# 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++ 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 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 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# 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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