Find K Closest Points to Origin
Last updated: April 5, 2025
Quick Overview
Given an array of points on a 2D plane, find the K closest points to the origin (0,0). Discuss trade-offs between sorting, heap, and quickselect approaches.
Canva
April 5, 20258
4
4,234 solved
Given an array of points on a 2D plane, find the K closest points to the origin (0,0). Discuss trade-offs between sorting, heap, and quickselect approaches.
This question tests fundamental algorithm design and analysis skills. At Canva, spatial algorithms are relevant to the design editor (element proximity, snap-to-grid, collision detection). The interviewer wants to see clean code and thorough analysis of time/space complexity trade-offs.
What the Interviewer Expects
- Implement at least two approaches with clear complexity analysis
- Handle edge cases (k equals array length, duplicate distances, k=0)
- Write clean, well-named code with proper function signatures
- Discuss when each approach is preferred based on constraints
Key Topics to Cover
How to Approach This
- Clarify input constraints and edge cases before writing code.
- Walk through your approach verbally and confirm with the interviewer before coding.
- Start with a brute force solution, then optimize. Mention time and space complexity.
- Test your solution with examples, including edge cases like empty input or duplicates.
- Consider common patterns: sliding window, two pointers, hash map, BFS/DFS, dynamic programming.
Possible Follow-up Questions
- How would you modify this for a streaming input where points arrive continuously?
- How would you extend this to find the K closest points to an arbitrary point, not just the origin?
- What if the points are in 3D space instead of 2D?
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Practice DSA ProblemsSample Answer
Problem Analysis
In this problem, we need to find the K closest points to the origin (0, 0) from a given list of points defined by their coordinates (x, y). The distance from the origin can be calculated using the Euc...
Approach
- Max-Heap Approach:
- Initialize an empty max-heap.
- Iterate through each point in the array:
- Calculate the squared distance from the origin.
- If the size of the heap is less...
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