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Find difference between sums of two diagonals

Given a matrix of n X n. The task is to calculate the absolute difference between the sums of its diagonal.

Examples:

Input : mat[][] = 11 2 4
                   4 5 6
                  10 8 -12 
Output : 15
Sum of primary diagonal = 11 + 5 + (-12) = 4.
Sum of primary diagonal = 4 + 5 + 10 = 19.
Difference = |19 - 4| = 15.


Input : mat[][] = 10 2
                   4 5
Output : 7



Calculate the sums across the two diagonals of a square matrix. Along the first diagonal of the matrix, row index = column index i.e mat[i][j] lies on the first diagonal if i = j. Along the other diagonal, row index = n – 1 – column index i.e mat[i][j] lies on the second diagonal if i = n-1-j. By using two loops we traverse the entire matrix and calculate the sum across the diagonals of the matrix.

Below is the implementation of this approach:

C++

// C++ program to find the difference
// between the sum of diagonal.
#include <bits/stdc++.h>
#define MAX 100
using namespace std;
  
int difference(int arr[][MAX], int n)
{
    // Initialize sums of diagonals
    int d1 = 0, d2 = 0;
  
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < n; j++)
        {
            // finding sum of primary diagonal
            if (i == j)
                d1 += arr[i][j];
  
            // finding sum of secondary diagonal
            if (i == n - j - 1)
                d2 += arr[i][j];
        }
    }
  
    // Absolute difference of the sums
    // across the diagonals
    return abs(d1 - d2);
}
  
// Driven Program
int main()
{
    int n = 3;
  
    int arr[][MAX] =
    {
        {11, 2, 4},
        {4 , 5, 6},
        {10, 8, -12}
    };
  
    cout << difference(arr, n);
    return 0;
}

Java

// JAVA Code for Find difference between sums
// of two diagonals
class GFG {
      
    public static int difference(int arr[][], int n)
    {
        // Initialize sums of diagonals
        int d1 = 0, d2 = 0;
       
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < n; j++)
            {
                // finding sum of primary diagonal
                if (i == j)
                    d1 += arr[i][j];
       
                // finding sum of secondary diagonal
                if (i == n - j - 1)
                    d2 += arr[i][j];
            }
        }
       
        // Absolute difference of the sums
        // across the diagonals
        return Math.abs(d1 - d2);
    }
      
    /* Driver program to test above function */
    public static void main(String[] args) 
    {
        int n = 3;
           
        int arr[][] =
        {
            {11, 2, 4},
            {4 , 5, 6},
            {10, 8, -12}
        };
       
        System.out.print(difference(arr, n));
         
    }
  }
// This code is contributed by Arnav Kr. Mandal.

Python3

# Python3 program to find the difference
# between the sum of diagonal.
def difference(arr, n):
  
    # Initialize sums of diagonals
    d1 = 0
    d2 = 0
  
    for i in range(0, n):
      
        for j in range(0, n):
          
            # finding sum of primary diagonal
            if (i == j):
                d1 += arr[i][j]
  
            # finding sum of secondary diagonal
            if (i == n - j - 1):
                d2 += arr[i][j]
          
    # Absolute difference of the sums
    # across the diagonals
    return abs(d1 - d2);
  
# Driver Code
n = 3
  
arr = [[11, 2, 4],
       [4 , 5, 6],
       [10, 8, -12]]
  
print(difference(arr, n))
      
# This code is contributed 
# by ihritik

C#

// C# Code for find difference between
// sums of two diagonals
using System;
  
public class GFG
{
  
    // Function to calculate difference
    public static int difference(int[,] arr,
                                 int n)
    {
          
        // Initialize sums of diagonals
        int d1 = 0, d2 = 0;
      
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < n; j++)
            {
                  
                // finding sum of primary diagonal
                if (i == j)
                    d1 += arr[i, j];
      
                // finding sum of secondary diagonal
                if (i == n - j - 1)
                    d2 += arr[i, j];
            }
        }
      
        // Absolute difference of the
        // sums across the diagonals
        return Math.Abs(d1 - d2);
    }
      
    // Driver Code
    public static void Main() 
    {
        int n = 3;
          
        int[,] arr ={{11, 2, 4},
                     {4 , 5, 6},
                     {10, 8, -12}};
      
        Console.Write(difference(arr, n));
          
    }
}
  
// This code is contributed by shiv_bhakt.

