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Find row with maximum sum in a Matrix
• Last Updated : 10 Oct, 2019

Given an N*N matrix. The task is to find the index of a row with the maximum sum. That is the row whose sum of elements is maximum.

Examples:

```Input : mat[][] = {
{ 1, 2, 3, 4, 5 },
{ 5, 3, 1, 4, 2 },
{ 5, 6, 7, 8, 9 },
{ 0, 6, 3, 4, 12 },
{ 9, 7, 12, 4, 3 },
};
Output : Row 3 has max sum 35

Input : mat[][] = {
{ 1, 2, 3 },
{ 4, 2, 1 },
{ 5, 6, 7 },
};
Output : Row 3 has max sum 18
```

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

The idea is to traverse the matrix row-wise and find the sum of elements in each row and check for every row if current sum is greater than the maximum sum obtained till the current row and update the maximum_sum accordingly.

Below is the implementation of the above approach:

## C++

 `// C++ program to find row with ` `// max sum in a matrix ` `#include ` `using` `namespace` `std; ` ` `  `#define N 5 // No of rows and column ` ` `  `// Function to find the row with max sum ` `pair<``int``, ``int``> colMaxSum(``int` `mat[N][N]) ` `{ ` `    ``// Variable to store index of row ` `    ``// with maximum ` `    ``int` `idx = -1; ` ` `  `    ``// Variable to store max sum ` `    ``int` `maxSum = INT_MIN; ` ` `  `    ``// Traverse matrix row wise ` `    ``for` `(``int` `i = 0; i < N; i++) { ` `        ``int` `sum = 0; ` ` `  `        ``// calculate sum of row ` `        ``for` `(``int` `j = 0; j < N; j++) { ` `            ``sum += mat[i][j]; ` `        ``} ` ` `  `        ``// Update maxSum if it is less than ` `        ``// current sum ` `        ``if` `(sum > maxSum) { ` `            ``maxSum = sum; ` ` `  `            ``// store index ` `            ``idx = i; ` `        ``} ` `    ``} ` ` `  `    ``pair<``int``, ``int``> res; ` ` `  `    ``res = make_pair(idx, maxSum); ` ` `  `    ``// return result ` `    ``return` `res; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` ` `  `    ``int` `mat[N][N] = { ` `        ``{ 1, 2, 3, 4, 5 }, ` `        ``{ 5, 3, 1, 4, 2 }, ` `        ``{ 5, 6, 7, 8, 9 }, ` `        ``{ 0, 6, 3, 4, 12 }, ` `        ``{ 9, 7, 12, 4, 3 }, ` `    ``}; ` ` `  `    ``pair<``int``, ``int``> ans = colMaxSum(mat); ` ` `  `    ``cout << ``"Row "` `<< ans.first + 1 << ``" has max sum "` `         ``<< ans.second; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java program to find row with ` `// max sum in a matrix ` `import` `java.util.ArrayList; ` ` `  `class` `MaxSum ` `{ ` `    ``public` `static` `int` `N; ` ` `  `    ``static` `ArrayList colMaxSum(``int` `mat[][]) ` `    ``{ ` `        ``// Variable to store index of row ` `        ``// with maximum ` `        ``int` `idx = -``1``; ` ` `  `        ``// Variable to store maximum sum ` `        ``int` `maxSum = Integer.MIN_VALUE; ` ` `  `        ``// Traverse the matrix row wise ` `        ``for` `(``int` `i = ``0``; i < N; i++)  ` `        ``{ ` `            ``int` `sum = ``0``; ` `            ``for` `(``int` `j = ``0``; j < N; j++) ` `            ``{ ` `                ``sum += mat[i][j]; ` `            ``} ` ` `  `            ``// Update maxSum if it is less than ` `            ``// current row sum ` `            ``if` `(maxSum < sum) ` `            ``{ ` `                ``maxSum = sum; ` ` `  `                ``// store index ` `                ``idx = i; ` `            ``} ` `        ``} ` `         `  `        ``// Arraylist to store values of index ` `        ``// of maximum sum and the maximum sum together ` `        ``ArrayList res = ``new` `ArrayList<>(); ` `        ``res.add(idx); ` `        ``res.add(maxSum); ` ` `  `        ``return` `res; ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` `        ``N = ``5``; ` `        ``int``[][] mat = {  ` `            ``{ ``1``, ``2``, ``3``, ``4``, ``5` `},  ` `            ``{ ``5``, ``3``, ``1``, ``4``, ``2` `},  ` `            ``{ ``5``, ``6``, ``7``, ``8``, ``9` `},  ` `            ``{ ``0``, ``6``, ``3``, ``4``, ``12` `}, ` `            ``{ ``9``, ``7``, ``12``, ``4``, ``3` `}, ` `        ``}; ` `        ``ArrayList ans = colMaxSum(mat); ` `        ``System.out.println(``"Row "``+ (ans.get(``0``)+``1``)+ ``" has max sum "` `        ``+ ans.get(``1``)); ` `    ``} ` `} ` ` `  `// This code is contributed by Vivekkumar Singh `

