I knew the clockwise version cold so I figured this was easy.
Clarify that the rotation is counter-clockwise and in-place, then explain that a 90° CCW rotation can be achieved by first reversing each row (horizontal flip) followed by transposing the matrix. Walk through a small example to verify the transformation, and analyze time and space complexity.
Pro tip: Mention that the same result can be achieved by reversing the columns then transposing, or by a 4-way cyclic swap, and note that the row-reverse-then-transpose method is simpler and less error-prone. Also, explicitly state that the operation is done in-place with O(1) extra space.
Restate the problem to ensure you understand: rotate an n x n matrix 90° counter-clockwise, in-place. Ask if n is always square and if the matrix can be modified.
Determine the mathematical mapping: element at (i, j) moves to (n-1-j, i). Alternatively, recognize that a horizontal flip (reverse each row) followed by a transpose achieves the rotation.
Describe the two-step process: first, reverse each row of the matrix; second, swap elements across the main diagonal (transpose). Explain that this yields the 90° CCW rotation.
State that the algorithm runs in O(n^2) time, which is optimal since every element must be moved. Space complexity is O(1) because the rotation is done in-place with only a few temporary variables.
Walk through a 3x3 or 4x4 matrix step-by-step to demonstrate the transformation and confirm correctness. Optionally, discuss edge cases like n=1 or n=0.
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