PHP

<?php
// PHP program to find the difference
// between the sum of diagonal.
  
function difference($arr, $n)
{
      
    // Initialize sums of diagonals
    $d1 = 0; $d2 = 0;
  
    for ($i = 0; $i < $n; $i++)
    {
        for ($j = 0; $j < $n; $j++)
        {
              
            // finding sum of 
            // primary diagonal
            if ($i == $j)
                $d1 += $arr[$i][$j];
  
            // finding sum of 
            // secondary diagonal
            if ($i == $n - $j - 1)
                $d2 += $arr[$i][$j];
        }
    }
  
    // Absolute difference of the sums
    // across the diagonals
    return abs($d1 - $d2);
}
  
// Driver Code
{
    $n = 3;
  
    $arr = array(array(11, 2, 4),
                 array(4 , 5, 6),
                 array(10, 8, -12));
  
    echo difference($arr, $n);
    return 0;
}
  
// This code is contributed by nitin mittal.
?>


Output:

15

Time complexity : O(n*n)

We can optimize above solution to work in O(n) using the patterns present in indexes of cells.

C++

// C++ program to find the difference
// between the sum of diagonal.
#include <bits/stdc++.h>
#define MAX 100
using namespace std;
  
int difference(int arr[][MAX], int n)
{
    // Initialize sums of diagonals
    int d1 = 0, d2 = 0;
  
    for (int i = 0; i < n; i++)
    {
        d1 += arr[i][i];
        d2 += arr[i][n-i-1];
    }
  
    // Absolute difference of the sums
    // across the diagonals
    return abs(d1 - d2);
}
  
// Driven Program
int main()
{
    int n = 3;
  
    int arr[][MAX] =
    {
        {11, 2, 4},
        {4 , 5, 6},
        {10, 8, -12}
    };
  
    cout << difference(arr, n);
    return 0;
}

Java

// JAVA Code for Find difference between sums
// of two diagonals
  
class GFG {
      
    public static int difference(int arr[][], int n)
    {
        // Initialize sums of diagonals
        int d1 = 0, d2 = 0;
       
        for (int i = 0; i < n; i++)
        {
            d1 += arr[i][i];
            d2 += arr[i][n-i-1];
        }
       
        // Absolute difference of the sums
        // across the diagonals
        return Math.abs(d1 - d2);
    }
      
    /* Driver program to test above function */
    public static void main(String[] args) 
    {
        int n = 3;
           
        int arr[][] =
        {
            {11, 2, 4},
            {4 , 5, 6},
            {10, 8, -12}
        };
       
        System.out.print(difference(arr, n));
         
    }
  }
// This code is contributed by Arnav Kr. Mandal.

Python3

# Python3 program to find the difference
# between the sum of diagonal.
def difference(arr, n):
  
    # Initialize sums of diagonals
    d1 = 0
    d2 = 0
  
    for i in range(0, n):
        d1 = d1 + arr[i][i]
        d2 = d2 + arr[i][n - i - 1]
          
    # Absolute difference of the sums
    # across the diagonals
    return abs(d1 - d2)
  
# Driver Code
n = 3
  
arr = [[11, 2, 4],
       [4 , 5, 6],
       [10, 8, -12]]
  
print(difference(arr, n))
      
# This code is contributed
# by ihritik

C#

// C# Code for find difference between 
// sums of two diagonals
using System;
  
public class GFG
  
{
      
    //Function to find difference
    public static int difference(int[,] arr,
                                 int n)
    {
          
        // Initialize sums of diagonals
        int d1 = 0, d2 = 0;
      
        for (int i = 0; i < n; i++)
        {
            d1 += arr[i, i];
            d2 += arr[i, n - i - 1];
        }
      
        // Absolute difference of the sums
        // across the diagonals
        return Math.Abs(d1 - d2);
    }
      
    // Driver Code
    public static void Main() 
    {
        int n = 3;
          
        int[,] arr ={{11, 2, 4},
                     {4 , 5, 6},
                     {10, 8, -12}};
      
        Console.Write(difference(arr, n));
          
    }
}
  
// This code is contributed by shiv_bhakt.

PHP

<?php
// PHP program to find the difference
// between the sum of diagonal.
  
function difference($arr, $n)
{
      
    // Initialize sums of diagonals
    $d1 = 0; $d2 = 0;
  
    for ($i = 0; $i < $n; $i++)
    {
        $d1 += $arr[$i][$i];
        $d2 += $arr[$i][$n-$i-1];
    }
  
    // Absolute difference of the sums
    // across the diagonals
    return abs($d1 - $d2);
}
  
// Driver Code
{
    $n = 3;
  
    $arr =array(array(11, 2, 4),
                array(4, 5, 6),
                array(10, 8, -12));
  
    echo difference($arr, $n);
    return 0;
}
  
// This code is contributed by nitin mittal.
?>


Output:

15

Time complexity : O(n)

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



This article is attributed to GeeksforGeeks.org

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