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Matrix Diagonal Sum

Difficulty: Easy

Problem Description

Given a square matrix mat, return the sum of the matrix diagonals. Only include the sum of all the elements on the primary diagonal and all the elements on the secondary diagonal that are not part of the primary diagonal.

Key Insights

  • The primary diagonal consists of elements where the row index equals the column index (i.e., mat[i][i]).
  • The secondary diagonal consists of elements where the row index and column index sum to n - 1 (i.e., mat[i][n - 1 - i]).
  • If the matrix has an odd size, the center element will be counted in both diagonals, so it should only be added once.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve this problem, we will iterate through the matrix and sum the values of the primary diagonal and the secondary diagonal. We will check if the current index belongs to both diagonals (which happens in the center of an odd-sized matrix) and ensure that we do not double-count it.

Code Solutions

def diagonalSum(mat):
    n = len(mat)
    total_sum = 0
    
    for i in range(n):
        total_sum += mat[i][i]  # Primary diagonal
        total_sum += mat[i][n - 1 - i]  # Secondary diagonal
        
    # If n is odd, subtract the center element which is counted twice
    if n % 2 == 1:
        total_sum -= mat[n // 2][n // 2]
        
    return total_sum
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