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Check if sums of i-th row and i-th column are same in matrix
  • Difficulty Level : Easy
  • Last Updated : 10 May, 2021

Given a matrix mat[][], we have to check if the sum of i-th row is equal to the sum of i-th column or not. 

Examples: 

Input : 1 2 3 4 
        9 5 3 1
        0 3 5 6 
        0 4 5 6
Output : Yes
Sums of 1st row = 10 and 1st column 
are same, i.e., 10

Expected time complexity is O(m x n) where m is a number of rows and n is a number of columns.

The idea is really simple. We use a nested loop to calculate the sum of each row and column and then check whether their sum is equal or not. 

The implementation of the above idea is given below.  

C++




#include <bits/stdc++.h>
using namespace std;
const int MAX = 100;
 
// Function to check the if sum of a row
// is same as corresponding column
bool areSumSame(int a[][MAX], int n, int m)
{
    int sum1 = 0, sum2 = 0;
    for (int i = 0; i < n; i++) {
        sum1 = 0, sum2 = 0;
        for (int j = 0; j < m; j++) {
            sum1 += a[i][j];
            sum2 += a[j][i];
        }
        if (sum1 == sum2)
            return true;
    }
    return false;
}
 
// Driver Code
int main()
{
    int n = 4; // number of rows
    int m = 4; // number of columns
    int M[n][MAX] = { { 1, 2, 3, 4 },
                      { 9, 5, 3, 1 },
                      { 0, 3, 5, 6 },
                      { 0, 4, 5, 6 } };
    cout << areSumSame(M, n, m) << "\n";
    return 0;
}
Java



// Java program to check if there are two
// adjacent set bits.
public class GFG {
     
    // Function to check the if sum of a row
    // is same as corresponding column
    static boolean areSumSame(int a[][],
                             int n, int m)
    {
        int sum1 = 0, sum2 = 0;
        for (int i = 0; i < n; i++)
        {
            sum1 = 0;
            sum2 = 0;
            for (int j = 0; j < m; j++)
            {
                sum1 += a[i][j];
                sum2 += a[j][i];
            }
             
            if (sum1 == sum2)
                return true;
        }
         
        return false;
    }
     
    // Driver code
    public static void main(String args[])
    {
 
        int n = 4; // number of rows
        int m = 4; // number of columns
         
        int M[][] = { { 1, 2, 3, 4 },
                      { 9, 5, 3, 1 },
                      { 0, 3, 5, 6 },
                      { 0, 4, 5, 6 } };
                         
        if(areSumSame(M, n, m) == true)
            System.out.print("1\n");
        else
            System.out.print("0\n");
    }
}
 
// This code is contributed by Sam007.
Python3



# Python3 program to check the if
# sum of a row is same as
# corresponding column
MAX = 100;
 
# Function to check the if sum
# of a row is same as
# corresponding column
def areSumSame(a, n, m):
    sum1 = 0
    sum2 = 0
    for i in range(0, n):
        sum1 = 0
        sum2 = 0
        for j in range(0, m):
            sum1 += a[i][j]
            sum2 += a[j][i]
         
        if (sum1 == sum2):
            return 1
     
    return 0
 
# Driver Code
n = 4; # number of rows
m = 4; # number of columns
M = [ [ 1, 2, 3, 4 ],
      [ 9, 5, 3, 1 ],
      [ 0, 3, 5, 6 ],
      [ 0, 4, 5, 6 ] ]
       
print(areSumSame(M, n, m))
 
# This code is contributed by Sam007.
C#



// C# program to check if there are two
// adjacent set bits.
using System;
 
class GFG {
     
    // Function to check the if sum of a row
    // is same as corresponding column
    static bool areSumSame(int [,]a, int n, int m)
    {
        int sum1 = 0, sum2 = 0;
        for (int i = 0; i < n; i++)
        {
            sum1 = 0;
            sum2 = 0;
            for (int j = 0; j < m; j++)
            {
                sum1 += a[i,j];
                sum2 += a[j,i];
            }
             
            if (sum1 == sum2)
                return true;
        }
         
        return false;
    }
     
    // Driver code   
    public static void Main ()
    {
        int n = 4; // number of rows
        int m = 4; // number of columns
         
        int [,] M = { { 1, 2, 3, 4 },
                      { 9, 5, 3, 1 },
                      { 0, 3, 5, 6 },
                      { 0, 4, 5, 6 } };
                       
        if(areSumSame(M, n, m) == true)
            Console.Write("1\n");
        else
            Console.Write("0\n");
    }
}
 
// This code is contributed by Sam007.
PHP



<?php
// Function to check the if
// sum of a row is same as
// corresponding column
function areSumSame($a, $n, $m)
{
    $sum1 = 0;
    $sum2 = 0;
     
    for($i = 0; $i < $n; $i++)
    {
        $sum1 = 0;
        $sum2 = 0;
        for($j = 0; $j < $m; $j++)
        {
            $sum1 += $a[$i][$j];
            $sum2 += $a[$j][$i];
        }
         
        if ($sum1 == $sum2)
            return true ;
    }
    return false ;
}
 
// Driver code
$n = 4 ; // number of rows
$m = 4 ; // number of columns
$M = array(array(1, 2, 3, 4),
           array(9, 5, 3, 1),
           array(0, 3, 5, 6),
           array(0, 4, 5, 6));
 
echo areSumSame($M, $n, $m) ;
 
// This code is contributed
// by ANKITRAI1
?>
Javascript



<script>
// Java script program to check if there are two
// adjacent set bits.
 
     
    // Function to check the if sum of a row
    // is same as corresponding column
    function areSumSame(a,n,m)
    {
        let sum1 = 0, sum2 = 0;
        for (let i = 0; i < n; i++)
        {
            sum1 = 0;
            sum2 = 0;
            for (let j = 0; j < m; j++)
            {
                sum1 += a[i][j];
                sum2 += a[j][i];
            }
             
            if (sum1 == sum2)
                return true;
        }
         
        return false;
    }
     
    // Driver code
     
 
        let n = 4; // number of rows
        let m = 4; // number of columns
         
        let M = [[1, 2, 3, 4 ],
                    [ 9, 5, 3, 1],
                    [ 0, 3, 5, 6 ],
                    [ 0, 4, 5, 6 ]];
                         
        if(areSumSame(M, n, m) == true)
            document.write("1\n");
        else
            document.write("0\n");
     
 
// This code is contributed by Bobby
</script>
Output: 
1
This article is contributed by Sarthak Kohli. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
 



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