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

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 <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; 
} 

Java

// 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 

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

Output:

Row 3 has max sum 35

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My Personal Notes

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

C++

Java

Python3

C#

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