# Find pair with maximum difference in any column of a Matrix

Given a N*N matrix of positive integers. The task is to find the maximum difference between any pair of elements in any column of the matrix.

Examples:

```Input : mat[N][N] = {
{ 1, 2, 3, 4, 5 },
{ 5, 3, 5, 4, 0 },
{ 5, 6, 7, 8, 9 },
{ 0, 6, 3, 4, 12 },
{ 9, 7, 12, 4, 3 },
};
Output : Max difference : 12
5th column has the pair with max difference
(0, 12)

Input : mat[N][N] = {
{ 1, 2, 3 },
{ 5, 3, 5 },
{ 9, 6, 7 }
};
Output : Max difference : 8
```

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

The idea is to observe that the pair with maximum difference in any column is the difference between the maximum and minimum element of that column. Now traverse the matrix column wise. Find the difference between the max and min element of every column and return the maximum difference.

Below is the implementation of the above approach:

## C++

 `// C++ program to find column with ` `// max difference of any pair of elements ` `#include ` `using` `namespace` `std; ` ` `  `#define N 5 // No of rows and column ` ` `  `// Function to find the column with max difference ` `int` `colMaxDiff(``int` `mat[N][N]) ` `{ ` `    ``int` `max_diff = INT_MIN; ` ` `  `    ``// Traverse matrix column wise ` `    ``for` `(``int` `i = 0; i < N; i++) { ` ` `  `        ``// Insert elements of column to vector ` `        ``int` `max_val = mat[0][i], min_val = mat[0][i]; ` `        ``for` `(``int` `j = 1; j < N; j++) { ` `            ``max_val = max(max_val, mat[j][i]); ` `            ``min_val = min(min_val, mat[j][i]); ` `        ``} ` ` `  `        ``// calculating difference between maximum and ` `        ``// minimum ` `        ``max_diff = max(max_diff, max_val - min_val); ` `    ``} ` ` `  `    ``return` `max_diff; ` `} ` ` `  `// driver code ` `int` `main() ` `{ ` `    ``int` `mat[N][N] = { ` `        ``{ 1, 2, 3, 4, 5 }, ` `        ``{ 5, 3, 5, 4, 0 }, ` `        ``{ 5, 6, 7, 8, 9 }, ` `        ``{ 0, 6, 3, 4, 12 }, ` `        ``{ 9, 7, 12, 4, 3 }, ` `    ``}; ` ` `  `    ``cout << ``"Max difference : "` `<< colMaxDiff(mat) << endl; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find column with  ` `// max difference of any pair of elements  ` ` `  `public` `class` `GOC1 { ` ` `  `    ``static` `int` `N = ``5``; ``// No of rows and column  ` ` `  `    ``// Function to find the column with max difference ` `    ``static` `int` `colMaxDiff(``int` `mat[][]) { ` `        ``int` `max_diff = Integer.MIN_VALUE; ` ` `  `        ``// Traverse matrix column wise ` `        ``for` `(``int` `i = ``0``; i < N; i++) { ` ` `  `            ``// Insert elements of column to vector ` `            ``int` `max_val = mat[``0``][i], min_val = mat[``0``][i]; ` `            ``for` `(``int` `j = ``1``; j < N; j++) { ` `                ``max_val = Math.max(max_val, mat[j][i]); ` `                ``min_val = Math.min(min_val, mat[j][i]); ` `            ``} ` ` `  `            ``// calculating difference between maximum and ` `            ``// minimum ` `            ``max_diff = Math.max(max_diff, max_val - min_val); ` `        ``} ` ` `  `        ``return` `max_diff; ` `    ``} ` ` `  `    ``// Driver Code ` `    ``public` `static` `void` `main(String args[]) { ` `        ``int` `mat[][] = {  ` `                ``{ ``1``, ``2``, ``3``, ``4``, ``5` `},  ` `                ``{ ``5``, ``3``, ``5``, ``4``, ``0` `},  ` `                ``{ ``5``, ``6``, ``7``, ``8``, ``9` `},  ` `                ``{ ``0``, ``6``, ``3``, ``4``, ``12` `},  ` `                ``{ ``9``, ``7``, ``12``, ``4``, ``3` `},  ` `            ``};  ` `           `  `        ``System.out.println(``"Max difference : "``+colMaxDiff(mat)); ` `    ``} ` `} `

