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Find column with maximum sum in a Matrix

  • Difficulty Level : Medium
  • Last Updated : 27 May, 2021

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#




// 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

 


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