feat: implement greatest common divisor of strings

Author: francislagares

Diff for: src/algorithms/common-divisor/common-divisor.ts

@@ -0,0 +1,33 @@
+/**
+ * Finds the greatest common divisor string of two strings.
+ * A string is a divisor if concatenating it multiple times produces the original string.
+ *
+ * @param str1 First string (1 <= length <= 1000)
+ * @param str2 Second string (1 <= length <= 1000)
+ * @returns The largest common divisor string, or empty string if none exists
+ */
+export const gcdOfStrings = (str1: string, str2: string): string => {
+  // If concatenation in both orders isn't equal, no solution exists
+  if (str1 + str2 !== str2 + str1) {
+    return '';
+  }
+
+  // Helper function to calculate GCD of two numbers using Euclidean algorithm
+  const gcd = (a: number, b: number): number => {
+    return b === 0 ? a : gcd(b, a % b);
+  };
+
+  // The length of the GCD string will be the GCD of the lengths
+  const gcdLength = gcd(str1.length, str2.length);
+
+  // The potential GCD string is the first gcdLength characters
+  const candidate = str1.slice(0, gcdLength);
+
+  // Verify if this candidate actually divides both strings
+  const divides = (str: string, divisor: string): boolean => {
+    const times = str.length / divisor.length;
+    return divisor.repeat(times) === str;
+  };
+
+  return divides(str1, candidate) && divides(str2, candidate) ? candidate : '';
+};

Diff for: src/algorithms/common-divisor/tests/common-divisor.test.ts

@@ -0,0 +1,30 @@
+import { describe, expect, test } from 'vitest';
+import { gcdOfStrings } from '../common-divisor';
+
+describe('gcdOfStrings', () => {
+  test('finds GCD when one string is a multiple of the other', () => {
+    expect(gcdOfStrings('ABCABC', 'ABC')).toBe('ABC');
+  });
+
+  test('finds GCD when both strings have a common divisor', () => {
+    expect(gcdOfStrings('ABABAB', 'ABAB')).toBe('AB');
+  });
+
+  test('returns empty string when no common divisor exists', () => {
+    expect(gcdOfStrings('LEET', 'CODE')).toBe('');
+  });
+
+  test('handles identical strings', () => {
+    expect(gcdOfStrings('AAA', 'AAA')).toBe('AAA');
+  });
+
+  test('handles single character strings', () => {
+    expect(gcdOfStrings('A', 'A')).toBe('A');
+  });
+
+  test('handles longer strings with common divisor', () => {
+    expect(
+      gcdOfStrings('TAUXXTAUXXTAUXXTAUXXTAUXX', 'TAUXXTAUXXTAUXXTAUXX'),
+    ).toBe('TAUXX');
+  });
+});