Determine Whether Matrix Can Be Obtained By Rotation

Determine Whether Matrix Can Be Obtained By Rotation

What is this problem about?

The Determine Whether Matrix Can Be Obtained By Rotation coding problem asks you to check if a square matrix mat can be transformed into another matrix target by rotating it 90 degrees clockwise, zero to three times.

Why is this asked in interviews?

This is a popular question at Microsoft and Meta to test your matrix manipulation skills. Rotating a matrix 2D array involves swapping elements in a specific pattern. It evaluations whether you can perform in-place rotations or whether you can correctly identify the coordinate transformations $(i, j) o (j, n-1-i)$ for a 90-degree turn.

Algorithmic pattern used

This problem uses Matrix Rotation and Simulation. There are two ways to check:

1. Simulate and Compare: Rotate mat 90 degrees, compare with target. Repeat up to 4 times.
2. Coordinate Mapping: For every cell $(i, j)$, check if mat[i][j] matches target in any of the four rotation positions:
   • 0 deg: $(i, j)$
   • 90 deg: $(j, n-1-i)$
   • 180 deg: $(n-1-i, n-1-j)$
   • 270 deg: $(n-1-j, i)$

Example explanation

Matrix mat:

0 1
1 1

Target target:

1 0
1 1

1. Original mat $eq$ target.
2. Rotate 90 deg: mat[0][0] o mat[0][1], etc.
   • New mat:

   1 0
   1 1
   

3. Now mat == target. Result: true.

Common mistakes candidates make

• Copying errors: Not creating a new matrix for the rotation if not doing it in-place, leading to mixed-up values.
• Missing 0 Rotation: Forgetting that if the matrices are already equal, it should return true.
• Incorrect Formula: Swapping $i$ and $j$ but forgetting to handle the $n-1$ offset correctly.

Interview preparation tip

The most concise way to rotate a matrix 90 degrees is to Transpose it (swap arr[i][j] with arr[j][i]) and then Reverse each row. This two-step process is much easier to code than direct coordinate swapping.