Greatest Common Divisor of Strings

Given two strings str1 and str2, return the largest string x such that x divides both str1 and str2.

Note: For any two strings a and b, we say "b divides a" if and only if a = b + b + ... + b (one or more times).

Examples

Example 1:
Input: str1 = "AB", str2 = "AB"
Output: "AB"

Example 2:
Input: str1 = "ABCABCABC", str2 = "ABCABC"
Output: "ABC"

Example 3:
Input: str1 = "ABABAB", str2 = "AB"
Output: "AB"

Example 4:
Input: str1 = "LEET", str2 = "CODE"
Output: ""

This problem is efficiently solved using Euclidean's algorithm for GCD:

If str1 + str2 !== str2 + str1, return "" (no common divisor string exists).
Compute the GCD of the lengths of str1 and str2.
The substring of length GCD from either string is the answer.

Time Complexity: O(n + m), where n and m are the lengths of the two strings (for concatenation and comparison), plus O(log(min(n, m))) for the GCD calculation.
Space Complexity: O(n + m), for the concatenated strings.