# Pair with maximum difference in a Matrix

Given a NxM matrix with N rows and M columns of **positive integers**. The task is to find the pair with the maximum difference in the given matrix.**Note**: Pairs at positions (a, b) and (b, a) are considered equivalent.**Examples**:

Input: mat[N][M] = {{1, 2, 3, 4}, {25, 6, 7, 8}, {9, 10, 11, 12}, {13, 14, 15, 16}}Output: 24 Pair (25, 1) has the maximum differenceInput: mat[N][M] = {{1, 2, 3}, {4, 6, 7}, {9, 10, 5}}Output: 9 Pair (10, 1) has the maximum difference.

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. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**

In case you wish to attend **live classes **with experts, please refer **DSA Live Classes for Working Professionals **and **Competitive Programming Live for Students**.

The idea is to observe that the elements contributing to the pair with maximum difference are the maximum and minimum elements in the matrix. So, find the maximum and minimum elements in the matrix and return the difference between them.

Below is the implementation of the above approach:

## C++

`// C++ program to find with maximum` `// difference in a matrix` `#include <bits/stdc++.h>` `using` `namespace` `std;` `#define N 4 // Rows` `#define M 4 // Columns` `// Function to find pair with maximum` `// difference in a matrix` `int` `maxDifferencePair(` `int` `mat[N][M])` `{` ` ` `int` `maxElement = INT_MIN; ` `// max` ` ` `int` `minElement = INT_MAX; ` `// min` ` ` `// Traverse the matrix` ` ` `for` `(` `int` `i = 0; i < N; i++) {` ` ` `for` `(` `int` `j = 0; j < M; j++) {` ` ` `// Find max element` ` ` `if` `(mat[i][j] > maxElement) {` ` ` `maxElement = mat[i][j];` ` ` `}` ` ` `// Find min element` ` ` `if` `(mat[i][j] < minElement) {` ` ` `minElement = mat[i][j];` ` ` `}` ` ` `}` ` ` `}` ` ` `return` `abs` `(maxElement - minElement);` `}` `// Driver Code` `int` `main()` `{` ` ` `// matrix` ` ` `int` `mat[N][M] = { { 1, 2, 3, 4 },` ` ` `{ 25, 6, 7, 8 },` ` ` `{ 9, 10, 11, 12 },` ` ` `{ 13, 14, 15, 16 } };` ` ` `cout << maxDifferencePair(mat) << endl;` ` ` `return` `0;` `}` |

## Java

`// Java program to find with maximum` `// difference in a matrix` `import` `java.io.*;` `class` `GFG {` ` ` `static` `int` `N= ` `4` `; ` `// Rows` `static` `int` `M = ` `4` `; ` `// Columns` `// Function to find pair with maximum` `// difference in a matrix` `static` `int` `maxDifferencePair(` `int` `mat[][])` `{` ` ` `int` `maxElement = Integer.MIN_VALUE; ` `// max` ` ` `int` `minElement = Integer.MAX_VALUE; ` `// min` ` ` `// Traverse the matrix` ` ` `for` `(` `int` `i = ` `0` `; i < N; i++) {` ` ` `for` `(` `int` `j = ` `0` `; j < M; j++) {` ` ` `// Find max element` ` ` `if` `(mat[i][j] > maxElement) {` ` ` `maxElement = mat[i][j];` ` ` `}` ` ` `// Find min element` ` ` `if` `(mat[i][j] < minElement) {` ` ` `minElement = mat[i][j];` ` ` `}` ` ` `}` ` ` `}` ` ` `return` `Math.abs(maxElement - minElement);` `}` `// Driver Code` ` ` `public` `static` `void` `main (String[] args) {` ` ` `// matrix` ` ` `int` `mat[][] = { { ` `1` `, ` `2` `, ` `3` `, ` `4` `},` ` ` `{ ` `25` `, ` `6` `, ` `7` `, ` `8` `},` ` ` `{ ` `9` `, ` `10` `, ` `11` `, ` `12` `},` ` ` `{ ` `13` `, ` `14` `, ` `15` `, ` `16` `} };` ` ` `System.out.println( maxDifferencePair(mat));` ` ` `}` `}` `// This code is contributed by inder_verma..` |

