Find column with maximum sum in a Matrix

Last Updated : 11 Jul, 2025

Given a N*N matrix. The task is to find the index of column with maximum sum. That is the column whose sum of elements are 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 : Column 5 has max sum 31

Input : mat[][] = {
        { 1, 2, 3 },
        { 4, 2, 1 },
        { 5, 6, 7 },
    };
Output : Column 3 has max sum 11

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

Below is the implementation of the above approach:

C++

// C++ program to find column 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 column with max sum
pair<int, int> colMaxSum(int mat[N][N])
{
    // Variable to store index of column
    // with maximum
    int idx = -1;

    // Variable to store max sum
    int maxSum = INT_MIN;

    // Traverse matrix column wise
    for (int i = 0; i < N; i++) {
        int sum = 0;

        // calculate sum of column
        for (int j = 0; j < N; j++) {
            sum += mat[j][i];
        }

        // 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 << "Column " << ans.first + 1 << " has max sum "
         << ans.second;

    return 0;
}

Java

// Java program to find column 
// with max sum in a matrix 
import java.util.*;

class GFG
{
// No of rows and column 
static final int N = 5; 

// structure for pair
static class Pair
{
    int first , second;
    
    Pair(int f, int s)
    {
        first = f;
        second = s;
    }
}

// Function to find the column
// with max sum 
static Pair colMaxSum(int mat[][]) 
{ 
    // Variable to store index of
    // column with maximum 
    int idx = -1; 

    // Variable to store max sum 
    int maxSum = Integer.MIN_VALUE; 

    // Traverse matrix column wise 
    for (int i = 0; i < N; i++)
    { 
        int sum = 0; 

        // calculate sum of column 
        for (int j = 0; j < N; j++)
        { 
            sum += mat[j][i]; 
        } 

        // Update maxSum if it is 
        // less than current sum 
        if (sum > maxSum) 
        { 
            maxSum = sum; 

            // store index 
            idx = i; 
        } 
    } 

    Pair res; 

    res = new Pair(idx, maxSum); 

    // return result 
    return res; 
} 

// Driver code 
public static void main(String args[])
{ 
    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 }}; 

    Pair ans = colMaxSum(mat); 

    System.out.println("Column " + (int)(ans.first + 1) +
                           " has max sum " + ans.second); 
} 
}

// This code is contributed
// by Arnab Kundu

Python3

# Python3 program to find column with
# max Sum in a matrix

N = 5

# Function to find the column with max Sum
def colMaxSum(mat):
    
    # Variable to store index of column
    # with maximum
    idx = -1

    # Variable to store max Sum
    maxSum = -10**9

    # Traverse matrix column wise
    for i in range(N):

        Sum = 0

        # calculate Sum of column
        for j in range(N):
            Sum += mat[j][i]

        # Update maxSum if it is less 
        # than current Sum
        if (Sum > maxSum):
            maxSum = Sum

            # store index
            idx = i
        
    # return result
    return idx, maxSum

# 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, ans0 = colMaxSum(mat)

print("Column", ans + 1,    
      "has max Sum", ans0)

# This code is contributed by
# Mohit kumar 29

// C# program to find column 
// with max sum in a matrix 
using System;

class GFG
{
    
// No of rows and column 
static readonly int N = 5; 

// structure for pair
public class Pair
{
    public int first , second;
    
    public Pair(int f, int s)
    {
        first = f;
        second = s;
    }
}

// Function to find the column
// with max sum 
static Pair colMaxSum(int [,]mat) 
{ 
    // Variable to store index of
    // column with maximum 
    int idx = -1; 

    // Variable to store max sum 
    int maxSum = int.MinValue; 

    // Traverse matrix column wise 
    for (int i = 0; i < N; i++)
    { 
        int sum = 0; 

        // calculate sum of column 
        for (int j = 0; j < N; j++)
        { 
            sum += mat[j, i]; 
        } 

        // Update maxSum if it is 
        // less than current sum 
        if (sum > maxSum) 
        { 
            maxSum = sum; 

            // store index 
            idx = i; 
        } 
    } 

    Pair res; 

    res = new Pair(idx, maxSum); 

    // return result 
    return res; 
} 

// Driver code 
public static void Main(String []args)
{ 
    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 }}; 

    Pair ans = colMaxSum(mat); 

    Console.WriteLine("Column " + (int)(ans.first + 1) +
                        " has max sum " + ans.second); 
} 
}

// This code has been contributed by 29AjayKumar

JavaScript

<script>
// Javascript program to find column 
// with max sum in a matrix 

// No of rows and column 
let N = 5; 

// Function to find the column
// with max sum 
function colMaxSum(mat)
{
    // Variable to store index of
    // column with maximum 
    let idx = -1; 
  
    // Variable to store max sum 
    let maxSum = Number.MIN_VALUE; 
  
    // Traverse matrix column wise 
    for (let i = 0; i < N; i++)
    { 
        let sum = 0; 
  
        // calculate sum of column 
        for (let j = 0; j < N; j++)
        { 
            sum += mat[j][i]; 
        } 
  
        // Update maxSum if it is 
        // less than current sum 
        if (sum > maxSum) 
        { 
            maxSum = sum; 
  
            // store index 
            idx = i; 
        } 
    } 
  
    let res; 
  
    res = [idx, maxSum]; 
  
    // return result 
    return res; 
}

// Driver code
let 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 ]];
       
let ans = colMaxSum(mat); 
document.write("Column " + (ans[0] + 1) +
                           " has max sum " + ans[1]); 


// This code is contributed by unknown2108
</script>

Output

Column 5 has max sum 31

Complexity Analysis

Time Complexity: O(N*N) where N is the size of each row or column in the matrix.
Auxiliary Space : O(1)

Types of Asymptotic Notations in Complexity Analysis of Algorithms

barykrg

Improve

Article Tags :

Practice Tags :

Find column with maximum sum in a Matrix

Similar Reads

Basics & Prerequisites

Data Structures

Algorithms

Advanced

Interview Preparation

Practice Problem

Thank You!

What kind of Experience do you want to share?