Matrix Transformations

What's being tested

These problems test 2D array indexing and in-place transformation skills: mapping between (row, col) coordinates and executing swaps without corrupting data. Interviewers probe correctness on edge cases, complexity reasoning, and succinct loop invariants for operations like swaps, reversals, and 90° rotations.

Patterns & templates

• Transpose + reverse rows — For a square matrix, transpose (swap (i,j) with (j,i)) then reverse each row yields a 90° clockwise rotation; O(n^2) time, O(1) extra.

• Layer-by-layer (ring) rotation — Rotate elements per concentric layer using four-way swaps; good for in-place arbitrary-angle multiples of 90° on square matrices.

• Index mapping formula — Use mapping (i,j) -> (j, n-1-i) for clockwise 90°; implement directly into a new matrix for non-square or simpler correctness.

• In-place swap primitive — Encapsulate swap(a[i][j], a[x][y]) and ensure you don't overwrite by sequencing or temporary variable; constant extra space.

• Row reversal / swap — Reverse a row with two-pointer l,r swaps; swap entire rows by looping columns for c: swap(row1[c], row2[c]); O(n) per row.

• Memory tradeoff — Prefer an extra matrix B (O(n^2) space) when matrix is rectangular or clarity > memory; avoid for in-place constraints.

• Cache/locality tip — Traverse contiguous memory (row-major) when possible for better cache performance on large matrices.

Common pitfalls

Pitfall: Trying to rotate a non-square matrix in-place — 90° rotation changes dimensions; allocate a new matrix or reject in-place requirement.

Pitfall: Off-by-one errors in loop bounds when processing layers; always test n odd/even and single-row/column cases.

Pitfall: Overwriting values during multi-way swaps — use a temp variable or perform cycle swaps correctly to preserve data.

Practice these

The practice cards below cover the canonical variants — solve all of them and time yourself.