# Largest gap in an array

Last Updated : 25 Apr, 2023

Given an unsorted array of length N, and we have to find the largest gap between any two elements of the array. In simple words, find max(|Ai-Aj|) where 1 ? i ? N and 1 ? j ? N.

Examples:

```Input : arr = {3, 10, 6, 7}
Output : 7
Explanation :
Here, we can see largest gap can be
found between 3 and 10 which is 7

Input : arr = {-3, -1, 6, 7, 0}
Output : 10
Explanation :
Here, we can see largest gap can be
found between -3 and 7 which is 10 ```

Simple Approach:

A simple solution is, we can use a naive approach. We will check the absolute difference of every pair in the array, and we will find the maximum value of it. So we will run two loops one is for i and one is for j complexity of this method is O(N^2)

Implementation:

## C++

 `// A C++ program to find largest gap ` `// between two elements in an array.` `#include` `using` `namespace` `std;`   `// function to solve the given problem` `int` `solve(``int` `a[], ``int` `n)` `{` `    ``int` `max1 = INT_MIN;` `    ``for` `(``int` `i = 0; i < n; i++) ` `    ``{` `        ``for` `(``int` `j = 0; j < n; j++) ` `        ``{` `            ``if` `(``abs``(a[i] - a[j]) > max1) ` `            ``{` `                ``max1 = ``abs``(a[i] - a[j]);` `            ``}` `        ``}` `    ``}` `    ``return` `max1;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `arr[] = { -1, 2, 3, -4, -10, 22 };` `    ``int` `size = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``cout << ``"Largest gap is : "` `         ``<< solve(arr, size);` `    ``return` `0;` `}`   `// This code is contributed ` `// by Akanksha Rai`

## C

 `// A C program to find largest gap ` `// between two elements in an array.` `#include ` `#include ` `#include `   `// function to solve the given problem` `int` `solve(``int` `a[], ``int` `n)` `{` `    ``int` `max1 = INT_MIN;` `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``for` `(``int` `j = 0; j < n; j++) {` `            ``if` `(``abs``(a[i] - a[j]) > max1) {` `                ``max1 = ``abs``(a[i] - a[j]);` `            ``}` `        ``}` `    ``}` `    ``return` `max1;` `}`   `int` `main()` `{` `    ``int` `arr[] = { -1, 2, 3, -4, -10, 22 };` `    ``int` `size = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``printf``(``"Largest gap is : %d"``, solve(arr, size));` `    ``return` `0;` `}`

## Java

 `// A Java program to find ` `// largest gap between ` `// two elements in an array.` `import` `java .io.*;`   `class` `GFG` `{`   `// function to solve` `// the given problem` `static` `int` `solve(``int` `[]a,` `                 ``int` `n)` `{` `    ``int` `max1 = Integer.MIN_VALUE ;` `    ``for` `(``int` `i = ``0``; i < n; i++) ` `    ``{` `        ``for` `(``int` `j = ``0``; j < n; j++) ` `        ``{` `            ``if` `(Math.abs(a[i] - ` `                         ``a[j]) > max1) ` `            ``{` `                ``max1 = Math.abs(a[i] - ` `                                ``a[j]);` `            ``}` `        ``}` `    ``}` `    ``return` `max1;` `}`   `// Driver Code` `static` `public` `void` `main (String[] args)` `{` `    ``int` `[]arr = {-``1``, ``2``, ``3``, ` `                 ``-``4``, -``10``, ``22``};` `    ``int` `size = arr.length;` `    ``System.out.println(``"Largest gap is : "` `+` `                        ``solve(arr, size));` `}` `}`   `// This code is contributed` `// by anuj_67.`

