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Heap•Pattern: Max-Heap / Quickselect•Medium

Find K closest points to the origin

Problem Intuition & Objective

Return the K points nearest to (0,0) using Euclidean distance.

Time ComplexityO(n log k)
Optimal
Space ComplexityO(k)
Memory Bounds
Optimal Algorithmic Approach

Max-heap of size K: evict the farthest point when heap exceeds K.

Core Invariants & Edge Cases

  • Compare squared distances to avoid sqrt
  • Max-heap of size K: if new point closer than max, replace it
  • Alternatively quickselect for O(n) average
Previous ProblemKth largest element in a streamNext Problem Task scheduler — minimum CPU intervals with cooldown

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