## Python3

 `# Python3 program to find column with ` `# max difference of any pair of elements ` ` `  `N ``=` `5` `# No of rows and column ` ` `  `# Function to find the column  ` `# with max difference ` `def` `colMaxDiff(mat): ` ` `  `    ``max_diff ``=` `0` ` `  `    ``# Traverse matrix column wise ` `    ``for` `i ``in` `range` `(N): ` ` `  `        ``# Insert elements of column  ` `        ``# to vector ` `        ``max_val ``=` `mat[``0``][i] ` `        ``min_val ``=` `mat[``0``][i] ` `        ``for` `j ``in` `range` `(``1``, N) : ` `            ``max_val ``=` `max``(max_val, mat[j][i]) ` `            ``min_val ``=` `min``(min_val, mat[j][i]) ` ` `  `        ``# calculating difference between  ` `        ``# maximum and minimum ` `        ``max_diff ``=` `max``(max_diff, max_val ``-`  `                                 ``min_val) ` ` `  `    ``return` `max_diff ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``: ` `    ``mat ``=` `[[ ``1``, ``2``, ``3``, ``4``, ``5` `], ` `           ``[``5``, ``3``, ``5``, ``4``, ``0` `], ` `           ``[ ``5``, ``6``, ``7``, ``8``, ``9` `], ` `           ``[ ``0``, ``6``, ``3``, ``4``, ``12` `], ` `           ``[ ``9``, ``7``, ``12``, ``4``, ``3` `]] ` ` `  `    ``print` `(``"Max difference :"``, colMaxDiff(mat)) ` ` `  `# This code is contributed by ita_c `

## C#

 `// C# program to find column   ` `// with max difference of  ` `// any pair of elements  ` `using` `System; ` ` `  `class` `GFG  ` `{ ` ` `  `static` `int` `N = 5; ``// No of rows and column  ` ` `  `// Function to find the column ` `// with max difference ` `static` `int` `colMaxDiff(``int` `[,]mat)  ` `{ ` `    ``int` `max_diff = ``int``.MinValue; ` ` `  `    ``// Traverse matrix column wise ` `    ``for` `(``int` `i = 0; i < N; i++) ` `    ``{ ` ` `  `        ``// Insert elements of column ` `        ``// to vector ` `        ``int` `max_val = mat[0, i],  ` `            ``min_val = mat[0, i]; ` `        ``for` `(``int` `j = 1; j < N; j++)  ` `        ``{ ` `            ``max_val = Math.Max(max_val,  ` `                               ``mat[j, i]); ` `            ``min_val = Math.Min(min_val,  ` `                               ``mat[j, i]); ` `        ``} ` ` `  `        ``// calculating difference between ` `        ``// maximum and minimum ` `        ``max_diff = Math.Max(max_diff,  ` `                            ``max_val - min_val); ` `    ``} ` ` `  `    ``return` `max_diff; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main()  ` `{ ` `    ``int` `[,]mat = { { 1, 2, 3, 4, 5 },  ` `                   ``{ 5, 3, 5, 4, 0 },  ` `                   ``{ 5, 6, 7, 8, 9 },  ` `                   ``{ 0, 6, 3, 4, 12 },  ` `                   ``{ 9, 7, 12, 4, 3 }};  ` `         `  `    ``Console.WriteLine(``"Max difference : "` `+  ` `                          ``colMaxDiff(mat)); ` `} ` `} ` ` `  `// This code is contributed ` `// by Subhadeep `

## PHP

 `

Output:

```Max difference : 12
```

Time Complexity: O(n^2)

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