The in-place constraint is what makes this annoying.
Clarify the problem constraints and then present the optimal in-place solution using a two-step transformation: transpose the matrix and then reverse each row. Walk through a small example to illustrate the steps, and analyze time and space complexity.
Pro tip: Mention that the rotation can also be achieved by reversing rows first and then transposing, but the transpose-then-reverse approach is more intuitive; also note that the solution works for any n x n matrix and uses O(1) extra space.
Restate the problem to ensure understanding: rotate an n x n matrix 90 degrees clockwise in-place. Ask about constraints (e.g., n >= 1, integer values) and confirm that no extra matrix should be used.
Recognize that a 90-degree clockwise rotation can be decomposed into two simpler operations: first transpose the matrix (swap elements across the main diagonal), then reverse each row.
Write code to perform the transpose by iterating over the upper triangle and swapping matrix[i][j] with matrix[j][i]. Then, for each row, swap elements from the ends moving inward to reverse the row.
Walk through a 3x3 or 4x4 example step by step to verify correctness. Show the matrix after transpose and after row reversal, and confirm it matches the expected rotated matrix.
State that the time complexity is O(n^2) because every element is visited a constant number of times, and space complexity is O(1) since the rotation is done in-place.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.