## Python3

`# Python3 program to find with maximum` `# difference in a matrix` `N ` `=` `4` `# Rows` `M ` `=` `4` `# Columns` `# Function to find pair with maximum` `# difference in a matrix` `def` `maxDifferencePair(mat):` ` ` `maxElement ` `=` `-` `10` `*` `*` `9` `# max` ` ` `minElement ` `=` `10` `*` `*` `9` `# min` ` ` `# Traverse the matrix` ` ` `for` `i ` `in` `range` `(N):` ` ` `for` `j ` `in` `range` `(M):` ` ` ` ` `# Find max element` ` ` `if` `(mat[i][j] > maxElement):` ` ` `maxElement ` `=` `mat[i][j]` ` ` `# Find min element` ` ` `if` `(mat[i][j] < minElement):` ` ` `minElement ` `=` `mat[i][j]` ` ` `return` `abs` `(maxElement ` `-` `minElement)` `# Driver Code` `# matrix` `mat ` `=` `[[ ` `1` `, ` `2` `, ` `3` `, ` `4` `],` ` ` `[ ` `25` `, ` `6` `, ` `7` `, ` `8` `],` ` ` `[ ` `9` `, ` `10` `, ` `11` `, ` `12` `],` ` ` `[ ` `13` `, ` `14` `, ` `15` `, ` `16` `]]` `print` `(maxDifferencePair(mat))` `# This code is contributed` `# by mohit kumar` |

## C#

`// C# program to find with maximum` `// difference in a matrix` `using` `System;` `class` `GFG` `{` `static` `int` `N = 4; ` `// Rows` `static` `int` `M = 4; ` `// Columns` `// Function to find pair with` `// maximum difference in a matrix` `static` `int` `maxDifferencePair(` `int` `[,]mat)` `{` ` ` `int` `maxElement = ` `int` `.MinValue; ` `// max` ` ` `int` `minElement = ` `int` `.MaxValue; ` `// min` ` ` `// Traverse the matrix` ` ` `for` `(` `int` `i = 0; i < N; i++)` ` ` `{` ` ` `for` `(` `int` `j = 0; j < M; j++)` ` ` `{` ` ` `// Find max element` ` ` `if` `(mat[i, j] > maxElement)` ` ` `{` ` ` `maxElement = mat[i, j];` ` ` `}` ` ` `// Find min element` ` ` `if` `(mat[i, j] < minElement)` ` ` `{` ` ` `minElement = mat[i, j];` ` ` `}` ` ` `}` ` ` `}` ` ` `return` `Math.Abs(maxElement -` ` ` `minElement);` `}` `// Driver Code` `public` `static` `void` `Main ()` `{` ` ` `// matrix` ` ` `int` `[,]mat = {{ 1, 2, 3, 4 },` ` ` `{ 25, 6, 7, 8 },` ` ` `{ 9, 10, 11, 12 },` ` ` `{ 13, 14, 15, 16 }};` ` ` ` ` `Console.WriteLine( maxDifferencePair(mat));` `}` `}` `// This code is contributed` `// by inder_verma` |

## Javascript

`<script>` `// JavaScript program to find with maximum` `// difference in a matrix` `let N= 4; ` `// Rows` `let M = 4; ` `// Columns` `// Function to find pair with maximum` `// difference in a matrix` `function` `maxDifferencePair(mat)` `{` ` ` `let maxElement = Number.MIN_VALUE; ` `// max` ` ` `let minElement = Number.MAX_VALUE; ` `// min` ` ` ` ` `// Traverse the matrix` ` ` `for` `(let i = 0; i < N; i++) {` ` ` `for` `(let j = 0; j < M; j++) {` ` ` `// Find max element` ` ` `if` `(mat[i][j] > maxElement) {` ` ` `maxElement = mat[i][j];` ` ` `}` ` ` ` ` `// Find min element` ` ` `if` `(mat[i][j] < minElement) {` ` ` `minElement = mat[i][j];` ` ` `}` ` ` `}` ` ` `}` ` ` ` ` `return` `Math.abs(maxElement - minElement);` `}` `// Driver Code` `let mat = [[ 1, 2, 3, 4 ],` ` ` `[ 25, 6, 7, 8 ],` ` ` `[ 9, 10, 11, 12 ],` ` ` `[ 13, 14, 15, 16]];` ` ` `document.write( maxDifferencePair(mat));` `// This code is contributed by unknown2108` `</script>` |

**Output:**

24