# Find difference between sums of two diagonals

• Difficulty Level : Basic
• Last Updated : 17 Jun, 2022

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 secondary 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 ``#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

 ``

## Javascript

 ``

Output:

`15`

Time complexity: O(n*n)

Auxiliary Space: O(1) using constant space to initialize diagonal sums

We can optimize the 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 ``#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 store the sum of diagonal from``          ``// top-left to bottom-right``        ``d1 += arr[i][i];``      ` `          ``// d2 store the sum of diagonal from``        ``// top-right to bottom-left``        ``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

 ``

## Javascript

 ``

Output:

`15`

Time complexity : O(n)

Auxiliary Space: O(1) using constant space to initialize diagonal sums

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