# Pair with maximum sum in a Matrix

Given a NxM matrix with N rows and M columns of positive integers. The task is to find the sum of pair with maximum sum in the matrix.

Examples:

```Input : mat[N][M] = {{1, 2, 3, 4},
{25, 6, 7, 8},
{9, 10, 11, 12},
{13, 14, 15, 16}}
Output : 41
Pair (25, 16) has the maximum sum

Input : mat[N][M] = {{1, 2, 3},
{4, 6, 7},
{9, 10, 5}}
Output : 19
```

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

Simple Approach: A simple approach is to traverse the matrix twice and find the first maximum and second maximum elements and return their sum.

Better Approach: A better approach is to find the first and second maximum in a single traversal of the matrix.

```1) Initialize two variables first and second to INT_MIN as,
first = second = INT_MIN
2) Start traversing the matrix,
a) If the current element in array say mat[i][j] is greater
than first. Then update first and second as,
second = first
first = mat[i][j]
b) If the current element is in between first and second,
then update second to store the value of current variable as
second = mat[i][j]
3) Return sum of both first and second maximum.
```

Below is the implementation of the above approach:

## C++

 `// C++ program to find maximum sum ` `// pair in a matrix ` ` `  `#include ` `using` `namespace` `std; ` ` `  `#define N 4 // Rows ` `#define M 4 // Columns ` ` `  `// Function to find maximum sum ` `// pair from matrix ` `int` `maxSumPair(``int` `mat[N][M]) ` `{ ` `    ``int` `max1 = INT_MIN; ``// First max ` `    ``int` `max2 = INT_MIN; ``// Second max ` ` `  `    ``// Traverse the matrix ` `    ``for` `(``int` `i = 0; i < N; i++) { ` `        ``for` `(``int` `j = 0; j < M; j++) { ` `            ``if` `(mat[i][j] > max1) { ` `                ``max2 = max1; ``// second max = first max ` `                ``max1 = mat[i][j]; ``// first max = current ` `            ``} ` `            ``// If second max is between current element ` `            ``// and first max ` `            ``else` `if` `(mat[i][j] > max2 && mat[i][j] <= max1) { ` `                ``max2 = mat[i][j]; ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``return` `max1 + max2; ` `} ` ` `  `// 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 << maxSumPair(mat) << endl; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find maximum sum ` `// pair in a matrix ` `import` `java.io.*; ` ` `  `class` `GFG { ` `    `  `static` `int`  `N = ``4``; ``// Rows ` `static` `int` `M = ``4``; ``// Columns ` ` `  `// Function to find maximum sum ` `// pair from matrix ` `static` `int` `maxSumPair(``int` `[][]mat) ` `{ ` `    ``int` `max1 = Integer.MIN_VALUE; ``// First max ` `    ``int` `max2 = Integer.MIN_VALUE; ``// Second max ` ` `  `    ``// Traverse the matrix ` `    ``for` `(``int` `i = ``0``; i < N; i++) { ` `        ``for` `(``int` `j = ``0``; j < M; j++) { ` `            ``if` `(mat[i][j] > max1) { ` `                ``max2 = max1; ``// second max = first max ` `                ``max1 = mat[i][j]; ``// first max = current ` `            ``} ` `            ``// If second max is between current element ` `            ``// and first max ` `            ``else` `if` `(mat[i][j] > max2 && mat[i][j] <= max1) { ` `                ``max2 = mat[i][j]; ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``return` `max1 + max2; ` `} ` ` `  `// 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(maxSumPair(mat)); ` `    ``} ` `} ` `// This code is contributed ` `// by shs `

