Check if Matrix Is X-Matrix

Check if Matrix Is X-Matrix

What is this problem about?

The "Check if Matrix Is X-Matrix interview question" is a matrix validation task. An $n imes n$ square matrix is an "X-Matrix" if:

1. Every element on the two main diagonals is non-zero.
2. Every other element (those NOT on the diagonals) is exactly zero. The two main diagonals are the primary diagonal (top-left to bottom-right) and the anti-diagonal (top-right to bottom-left).

Why is this asked in interviews?

Companies like Google and Amazon use the "Check if Matrix Is X-Matrix coding problem" to assess a candidate's comfort with 2D array indexing. It’s a foundational "Matrix interview pattern" exercise that requires identifying specific cells based on their $(row, col)$ coordinates.

Algorithmic pattern used

This problem follows the Coordinate Geometry in Matrices pattern. For a square matrix of size $n$:

• A cell $(i, j)$ is on the primary diagonal if i == j.
• A cell $(i, j)$ is on the anti-diagonal if i + j == n - 1.

1. Loop: Iterate through every cell $(i, j)$ in the matrix.
2. Conditional Check:
   • If i == j or i + j == n - 1: The value must be non-zero.
   • Else: The value must be zero.
3. Failure: Return false as soon as a condition is violated.

Example explanation

Matrix $3 imes 3$:

2 0 2
0 5 0
2 0 2

• (0,0): i=j. Val 2 (!= 0). OK.
• (0,1): Not diagonal. Val 0. OK.
• (0,2): i+j=2. Val 2 (!= 0). OK.
• (1,1): i=j and i+j=2. Val 5 (!= 0). OK. Result: True.

Common mistakes candidates make

• Diagonal Logic: Miscalculating the anti-diagonal condition (using i + j == n instead of n - 1).
• Incorrect Bounds: Hardcoding the matrix size instead of using length.
• Logic Flip: Confusing the requirements (e.g., checking if non-diagonals are non-zero).

Interview preparation tip

Practice identifying "special" indices in matrices. The primary and anti-diagonals are the most common, but also know how to identify the "middle row" or "outer boundary." This is a core "Array interview pattern" for grid problems.