Let's learn how to solve the Diagonal Difference challenge from the HackerRank website.

Given a square matrix, we must calculate the absolute difference between the sums of its two diagonals. Consider the following example of a 3x3 matrix.

1 2 3
4 5 6
9 8 9

The sum of the left-to-right diagonal is 1+5+9 = 15. The sum of the right-to-left diagonal is 3+5+9 = 17. The absolute difference of the two is 15 - 17 = 2.

To solve this problem, the function that we must define will receive a multi-dimensional array as input. Each inner array in the outer array will represent a row of the matrix.

Pseudo code solution

1. Create a rightDiagonalSum variable to store the sum of the left-to-right diagonal.
2. Create a leftDiagonalSum variable to store the sum of the right-to-left diagonal.
3. Get the matrix size by taking the length of the multi-dimensional array.
4. Loop over the length of the multi-dimensional array.
   • Compute the rightDiagonalSum by using the loop counter to reference the row and column indices for the left diagonal.
   • Compute the leftDiagonalSum by using the loop counter and the matrix size to reference the row and column indices for the right diagonal.
5. Compute the absolute value of the difference between both diagonal sums.
6. Return the absolute value.

Code solution

function diagonalDifference(arr) {    
  let rightDiagonalSum = 0;
  let leftDiagonalSum = 0;
  const matrixSize = arr.length;
  
  for(let i = 0; i < matrixSize; i++) {
    rightDiagonalSum += arr[i][i];
    leftDiagonalSum += arr[i][(matrixSize - 1) - i];
  }

  return Math.abs(rightDiagonalSum - leftDiagonalSum);
}

Consider a 3x3 matrix. Let's see what happens during each loop iteration.

When i is 0

• arr[0][0], the top-left number in the matrix, is added to rightDiagonalSum,
• arr[0][2], the top-right number in the matrix, is added to leftDiagonalSum,

When i is 1

• arr[1][1], the center number in the matrix, is added to rightDiagonalSum,
• arr[1][1], the center number in the matrix, is added to leftDiagonalSum,

When i is 2

• arr[2][2], the bottom-right number in the matrix, is added to rightDiagonalSum,
• arr[2][0], the bottom-left number in the matrix, is added to leftDiagonalSum,

Test cases

Let's test the diagonalDifference function above. For the first test case, we will use the very first matrix we defined above. The absolute difference between the two diagonals should be 2.

const arr = [[1, 2, 3], [4, 5, 6], [9, 8, 9]];
console.log(diagonalDifference(arr)); // 2

The diagonalDifference function returns the correct value of 2 for the above test case.

The next test case will use the following matrix.

11 2 4
4  5 6
10 8 -12

The diagonal difference of this matrix should be 15.

const arr = [[11, 2, 4], [4, 5, 6], [10, 8, -12]];
console.log(diagonalDifference(arr)); // 15

The diagonalDifference function returns the correct value of 15 for the above test case.

Time and space complexity

The Big O time complexity of the solution is linear, or O(n), where n consists of the number of rows in the square matrix. The loop iterates over n rows, represented by the array length assigned to matrixSize.

The space complexity of the solution is constant, or O(1). Regardless of the size of the input, we'll always require the same numeric variables to be stored in memory.