The parametric approach clicked for me pretty quickly, set up the 2x2 system, compute the cross product determinant, check t1 and t2 are both in [0,1].
Start by clarifying the problem constraints (number of segments, coordinate ranges, whether segments are closed, and expected output format). Then propose a solution that balances efficiency and simplicity, such as a sweep-line algorithm for O((n + k) log n) time, and discuss trade-offs with the naive O(n^2) approach. Finally, address deduplication of intersection points using a set with appropriate hashing or rounding.
Pro tip: Mention that floating-point precision can cause duplicate points to appear distinct; propose using exact rational arithmetic or rounding to a tolerance, and deduplicate with a hash set. This shows attention to real-world robustness.
Ask about input size, coordinate types (integer vs. floating-point), whether segments are closed, and if overlapping collinear segments should be handled. This ensures you solve the right problem.
For small n, O(n^2) pairwise checking is acceptable. For large n, use a sweep-line algorithm (e.g., Bentley-Ottmann) to achieve O((n + k) log n) where k is the number of intersections.
Implement robust segment intersection using orientation tests and parametric equations. Use exact arithmetic or epsilon comparisons to avoid precision issues.
Store points in a hash set with a custom hash that accounts for floating-point tolerance, or round coordinates to a fixed precision before insertion.
Discuss time and space complexity of your approach, and compare with alternatives. Mention edge cases like parallel segments, shared endpoints, and collinear overlaps.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.