← Applied intuition Interview Insights
The base case clicked fast for me: group by slope and intercept, check overlap, merge.
Start by clarifying the problem: define collinearity with floating-point tolerance, and confirm that merging requires overlapping projections along the shared line. Then propose a sweep-line or sorting-based algorithm that groups segments by their infinite line (normalized direction and offset), and within each group merges overlapping intervals while preserving all original points sorted along the line direction.
Pro tip: Mention that floating-point comparisons need an epsilon-based tolerance, and that you would normalize the line representation (e.g., canonical direction and offset) to avoid precision issues when grouping collinear segments.
Confirm definitions: collinearity with tolerance, overlap of projections, handling of duplicate points, and whether segments can be merged transitively. Ask about input size and performance expectations.
For each segment, compute a canonical representation of its supporting line: a normalized direction vector and a signed distance from origin. Use epsilon-based comparisons to group segments that lie on the same line.
Group segments by their canonical line key. Within each group, project all points onto the line direction to obtain scalar intervals, and sort the segments by their start projection.
Iterate through sorted intervals, merging those that overlap (including touching within tolerance). Collect all original points from merged segments, then sort them along the line direction.
For each merged group, output the sorted list of unique points (preserving original points). Validate that no two output segments are collinear and overlapping, and that all original points are present.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.