# Longest sub-array with maximum GCD

• Difficulty Level : Easy
• Last Updated : 24 Feb, 2022

Given an array arr[] of length N, the task is the find the length of the longest sub-array with the maximum possible GCD value.

Examples:

Input: arr[] = {1, 2, 2}
Output:
Here all possible sub-arrays and there GCD’s are:
1) {1} -> 1
2) {2} -> 2
3) {2} -> 2
4) {1, 2} -> 1
5) {2, 2} -> 2
6) {1, 2, 3} -> 1
Here, the maximum GCD value is 2 and longest sub-array having GCD = 2 is {2, 2}.
Thus, the answer is {2, 2}.

Input: arr[] = {3, 3, 3, 3}
Output:

Naive approach: Generate all the possible sub-arrays and find the GCD of each of them individually in order to find the longest such sub-array. This approach will take O(N3) time to solve the problem.

Better approach: The maximum GCD value will always be equal to the largest number present in the array. Let’s say that the largest number present in the array is X. Now, the task is to find the largest sub-array having all X. The same can be done using the two-pointer approach. Below is the algorithm:

• Find the largest number in the array. Let us call this number X.
• Run a loop from i = 0
• If arr[i] != X then increment i and continue.
• Else initialize j = i.
• While j < n and arr[j] = X, increment j.
• Update the answer as ans = max(ans, j – i).
• Update i as i = j.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;` `// Function to return the length of``// the largest subarray with``// maximum possible GCD``int` `findLength(``int``* arr, ``int` `n)``{``    ``// To store the maximum number``    ``// present in the array``    ``int` `x = 0;` `    ``// Finding the maximum element``    ``for` `(``int` `i = 0; i < n; i++)``        ``x = max(x, arr[i]);` `    ``// To store the final answer``    ``int` `ans = 0;` `    ``// Two pointer``    ``for` `(``int` `i = 0; i < n; i++) {` `        ``if` `(arr[i] != x)``            ``continue``;` `        ``// Running a loop from j = i``        ``int` `j = i;` `        ``// Condition for incrementing 'j'``        ``while` `(arr[j] == x)``            ``j++;` `        ``// Updating the answer``        ``ans = max(ans, j - i);``    ``}` `    ``return` `ans;``}` `// Driver code``int` `main()``{``    ``int` `arr[] = { 1, 2, 2 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``);` `    ``cout << findLength(arr, n);` `    ``return` `0;``}`

## Java

 `// Java implementation of the approach``class` `GFG``{` `    ``// Function to return the length of``    ``// the largest subarray with``    ``// maximum possible GCD``    ``static` `int` `findLength(``int` `[]arr, ``int` `n)``    ``{``        ``// To store the maximum number``        ``// present in the array``        ``int` `x = ``0``;``    ` `        ``// Finding the maximum element``        ``for` `(``int` `i = ``0``; i < n; i++)``            ``x = Math.max(x, arr[i]);``    ` `        ``// To store the final answer``        ``int` `ans = ``0``;``    ` `        ``// Two pointer``        ``for` `(``int` `i = ``0``; i < n; i++)``        ``{``            ``if` `(arr[i] != x)``                ``continue``;``    ` `            ``// Running a loop from j = i``            ``int` `j = i;``    ` `            ``// Condition for incrementing 'j'``            ``while` `(arr[j] == x)``            ``{``                ``j++;``                ``if` `(j >= n )``                ``break``;``            ``}``    ` `            ``// Updating the answer``            ``ans = Math.max(ans, j - i);``        ``}``        ``return` `ans;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main (String[] args)``    ``{``        ``int` `arr[] = { ``1``, ``2``, ``2` `};``        ``int` `n = arr.length;``    ` `        ``System.out.println(findLength(arr, n));``    ``}``}` `// This code is contributed by AnkitRai01`

## Python3

 `# Python3 implementation of the approach` `# Function to return the length of``# the largest subarray with``# maximum possible GCD``def` `findLength(arr, n) :` `    ``# To store the maximum number``    ``# present in the array``    ``x ``=` `0``;` `    ``# Finding the maximum element``    ``for` `i ``in` `range``(n) :``        ``x ``=` `max``(x, arr[i]);` `    ``# To store the final answer``    ``ans ``=` `0``;` `    ``# Two pointer``    ``for` `i ``in` `range``(n) :` `        ``if` `(arr[i] !``=` `x) :``            ``continue``;` `        ``# Running a loop from j = i``        ``j ``=` `i;` `        ``# Condition for incrementing 'j'``        ``while` `(arr[j] ``=``=` `x) :``            ``j ``+``=` `1``;``            ` `            ``if` `j >``=` `n :``                ``break` `        ``# Updating the answer``        ``ans ``=` `max``(ans, j ``-` `i);` `    ``return` `ans;` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:` `    ``arr ``=` `[ ``1``, ``2``, ``2` `];``    ``n ``=` `len``(arr);` `    ``print``(findLength(arr, n));``    ` `# This code is contributed by AnkitRai01`

## C#

 `// C# implementation of the approach``using` `System;` `class` `GFG``{` `    ``// Function to return the length of``    ``// the largest subarray with``    ``// maximum possible GCD``    ``static` `int` `findLength(``int` `[]arr, ``int` `n)``    ``{``        ``// To store the maximum number``        ``// present in the array``        ``int` `x = 0;``    ` `        ``// Finding the maximum element``        ``for` `(``int` `i = 0; i < n; i++)``            ``x = Math.Max(x, arr[i]);``    ` `        ``// To store the final answer``        ``int` `ans = 0;``    ` `        ``// Two pointer``        ``for` `(``int` `i = 0; i < n; i++)``        ``{``            ``if` `(arr[i] != x)``                ``continue``;``    ` `            ``// Running a loop from j = i``            ``int` `j = i;``    ` `            ``// Condition for incrementing 'j'``            ``while` `(arr[j] == x)``            ``{``                ``j++;``                ``if` `(j >= n )``                ``break``;``            ``}``    ` `            ``// Updating the answer``            ``ans = Math.Max(ans, j - i);``        ``}``        ``return` `ans;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main ()``    ``{``        ``int` `[]arr = { 1, 2, 2 };``        ``int` `n = arr.Length;``    ` `        ``Console.WriteLine(findLength(arr, n));``    ``}``}` `// This code is contributed by AnkitRai01`

## Javascript

 ``

Output:

`2`

Time Complexity: O(n)

Auxiliary Space: O(1)

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