**Problem: **Given a square matrix of size N×N, calculate the absolute difference between the sums of its diagonals.

This question was asked in HackerRank. We will see a simple and elegent solution for this problem in Java.

**Input format:
**The first line contains a single integer, N. The next N lines denote the matrix’s rows, with each line containing N space-separated integers describing the columns.

**Output format:
**Print the absolute difference between the two sums of the matrix’s diagonals as a single integer.

**Sample input:
**3

11 2 4

4 5 6

10 8 -12

**Sample output:
**15

## Explanation for diagonal difference:

The primary diagonal is:

11

5

-12

Sum across the primary diagonal: 11 + 5 – 12 = 4

The secondary diagonal is:

4

5

10

Sum across the secondary diagonal: 4 + 5 + 10 = 19

Difference: |4 – 19| = 15

**Java code:
**We will see how to find diagonal difference in Java.

import java.util.Scanner; public class DiagonalDifference { private static int calculateDiagonalDifference(int[][] arr) { int len = arr.length; int leftDiagonalSum = 0; int rightDiagonalSum = 0; int index = 0; while(index < len) { leftDiagonalSum += arr[index][index]; rightDiagonalSum += arr[index][len-1-index]; index++; } return Math.abs(leftDiagonalSum - rightDiagonalSum); } public static void main(String[] args) { Scanner in = new Scanner(System.in); int n = in.nextInt(); int arr[][] = new int[n][n]; for(int i=0; i < n; i++){ for(int j=0; j < n; j++){ arr[i][j] = in.nextInt(); } } in.close(); System.out.println(calculateDiagonalDifference(arr)); } }

**Analysis:
**Above program has a run-time of

**Ο(n)**.

To calculate sum of right and left diagonal, we are running a loop n times. So run-time of algorithm is Ο(n).

I hope you liked the solution for diagonal difference.

Please comment for questions and doubts.

On the first run of the while loop, I would expect ‘arr[index][index]’ to equal 3 (the first piece if information in the multidimensional array), but I’m pretty confused as to why it accesses the 11 first, instead of the 3