2] * 2;
+    nextx3 = uglyNums[idx3] * 3;
+    nextx5 = uglyNums[idx5] * 5;
 
-    nextUglyNum = Math.min(nextx2, nextx3, nextx5)
-    yield nextUglyNum
+    nextUglyNum = Math.min(nextx2, nextx3, nextx5);
+    yield nextUglyNum;
 
-    if(nextx2 === nextUglyNum) idx2++
-    if(nextx3 === nextUglyNum) idx3++
-    if(nextx5 === nextUglyNum) idx5++
-    
-    uglyNumbers.push(nextUglyNum)
+    if (nextx2 === nextUglyNum) idx2++;
+    if (nextx3 === nextUglyNum) idx3++;
+    if (nextx5 === nextUglyNum) idx5++;
+
+    uglyNums.push(nextUglyNum);
   }
 }
 
-export { UglyNumbers }
+export { uglyNumbers };