Added Extended Euclidean Algorithm (ExtendedEuclideanGCD.js) to Maths folder, along with relevant test

Author: Star-325

Maths/ExtendedEuclideanGCD.js

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+/**
+ * Problem statement and explanation: https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm
+ * 
+ * This algorithm plays an important role for modular arithmetic, and by extension for cyptography algorithms
+ * 
+ * This implementation uses an iterative approach to calculate
+ */
+
+/**
+ * 
+ * @param {Number} arg1 first argument
+ * @param {Number} arg2 second argument
+ * @returns Array with GCD and first and second Bézout coefficients
+ */
+const extendedEuclideanGCD = (arg1, arg2) => {
+    if(typeof arg1 != 'number' || typeof arg2 != 'number') throw new TypeError('Not a Number');
+    if(arg1 < 1 || arg2 < 1) throw new TypeError('Must be positive numbers');
+
+    // Make the order of coefficients correct, as the algorithm assumes r0 > r1
+    if (arg1 < arg2) {
+        const res = extendedEuclideanGCD(arg2,arg1)
+        const temp = res[1]
+        res[1] = res[2]
+        res[2] = temp
+        return res;
+    }
+
+    // At this point arg1 > arg2
+
+    // Remainder values
+    let r0 = arg1
+    let r1 = arg2
+
+    // Coefficient1 values
+    let s0 = 1
+    let s1 = 0
+
+    // Coefficient 2 values
+    let t0 = 0
+    let t1 = 1
+    
+    while(r1 != 0) {
+        const q = Math.floor(r0 / r1);
+
+        const r2 = r0 - r1*q;
+        const s2 = s0 - s1*q;
+        const t2 = t0 - t1*q;
+        
+        r0 = r1
+        r1 = r2
+        s0 = s1
+        s1 = s2
+        t0 = t1
+        t1 = t2
+    }
+    return [r0,s0,t0];
+}
+
+export { extendedEuclideanGCD };
+// ex

Maths/test/ExtendedEuclideanGCD.test.js

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+import { extendedEuclideanGCD } from '../ExtendedEuclideanGCD'
+
+describe('extendedEuclideanGCD', () => {
+  it('should return valid values in order for positive arguments', () => {
+    expect(extendedEuclideanGCD(240, 46)).toMatchObject([2, -9, 47])
+    expect(extendedEuclideanGCD(46, 240)).toMatchObject([2, 47, -9])
+  })
+  it('should give error on non-positive arguments', () => {
+      expect(() => extendedEuclideanGCD(0,240)).toThrowError(new TypeError('Must be positive numbers'))
+      expect(() => extendedEuclideanGCD(46,-240)).toThrowError(new TypeError('Must be positive numbers'))
+  })
+  it('should give error on non-numeric arguments', () => {
+      expect(() => extendedEuclideanGCD('240',46)).toThrowError(new TypeError('Not a Number'));
+      expect(() => extendedEuclideanGCD([240,46])).toThrowError(new TypeError('Not a Number'));
+  })
+})