## Python3

 `# A Python 3 program to find largest gap ` `# between two elements in an array.` `import` `sys`   `# function to solve the given problem` `def` `solve(a, n):` `    ``max1 ``=` `-``sys.maxsize ``-` `1` `    ``for` `i ``in` `range``(``0``, n, ``1``):` `        ``for` `j ``in` `range``(``0``, n, ``1``):` `            ``if` `(``abs``(a[i] ``-` `a[j]) > max1):` `                ``max1 ``=` `abs``(a[i] ``-` `a[j])`   `    ``return` `max1`   `# Driver Code` `if` `__name__ ``=``=` `'__main__'``:` `    ``arr ``=` `[``-``1``, ``2``, ``3``, ``-``4``, ``-``10``, ``22``]` `    ``size ``=` `len``(arr)` `    ``print``(``"Largest gap is :"``, solve(arr, size))`   `# This code is contributed by` `# Sanjit_Prasad`

## C#

 `// A C# program to find ` `// largest gap between ` `// two elements in an array.` `using` `System;`   `class` `GFG` `{`   `// function to solve` `// the given problem` `static` `int` `solve(``int` `[]a,` `                 ``int` `n)` `{` `    ``int` `max1 = ``int``.MinValue ;` `    ``for` `(``int` `i = 0; i < n; i++) ` `    ``{` `        ``for` `(``int` `j = 0; j < n; j++) ` `        ``{` `            ``if` `(Math.Abs(a[i] - ` `                         ``a[j]) > max1) ` `            ``{` `                ``max1 = Math.Abs(a[i] - ` `                                ``a[j]);` `            ``}` `        ``}` `    ``}` `    ``return` `max1;` `}`   `// Driver Code` `static` `public` `void` `Main ()` `{` `    ``int` `[]arr = {-1, 2, 3, ` `                 ``-4, -10, 22};` `    ``int` `size = arr.Length;` `    ``Console.WriteLine(``"Largest gap is : "` `+` `                         ``solve(arr, size));` `}` `}`   `// This code is contributed` `// by anuj_67.`

## PHP

 ` ``\$max1``)` `            ``{` `                ``\$max1` `= ``abs``(``\$a``[``\$i``] - ` `                            ``\$a``[``\$j``]);` `            ``}` `        ``}` `    ``}` `    ``return` `\$max1``;` `}`   `// Driver Code` `\$arr` `= ``array``(-1, 2, 3, ` `             ``-4, -10, 22);` `\$size` `= ``count``(``\$arr``);` `echo` `"Largest gap is : "``, ` `      ``solve(``\$arr``, ``\$size``);`   `// This code is contributed` `// by anuj_67.` `?>`

## Javascript

 ``

Output

`Largest gap is : 32`

Time Complexity: O(N2)
Space  Complexity: O(1)

Better Approach:

Now we will see a better approach it is a greedy approach that can solve this problem in O(N). We will find the maximum and minimum element of the array which can be done in O(N) and then we will return the value of (maximum-minimum).

Implementation:

## C++

 `// A C++ program to find largest gap between ` `// two elements in an array.` `#include` `using` `namespace` `std;`   `// function to solve the given problem` `int` `solve(``int` `a[], ``int` `n)` `{` `    ``int` `min1 = a[0];` `    ``int` `max1 = a[0];`   `    ``// finding maximum and minimum of an array` `    ``for` `(``int` `i = 0; i < n; i++)` `    ``{` `        ``if` `(a[i] > max1)` `            ``max1 = a[i];` `        ``if` `(a[i] < min1)` `            ``min1 = a[i];` `    ``}` `    ``return` `abs``(min1 - max1);` `}`   `// Driver code` `int` `main()` `{` `    ``int` `arr[] = { -1, 2, 3, 4, -10 };` `    ``int` `size = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``cout << ``"Largest gap is : "` `<< solve(arr, size);` `    ``return` `0;` `}`   `//This code is contributed by Mukul Singh.`

## C

 `// A C program to find largest gap between ` `// two elements in an array.` `#include ` `#include ` `#include `   `// function to solve the given problem` `int` `solve(``int` `a[], ``int` `n)` `{` `    ``int` `min1 = a[0];` `    ``int` `max1 = a[0];`   `    ``// finding maximum and minimum of an array` `    ``for` `(``int` `i = 0; i < n; i++) {` `        ``if` `(a[i] > max1)` `            ``max1 = a[i];` `        ``if` `(a[i] < min1)` `            ``min1 = a[i];` `    ``}` `    `  `    ``return` `abs``(min1 - max1);` `}`   `int` `main()` `{` `    ``int` `arr[] = { -1, 2, 3, 4, -10 };` `    ``int` `size = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``printf``(``"Largest gap is : %d"``, solve(arr, size));` `    ``return` `0;` `}`