## Python3

 `# Python3 program to find row with  ` `# max sum in a matrix  ` `import` `sys ` ` `  `N ``=` `5` `# No of rows and column  ` ` `  `# Function to find the row with max sum  ` `def` `colMaxSum(mat): ` ` `  `    ``# Variable to store index of row  ` `    ``# with maximum  ` `    ``idx ``=` `-``1` ` `  `    ``# Variable to store max sum  ` `    ``maxSum ``=` `-``sys.maxsize ` ` `  `    ``# Traverse matrix row wise  ` `    ``for` `i ``in` `range``(``0``, N):  ` `        ``sum` `=` `0` ` `  `        ``# calculate sum of row  ` `        ``for` `j ``in` `range``(``0``, N):  ` `            ``sum` `+``=` `mat[i][j]  ` ` `  `        ``# Update maxSum if it is less than  ` `        ``# current sum  ` `        ``if` `(``sum` `> maxSum): ` `            ``maxSum ``=` `sum` ` `  `            ``# store index  ` `            ``idx ``=` `i  ` ` `  `    ``res ``=` `[idx, maxSum] ` ` `  `    ``# return result  ` `    ``return` `res ` ` `  `# Driver code  ` `mat ``=` `[[ ``1``, ``2``, ``3``, ``4``, ``5``],  ` `       ``[ ``5``, ``3``, ``1``, ``4``, ``2``],  ` `       ``[ ``5``, ``6``, ``7``, ``8``, ``9``],  ` `       ``[ ``0``, ``6``, ``3``, ``4``, ``12``],  ` `       ``[ ``9``, ``7``, ``12``, ``4``, ``3``]]  ` ` `  `ans ``=` `colMaxSum(mat) ` `print``(``"Row"``, ans[``0``] ``+` `1``, ``"has max sum"``, ans[``1``]) ` ` `  `# This code is contributed by Sanjit_Prasad `

## C#

 `// C# program to find row with ` `// max sum in a matrix ` `using` `System; ` `using` `System.Collections.Generic;  ` ` `  `public` `class` `MaxSum ` `{ ` `    ``public` `static` `int` `N; ` ` `  `    ``static` `List<``int``> colMaxSum(``int` `[,]mat) ` `    ``{ ` `        ``// Variable to store index of row ` `        ``// with maximum ` `        ``int` `idx = -1; ` ` `  `        ``// Variable to store maximum sum ` `        ``int` `maxSum = ``int``.MinValue; ` ` `  `        ``// Traverse the matrix row wise ` `        ``for` `(``int` `i = 0; i < N; i++)  ` `        ``{ ` `            ``int` `sum = 0; ` `            ``for` `(``int` `j = 0; j < N; j++) ` `            ``{ ` `                ``sum += mat[i, j]; ` `            ``} ` ` `  `            ``// Update maxSum if it is less than ` `            ``// current row sum ` `            ``if` `(maxSum < sum) ` `            ``{ ` `                ``maxSum = sum; ` ` `  `                ``// store index ` `                ``idx = i; ` `            ``} ` `        ``} ` `         `  `        ``// Arraylist to store values of index ` `        ``// of maximum sum and the maximum sum together ` `        ``List<``int``> res = ``new` `List<``int``>(); ` `        ``res.Add(idx); ` `        ``res.Add(maxSum); ` ` `  `        ``return` `res; ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main(String[] args) ` `    ``{ ` `        ``N = 5; ` `        ``int``[,] mat = {  ` `            ``{ 1, 2, 3, 4, 5 },  ` `            ``{ 5, 3, 1, 4, 2 },  ` `            ``{ 5, 6, 7, 8, 9 },  ` `            ``{ 0, 6, 3, 4, 12 }, ` `            ``{ 9, 7, 12, 4, 3 }, ` `        ``}; ` `        ``List<``int``> ans = colMaxSum(mat); ` `        ``Console.WriteLine(``"Row "``+ (ans+1)+ ``" has max sum "` `        ``+ ans); ` `    ``} ` `} ` ` `  `// This code has been contributed by 29AjayKumar `

Output:

```Row 3 has max sum 35
```

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