# Program to find Greatest Common Divisor (GCD) of N strings

Given an array of string arr[], the task is the Greatest Common Divisor of the given array of string.

In strings ‘A’ and ‘B’, we say “B divides A” if and only if A = concatenation of B more than 1 times.Find the largest string which divides both A and B.

Examples:

Input: arr[] = { “GFGGFG”, “GFGGFG”, “GFGGFGGFGGFG” }
Output: “GFGGFG”
Explanation:
“GFGGFG” is the largest string which divides the whole array elements.
Input: arr = { “Geeks”, = “GFG”}
Output: “”

Approach: The idea is to use recursion. Below are the steps:

1. Create a recursive function gcd(str1, str2).
2. If the length of str2 is more than str1 then we will recur with gcd(str2, str1).
3. Now if str1 doesn’t start with str2 then return an empty string.
4. If the longer string begins with a shorter string, cut off the common prefix part of the longer string and recur or repeat until one is empty.
5. The string returned after the above steps are the gcd of the given array of string.

Below is the implementation of the above approach:

## Java

 `// Java program for the above approach`   `class` `GCD {`   `    ``// Function that finds gcd of 2 strings` `    ``static` `String gcd(String str1, String str2)` `    ``{` `        ``// If str1 length is less than` `        ``// that of str2 then recur` `        ``// with gcd(str2, str1)` `        ``if` `(str1.length() < str2.length()) {` `            ``return` `gcd(str2, str1);` `        ``}`   `        ``// If str1 is not the` `        ``// concatenation of str2` `        ``else` `if` `(!str1.startsWith(str2)) {` `            ``return` `""``;` `        ``}`   `        ``else` `if` `(str2.isEmpty()) {`   `            ``// GCD string is found` `            ``return` `str1;` `        ``}` `        ``else` `{`   `            ``// Cut off the common prefix` `            ``// part of str1 & then recur` `            ``return` `gcd(str1.substring(str2.length()),` `                       ``str2);` `        ``}` `    ``}`   `    ``// Function to find GCD of array of` `    ``// strings` `    ``static` `String findGCD(String arr[], ``int` `n)` `    ``{` `        ``String result = arr[``0``];`   `        ``for` `(``int` `i = ``1``; i < n; i++) {` `            ``result = gcd(result, arr[i]);` `        ``}`   `        ``// Return the GCD of strings` `        ``return` `result;` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `        ``main(String[] args)` `    ``{` `        ``// Given array  of strings` `        ``String arr[]` `            ``= ``new` `String[] { ``"GFGGFG"``,` `                             ``"GFGGFG"``,` `                             ``"GFGGFGGFGGFG"` `};` `        ``int` `n = arr.length;`   `        ``// Function Call` `        ``System.out.println(findGCD(arr, n));` `    ``}` `}`

## C#

 `// C# program for ` `// the above approach` `using` `System;` `class` `GFG{`   `// Function that finds gcd ` `// of 2 strings` `static` `String gcd(String str1, ` `                  ``String str2)` `{` `  ``// If str1 length is less than` `  ``// that of str2 then recur` `  ``// with gcd(str2, str1)` `  ``if` `(str1.Length < str2.Length) ` `  ``{` `    ``return` `gcd(str2, str1);` `  ``}`   `  ``// If str1 is not the` `  ``// concatenation of str2` `  ``else` `if` `(!str1.StartsWith(str2)) ` `  ``{` `    ``return` `""``;` `  ``}` `  ``else` `if` `(str2.Length == 0) ` `  ``{` `    ``// GCD string is found` `    ``return` `str1;` `  ``}` `  ``else` `  ``{` `    ``// Cut off the common prefix` `    ``// part of str1 & then recur` `    ``return` `gcd(str1.Substring(str2.Length),` `                              ``str2);` `  ``}` `}`   `// Function to find GCD ` `// of array of strings` `static` `String findGCD(String []arr, ` `                      ``int` `n)` `{` `  ``String result = arr;`   `  ``for` `(``int` `i = 1; i < n; i++) ` `  ``{` `    ``result = gcd(result, arr[i]);` `  ``}`   `  ``// Return the GCD of strings` `  ``return` `result;` `}`   `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` `  ``// Given array  of strings` `  ``String []arr = ``new` `String[] {``"GFGGFG"``,` `                               ``"GFGGFG"``,` `                               ``"GFGGFGGFGGFG"``};` `  ``int` `n = arr.Length;`   `  ``// Function Call` `  ``Console.WriteLine(findGCD(arr, n));` `}` `}`   `// This code is contributed by shikhasingrajput`

Output:

```GFGGFG

```

Time Complexity: O(N*log(B)), where N is the number of strings, and B is the maximum length of any string in arr[].
Auxiliary Space: O(1)

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Improved By : shikhasingrajput