## Java

 `// A Java program to find largest gap` `// between two elements in an array.` `import` `java.io.*;`   `class` `GFG {`   `    ``// function to solve the given` `    ``// problem` `    ``static` `int` `solve(``int` `a[], ``int` `n)` `    ``{` `        ``int` `min1 = a[``0``];` `        ``int` `max1 = a[``0``];` `    `  `        ``// finding maximum and minimum ` `        ``// of an array` `        ``for` `(``int` `i = ``0``; i < n; i++) ` `        ``{` `            ``if` `(a[i] > max1)` `                ``max1 = a[i];` `            ``if` `(a[i] < min1)` `                ``min1 = a[i];` `        ``}` `        `  `        ``return` `Math.abs(min1 - max1);` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main (String[] args)` `    ``{` `        ``int` `[]arr = { -``1``, ``2``, ``3``, ``4``, -``10` `};` `        ``int` `size = arr.length;` `        ``System.out.println(``"Largest gap is : "` `                         ``+ solve(arr, size));` `    ``}` `}`   `// This code is contributed by anuj_67.`

## Python3

 `# A python 3 program to find largest gap between ` `# two elements in an array.` ` `  `# function to solve the given problem` `def` `solve(a,  n):`   `    ``min1 ``=` `a[``0``]` `    ``max1 ``=` `a[``0``]` ` `  `    ``# finding maximum and minimum of an array` `    ``for` `i ``in` `range` `( n):` `    `  `        ``if` `(a[i] > max1):` `            ``max1 ``=` `a[i]` `        ``if` `(a[i] < min1):` `            ``min1 ``=` `a[i]` `    `  `    ``return` `abs``(min1 ``-` `max1)`   `# Driver code` `if` `__name__ ``=``=` `"__main__"``:`   `    ``arr ``=` `[ ``-``1``, ``2``, ``3``, ``4``, ``-``10` `]` `    ``size ``=` `len``(arr)` `    ``print``(``"Largest gap is : "` `,solve(arr, size))`   `# This code is contributed by chitranayal  `

## C#

 `// A C# program to find ` `// largest gap between ` `// two elements in an array.` `using` `System;`   `class` `GFG ` `{`   `    ``// function to solve ` `    ``// the given problem` `    ``static` `int` `solve(``int` `[]a, ` `                     ``int` `n)` `    ``{` `        ``int` `min1 = a[0];` `        ``int` `max1 = a[0];` `    `  `        ``// finding maximum and ` `        ``// minimum of an array` `        ``for` `(``int` `i = 0; i < n; i++) ` `        ``{` `            ``if` `(a[i] > max1)` `                ``max1 = a[i];` `            ``if` `(a[i] < min1)` `                ``min1 = a[i];` `        ``}` `        `  `        ``return` `Math.Abs(min1 - ` `                        ``max1);` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main ()` `    ``{` `        ``int` `[]arr = {-1, 2, 3, 4, -10};` `        ``int` `size = arr.Length;` `        ``Console.WriteLine(``"Largest gap is : "` `+ ` `                             ``solve(arr, size));` `    ``}` `}`   `// This code is contributed` `// by anuj_67.`

## PHP

 ` ``\$max1``)` `            ``\$max1` `= ``\$a``[``\$i``];` `        ``if` `(``\$a``[``\$i``] < ``\$min1``)` `            ``\$min1` `= ``\$a``[``\$i``];` `    ``}` `    `  `    ``return` `abs``(``\$min1` `- ``\$max1``);` `}`   `// Driver Code` `\$arr` `= ``array``(-1, 2, 3, 4, -10);` `\$size` `= ``count``(``\$arr``);` `echo` `"Largest gap is : "``, ` `      ``solve(``\$arr``, ``\$size``);`   `// This code is contributed` `// by anuj_67.` `?>`

## Javascript

 ``

Output

`Largest gap is : 14`

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