InterviewDB Question

Points Search: Find the K Nearest Points to an Origin Using a Priority Queue

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Question Details

Problem

Given an array of 2D points and an integer k,

return the k points closest to the origin (0, 0). Distance is Euclidean. The result can be in any order.

python
def k_closest(points: list[list[int]], k: int) -> list[list[int]]:
    pass

Example:

points = [[1,3],[-2,2],[5,8],[0,1]], k = 2
-> [[-2,2],[0,1]]   # distances: sqrt(10), sqrt(8), sqrt(89), 1

points = [[3,3],[5,-1],[-2,4]], k = 2
-> [[3,3],[-2,4]]   # distances: sqrt(18), sqrt(26), sqrt(20)

Round 1 Coding

Implement a solution using a max-heap of size k.

Follow-ups

  1. What is the time complexity of the heap approach vs. a full sort? When does each become preferable?
  2. How would you use the Quickselect algorithm to achieve average O(n) time?
  3. If points arrive as a stream and you must always return the current k closest, how do you maintain the heap efficiently?
  4. How does the solution change if distance is Manhattan distance instead of Euclidean?

Full Details

Problem

Given an array of 2D points and an integer k,

return the k points closest to the origin (0, 0). Distance is Euclidean. The result can be in any order.

python
def k_closest(points: list[list[int]], k: int) -> list[list[int]]:
    pass

Example:

points = [[1,3],[-2,2],[5,8],[0,1]], k = 2
-> [[-2,2],[0,1]]   # distances: sqrt(10), sqrt(8), sqrt(89), 1

points = [[3,3],[5,-1],[-2,4]], k = 2
-> [[3,3],[-2,4]]   # distances: sqrt(18), sqrt(26), sqrt(20)

Round 1 Coding

Implement a solution using a max-heap of size k.

Follow-ups

  1. What is the time complexity of the heap approach vs. a full sort? When does each become preferable?
  2. How would you use the Quickselect algorithm to achieve average O(n) time?
  3. If points arrive as a stream and you must always return the current k closest, how do you maintain the heap efficiently?
  4. How does the solution change if distance is Manhattan distance instead of Euclidean?
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About This Question

This is a reported interview question from a applied intuition interview during the phone round.

It covers the following topics: Heap, Phone, Coding, Queue, Arrays, Onsite .

Topics

Heap Phone Coding Queue Arrays Onsite

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About Applied Intuition Interview Reports

This question was reported by a candidate who interviewed at Applied Intuition. LeakCode aggregates interview reports from 10+ sources, including 1Point3Acres, Glassdoor, LeetCode Discuss, Blind, Reddit, Indeed, and Nowcoder. Each report is translated where necessary, deduplicated against existing entries, and tagged by company, role, round type, and reporting date.

Use this question as one calibration data point, not a memorization target. Companies typically rotate their question pools every 2-4 months; the exact wording of a 2024 question may differ from what you encounter today. The underlying pattern, difficulty level, and follow-up depth at Applied Intuition are the higher-signal extractions to take from this report.

For broader preparation context, the Applied Intuition interview process typically includes a recruiter screen, one or two technical phone screens, and a 4-5 round on-site loop covering coding, system design (at L4+ levels), and behavioral. Reports tagged on LeakCode show the round-by-round distribution and typical difficulty calibration. To browse questions filtered by round type and seniority, use the company hub linked above.

How To Practice This Type of Question

Solve similar problems on LeetCode under timed conditions (25-35 minutes per medium difficulty). The goal is pattern recognition: recognize the underlying technique (sliding window, two-pointer, BFS, memoized recursion, etc.) within 60-90 seconds of reading. Strong candidates verbalize their hypothesis out loud before coding, then iterate based on feedback. Weak candidates dive into implementation immediately, lose time on the wrong approach, and run out of time for follow-ups.

Companies update their question pools every 2-4 months. The exact wording of any given question may have been retired by the time you interview. Focus your prep on the pattern, not the specific problem. The patterns that appear in Applied Intuition reports consistently are the ones worth investing in; one-off niche problems are not.

During Your Applied Intuition Round

Apply the standard interview round template: clarify requirements (2-3 minutes), state your approach out loud and confirm direction with the interviewer (3-5 minutes), code with narration (15-25 minutes), test with concrete examples including edge cases (5 minutes), discuss optimization or trade-offs if time permits (5 minutes). This template is universally accepted across FAANG and adjacent companies; deviating from it produces weaker interviewer feedback signal.

The single most predictive failure mode in Applied Intuition reports tagged "no hire": not asking clarifying questions. Interviewers are explicitly trained to weight this. Strong candidates ask 3-5 clarifying questions even on problems that look obvious; weak candidates dive into code immediately. The clarifying-question check is often the first signal recorded in the interviewer's written notes.