Diagonal Difference

 

Given a square matrix, calculate the absolute difference between the sums of its diagonals.

For example, the square matrix arr is shown below:

1 2 3
4 5 6
9 8 9  

The left-to-right diagonal = 1+5+9=15. The right to left diagonal = 3+5+9=17. Their absolute difference is |15-17|=2

Sample Input

3
11 2 4
4 5 6
10 8 -12

Sample Output

15

Explanation

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

Algo:

1.We take two pointer i.e variable i,j to traverse the matrix.To sum the left diagonal assign i=0,j=0 .

2. To sum the right diagonal, make j as "n-1" and i=0, it will point to the last element in the first row , and now decrement j and increment i to add all diagonal values.

 

3.Finally return the difference between them

Code:

public static int diagonalDifference(List<List<Integer>> arr) {

        int sum1=0;

        int sum2=0;

        int n=arr.size();

        int i=0,j=0;

    while(i<n && j<n)

    {

        //positive diagonal sum "top left to bottom right"

        sum1+=arr.get(i++).get(j++);

    }

    i=0;

    j=n-1;

    

    while(i<n && j>=0)

    {

        //"top right to bottom left"

        sum2+=arr.get(i++).get(j--);

    }

    

        return Math.abs(sum1-sum2);

    }

}