## Python3

 `# Python 3 program to find maximum sum ` `# pair in a matrix ` `import` `sys ` ` `  `N ``=` `4` `# Rows ` `M ``=` `4` `# Columns ` ` `  `# Function to find maximum sum ` `# pair from matrix ` `def` `maxSumPair(mat): ` ` `  `    ``max1 ``=` `-``sys.maxsize ``-` `1` `# First max ` `    ``max2 ``=` `-``sys.maxsize ``-` `1` `# Second max ` ` `  `    ``# Traverse the matrix ` `    ``for` `i ``in` `range``(``0``, N):  ` `        ``for` `j ``in` `range` `(``0``, M):  ` `            ``if` `(mat[i][j] > max1):  ` `                ``max2 ``=` `max1 ``# second max = first max ` `                ``max1 ``=` `mat[i][j] ``# first max = current ` `             `  `            ``# If second max is between current  ` `            ``# element and first max ` `            ``elif` `(mat[i][j] > max2 ``and`  `                  ``mat[i][j] <``=` `max1):  ` `                ``max2 ``=` `mat[i][j] ` `             `  `    ``return` `max1 ``+` `max2 ` ` `  `# Driver Code ` ` `  `# matrix ` `mat ``=` `[ [``1``, ``2``, ``3``, ``4` `], ` `        ``[``25``, ``6``, ``7``, ``8` `], ` `        ``[``9``, ``10``, ``11``, ``12` `], ` `        ``[``13``, ``14``, ``15``, ``16` `]] ` ` `  `print``(maxSumPair(mat)) ` ` `  `# This code is contributed  ` `# by ihritik `

## C#

 `// C# program to find maximum sum ` `// pair in a matrix ` `using` `System;  ` `public` `class` `GFG { ` `     `  `static` `int`  `N = 4; ``// Rows ` `static` `int` `M = 4; ``// Columns ` `  `  `// Function to find maximum sum ` `// pair from matrix ` `static` `int` `maxSumPair(``int` `[,]mat) ` `{ ` `    ``int` `max1 = ``int``.MinValue; ``// First max ` `    ``int` `max2 = ``int``.MinValue; ``// Second max ` `  `  `    ``// Traverse the matrix ` `    ``for` `(``int` `i = 0; i < N; i++) { ` `        ``for` `(``int` `j = 0; j < M; j++) { ` `            ``if` `(mat[i,j] > max1) { ` `                ``max2 = max1; ``// second max = first max ` `                ``max1 = mat[i,j]; ``// first max = current ` `            ``} ` `            ``// If second max is between current element ` `            ``// and first max ` `            ``else` `if` `(mat[i,j] > max2 && mat[i,j] <= max1) { ` `                ``max2 = mat[i,j]; ` `            ``} ` `        ``} ` `    ``} ` `  `  `    ``return` `max1 + max2; ` `} ` `  `  `// 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(maxSumPair(mat)); ` `    ``} ` `} ` `// This code is contributed by PrinciRaj1992 `

## PHP

 ` ``\$max1``)  ` `            ``{ ` `                ``\$max2` `= ``\$max1``; ``// second max = first max ` `                ``\$max1` `= ``\$mat``[``\$i``][``\$j``]; ``// first max = current ` `            ``} ` `             `  `            ``// If second max is between current  ` `            ``// element and first max ` `            ``else` `if` `(``\$mat``[``\$i``][``\$j``] > ``\$max2` `&&  ` `                     ``\$mat``[``\$i``][``\$j``] <= ``\$max1``)  ` `            ``{ ` `                ``\$max2` `= ``\$mat``[``\$i``][``\$j``]; ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``return` `\$max1` `+ ``\$max2``; ` `} ` ` `  `// Driver Code ` ` `  `// matrix ` `\$mat` `= ``array``(``array``(1, 2, 3, 4 ), ` `             ``array``(25, 6, 7, 8 ), ` `             ``array``(9, 10, 11, 12 ), ` `             ``array``(13, 14, 15, 16 )); ` ` `  `echo` `maxSumPair(``\$mat``); ` ` `  `// This code is contributed  ` `// by ihritik ` `?> `

Output:

```41
```

My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.