# 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 difference

Input : mat[N][M] = {{1, 2, 3},
{4, 6, 7},
{9, 10, 5}}
Output : 9
Pair (10, 1) has the maximum difference.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 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

Output:

24

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Improved By : inderDuMCA, mohit kumar 29

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