Hackerrank Problems | Diagonal Difference

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

For example, the square matrix  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.

Function description

Complete the  diagonalDifference function in the editor below.

diagonalDifference takes the following parameter:

• int arr[n][m]: an array of integers

Return

• int: the absolute diagonal difference

Input Format

The first line contains a single integer, n, the number of rows and columns in the square matrix arr .
Each of the next  lines describes a row,a[i] , and consists of  space-separated integers a[i][j].

Constraints

• -100<=a[i][j]<=100

Output Format

Return the absolute difference between the sums of the matrix’s two diagonals as a single integer.

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

Implementation

def diagonalDifference(arr):
    n = len(arr)
    
    left_to_right_sum = sum(arr[i][i] for i in range(n))
    right_to_left_sum = sum(arr[i][n - 1 - i] for i in range(n))
    
    return abs(left_to_right_sum - right_to_left_sum)

# Example usage:
matrix = [
    [1, 2, 3],
    [4, 5, 6],
    [9, 8, 9]
]

result = diagonalDifference(matrix)
print("Absolute Diagonal Difference:", result)

Time Complexity

In the given solution:

1. Calculating the sum of the left-to-right diagonal involves iterating through the elements along the diagonal once. The sum function itself has a linear time complexity in the number of elements, which is O(n) where n is the size of the diagonal.
2. Calculating the sum of the right-to-left diagonal also involves iterating through the elements along the diagonal once. Similar to the left-to-right diagonal, the sum function has a linear time complexity, which is O(n).
3. The abs function has a constant time complexity, as it simply performs a mathematical operation.

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