← Capital One Interview Insights
Started with the extra-space version which is pretty mechanical, just map (i, j) to (j, n-1-i) in a new matrix.
Start by clearly stating the problem and the two approaches: extra space and in-place. For the extra space approach, describe creating a new matrix and mapping each element (i, j) to (j, n-1-i). For the in-place approach, explain the two-step process: transpose the matrix and then reverse each row. Then discuss time and space complexities, and walk through edge cases.
Pro tip: Emphasize that the in-place method is not only space-efficient but also demonstrates a deeper understanding of matrix manipulation, which is valuable in ML engineering where memory optimization is crucial. Also, mention that negative values don't affect the rotation logic, showing attention to detail.
Restate the problem: rotate an n x n matrix 90 degrees clockwise. Confirm that extra space is allowed for the first approach, and that we need to discuss an in-place method and trade-offs. Mention edge cases upfront.
Describe creating a new n x n matrix. For each element at (i, j), place it at (j, n-1-i) in the new matrix. Provide pseudocode or a clear explanation. State time complexity O(n^2) and space complexity O(n^2).
Explain the two-step process: first transpose the matrix (swap matrix[i][j] with matrix[j][i] for i < j), then reverse each row. This rotates the matrix 90 degrees clockwise. Time complexity O(n^2), space complexity O(1).
Compare the two approaches: extra space is simpler and less error-prone but uses O(n^2) memory; in-place is memory-efficient but requires careful implementation. Mention that in ML engineering, memory efficiency can be critical for large matrices.
Walk through edge cases: 1x1 matrix (no change), 2x2 matrix (verify rotation), odd vs even n (in-place works for both), and negative values (rotation is independent of values). Emphasize that the algorithms handle all these correctly.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Sweep line was the right call and I got there, but the merge step for outputting the maximal segments tripped me up.
Use a sweep line algorithm with events for interval starts and ends, maintaining a running count of active intervals. Track the maximum count and the segments where it occurs, then merge adjacent segments. Discuss edge cases for open intervals and integer coordinates.
Pro tip: Emphasize that sorting events by coordinate and handling ties correctly (e.g., processing all starts before ends for closed intervals) is crucial for correctness, and mention that the merged segments can be output in O(N) time after sorting.
Confirm whether intervals are closed or open, and whether coordinates are integers or reals. Note that N can be up to 200,000 and coordinates up to 1e9, so O(N log N) is required.
Create events for each interval: start at left endpoint, end at right endpoint. Sort events by coordinate. For closed intervals, process starts before ends at the same coordinate; for open intervals, process ends before starts.
Sweep through events, maintaining current count. When count reaches a new maximum, record the start of a segment; when count drops below maximum, record the end. Merge adjacent segments where maximum occurs.
For open intervals, adjust event ordering and segment boundaries (e.g., use open intervals for output). For integer coordinates, consider that coverage only changes at integer points, and segments may be discrete.
Argue that the sweep line correctly computes coverage at all points because coverage only changes at endpoints. Sorting takes O(N log N), sweep takes O(N), so total O(N log N).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.