I knew what a quadtree was in theory but had never actually coded one.
Start by clarifying requirements and constraints, then explain the quadtree structure and its operations. Walk through the insert and query algorithms, emphasizing edge cases like duplicate coordinates and boundary points. Finally, discuss trade-offs and potential optimizations.
Pro tip: Mention that you would handle duplicate coordinates by storing a list of points per node or by using a counter, and explicitly define boundary inclusion rules (e.g., points exactly on the query rectangle's edge are included) to avoid ambiguity.
Ask about expected data volume, query patterns, coordinate precision, and whether duplicates are allowed. Confirm that the quadtree should support dynamic inserts and rectangular range queries.
Define the node structure: each node represents a rectangular region and stores points (or a list for duplicates) and four children (NW, NE, SW, SE). Explain splitting logic when capacity is exceeded.
Describe the recursive insert: if node is a leaf and has capacity, add point; if full, split and redistribute points, then insert into appropriate child. Handle duplicates by storing multiple points or incrementing a count.
Explain recursive query: if node's region does not intersect the query rectangle, return; if leaf, check each point for inclusion; otherwise, recurse into children that intersect. Define boundary inclusion (e.g., inclusive on all edges).
Discuss handling of duplicate coordinates, points on boundaries, and degenerate cases (e.g., all points collinear). Compare quadtree with alternatives like k-d tree or R-tree, and mention balancing and performance considerations.
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