Check if Matrix Is X-Matrix

Problem Description

A square matrix is said to be an X-Matrix if both of the following conditions hold:

1. All the elements in the diagonals of the matrix are non-zero.
2. All other elements are 0.

Given a 2D integer array grid of size n x n representing a square matrix, return true if grid is an X-Matrix. Otherwise, return false.

Key Insights

• The matrix must be square, so the number of rows is equal to the number of columns.
• The diagonal elements are located at positions (i, i) and (i, n-i-1).
• Non-diagonal elements must be zero for the matrix to qualify as an X-Matrix.

Space and Time Complexity

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

Solution

To determine if the given matrix is an X-Matrix, we will iterate through each element of the matrix. We will check:

• If the element is a diagonal element (i.e., where row index equals column index or where the sum of row and column indices equals n-1), then it must be non-zero.
• If the element is not a diagonal element, then it must be zero.

This approach ensures that we are only traversing the matrix once, yielding a time complexity of O(n). The space complexity remains O(1) since we are not using any additional data structures that grow with input size.

Code Solutions