# GCD of all subarrays of size K

Given an array, arr[] of size N, the task is to print the GCD of all subarrays of size K.

Examples:

Input: arr[] = {2, 4, 3, 9, 14, 20, 25, 17}, K = 2
Output: 2 1 3 1 2 5 1
Explanation:
gcd(2, 4}) = 2
gcd(4, 3) = 1
gcd(3, 9) = 3
gcd(9, 14) = 1
gcd(14, 20) = 2
gcd(20, 25) = 5
gcd(25, 17) = 1
Therefore, the required output is {2, 1, 3, 1, 2, 5, 1}

Input: arr[] = {2, 4, 8, 24, 14, 20, 25, 35, 7, 49, 7}, K = 3
Output: 2 4 2 2 1 5 1 7 7

Approach: The idea is to generate all subarrays of size K and print the GCD of each subarray. To efficiently compute the GCD of each subarray, the idea is to use the following property of GCD.

GCD(A1, A2, A3, …, AK) = GCD(A1, GCD(A2, A3, A4, …., AK))

Follow the steps below to solve the problem:

1. Initialize a variable, say gcd, to store the GCD of the current subarray.
2. Generate K-length subarrays from the given array.
3. Applying the above property of GCD, compute the GCD of each subarray, and print the obtained result.

Below is the implementation of the above approach:

## C++

 `// C++ program to implement` `// the above approach`   `#include ` `using` `namespace` `std;`   `// Function to print the gcd` `// of each subarray of length K` `void` `printSub(``int` `arr[], ``int` `N,` `              ``int` `K)` `{` `    ``for` `(``int` `i = 0; i <= N - K; i++) {`   `        ``// Store GCD of subarray` `        ``int` `gcd = arr[i];`   `        ``for` `(``int` `j = i + 1; j < i + K;` `             ``j++) {`   `            ``// Update GCD of subarray` `            ``gcd = __gcd(gcd, arr[j]);` `        ``}`   `        ``// Print GCD of subarray` `        ``cout << gcd << ``" "``;` `    ``}` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `arr[] = { 2, 4, 3, 9, 14,` `                  ``20, 25, 17 };` `    ``int` `K = 2;` `    ``int` `N = ``sizeof``(arr)` `            ``/ ``sizeof``(arr);`   `    ``printSub(arr, N, K);` `}`

## Java

 `// Java program to implement` `// the above approach` `class` `GFG{`   `static` `int` `__gcd(``int` `a, ``int` `b)` `{` `  ``if` `(b == ``0``)` `    ``return` `a;` `  ``return` `__gcd(b, a % b);` `}` `  `  `// Function to print the gcd` `// of each subarray of length K` `static` `void` `printSub(``int` `arr[], ` `                     ``int` `N, ``int` `K)` `{` `  ``for` `(``int` `i = ``0``; i <= N - K; i++) ` `  ``{` `    ``// Store GCD of subarray` `    ``int` `gcd = arr[i];`   `    ``for` `(``int` `j = i + ``1``; j < i + K; j++) ` `    ``{` `      ``// Update GCD of subarray` `      ``gcd = __gcd(gcd, arr[j]);` `    ``}`   `    ``// Print GCD of subarray` `    ``System.out.print(gcd + ``" "``);` `  ``}` `}`   `// Driver Code` `public` `static` `void` `main(String[] args)` `{` `  ``int` `arr[] = {``2``, ``4``, ``3``, ``9``, ` `               ``14``, ``20``, ``25``, ``17``};` `  ``int` `K = ``2``;` `  ``int` `N = arr.length;` `  ``printSub(arr, N, K);` `}` `}`   `// This code is contributed by Chitranayal`

## Python3

 `# Python3 program to implement` `# the above approach` `from` `math ``import` `gcd`   `# Function to prthe gcd` `# of each subarray of length K` `def` `printSub(arr, N, K):` `    `  `    ``for` `i ``in` `range``(N ``-` `K ``+` `1``):`   `        ``# Store GCD of subarray` `        ``g ``=` `arr[i]`   `        ``for` `j ``in` `range``(i ``+` `1``, i ``+` `K):` `            `  `            ``# Update GCD of subarray` `            ``g ``=` `gcd(g, arr[j])`   `        ``# Print GCD of subarray` `        ``print``(g, end ``=` `" "``)`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `    `  `    ``arr ``=` `[ ``2``, ``4``, ``3``, ``9``, ``14``,` `            ``20``, ``25``, ``17` `]` `    ``K ``=` `2` `    ``N ``=` `len``(arr)`   `    ``printSub(arr, N, K)`   `# This code is contributed by mohit kumar 29`

## C#

 `// C# program to implement` `// the above approach` `using` `System;` `class` `GFG{`   `static` `int` `__gcd(``int` `a, ``int` `b)` `{` `  ``if` `(b == 0)` `    ``return` `a;` `  ``return` `__gcd(b, a % b);` `}` `  `  `// Function to print the gcd` `// of each subarray of length K` `static` `void` `printSub(``int` `[]arr, ` `                     ``int` `N, ``int` `K)` `{` `  ``for` `(``int` `i = 0; i <= N - K; i++) ` `  ``{` `    ``// Store GCD of subarray` `    ``int` `gcd = arr[i];`   `    ``for` `(``int` `j = i + 1; j < i + K; j++) ` `    ``{` `      ``// Update GCD of subarray` `      ``gcd = __gcd(gcd, arr[j]);` `    ``}`   `    ``// Print GCD of subarray` `    ``Console.Write(gcd + ``" "``);` `  ``}` `}`   `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` `  ``int` `[]arr = {2, 4, 3, 9, ` `               ``14, 20, 25, 17};` `  ``int` `K = 2;` `  ``int` `N = arr.Length;` `  ``printSub(arr, N, K);` `}` `}`     `// This code is contributed by Princi Singh`

Output:

```2 1 3 1 2 5 1

```

Time Complexity: O((N – K + 1) * K)
Auxiliary Space: O(1)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Article Tags :
Practice Tags :

1

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.