Rotate matrix and find max lamp coverage

Q: Rotate matrix and find max lamp coverage

This is a Coding & Algorithms interview question from Capital One for Machine Learning Engineer roles. View the full question and solution on PracHub.

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Question

Square-matrix rotation with extra space: Given an n x n integer matrix, return a new matrix that is the 90-degree clockwise rotation of the input. Extra space is allowed; target O(n^
time. Then explain how to perform the rotation in-place and compare time/space trade-offs. Describe edge cases (e.g., 1x1, 2x2, odd/even n, negative values) and basic tests.
One-dimensional lamp coverage maximum: You are given N lamps on a number line. Lamp i at position xi illuminates the closed interval [xi - ri, xi + ri]. Compute the maximum number of lamps illuminating any point and output all maximal closed segments where this maximum occurs, merged and sorted by coordinate. Constraints: 1 ≤ N ≤ 2e5; |xi| ≤ 1e9; 1 ≤ ri ≤ 1e9. Design an O(N log N) time, O(N) space algorithm (e.g., sweep line) and justify correctness and complexity. Discuss how results change for open intervals or integer-only coordinates.

Rotate matrix and find max lamp coverage

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