Find row with maximum sum in a Matrix

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

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++

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// C++ program to find row with
// max sum in a matrix
#include <bits/stdc++.h>
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;
}

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Java

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// Java program to find row with
// max sum in a matrix
import java.util.ArrayList;
  
class MaxSum
{
    public static int N;
  
    static ArrayList<Integer> 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<Integer> 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<Integer> ans = colMaxSum(mat);
        System.out.println("Row "+ (ans.get(0)+1)+ " has max sum "
        + ans.get(1));
    }
}
  
// This code is contributed by Vivekkumar Singh

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Python3

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# 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 =
  
    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

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C#

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// 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[0]+1)+ " has max sum "
        + ans[1]);
    }
}
  
// This code has been contributed by 29AjayKumar

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Output:

Row 3 has max sum 35


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