You’re in a coding interview. The interviewer says: “Given a list of points on a 2D plane, return the k closest to the origin.” The obvious answer is sort by distance. But interviewers want the heap solution — O(n log k) instead of O(n log n) — and strong candidates mention Quickselect.

---

The Problem

Given an array of points where points[i] = [xi, yi], return the k closest to the origin (0, 0). Return the answer in any order.

Example

Input: points = [[3,3],[5,-1],[-2,4]], k = 2 Output: [[3,3],[-2,4]]

Already comfortable with the solution? Practice it in a mock interview →

---

What Interviewers Are Actually Testing

Skill	What Interviewers Observe
Distance comparison	Do you skip sqrt and compare squared distances?
Heap vs. sort	Do you know when a max-heap of size k beats full sort?
Python heapq	Do you know it’s a min-heap and how to simulate max-heap?

---

Step 1: The Key Insight

You don’t need sorted order — just the k smallest. A max-heap of size k evicts the farthest candidate each time a closer point arrives.

---

Python Implementation

Max-heap of size k:

import heapq

def kClosest(points: list[list[int]], k: int) -> list[list[int]]:
    max_heap = []
    for x, y in points:
        dist = x**2 + y**2
        heapq.heappush(max_heap, (-dist, x, y))
        if len(max_heap) > k:
            heapq.heappop(max_heap)
    return [[x, y] for _, x, y in max_heap]

---

Time & Space Complexity

Approach	Time	Space
Sort	O(n log n)	O(1)
Max-heap of k	O(n log k)	O(k)
Quickselect	O(n) expected	O(1)

---

Common Interview Mistakes

1. Using sqrt. Unnecessary — compare x² + y² directly.
2. Not knowing heapq is min-heap. Negate the key for max-heap behavior.
3. Proposing Quickselect without O(n²) caveat. Mention randomized pivoting mitigates worst case.

---

What a Strong Candidate Sounds Like

“Sort by squared distance is O(n log n). When k ≪ n, a max-heap of size k drops to O(n log k). For each point I push onto the heap; if size exceeds k, I pop the farthest. Quickselect gives O(n) expected but I’d go with the heap unless asked to optimize further.”

---

Related Problems to Practice

• Merge K Sorted Lists — Heap-based merging.
• Kth Smallest Element in a BST — K-th order selection.

---

Practice This in a Mock Interview

Start a mock interview for K Closest Points to Origin on Intervu.

---

Further reading:

• How to Prepare for a Coding Interview in 2026, the complete roadmap
• Why LeetCode alone isn’t enough, and what to practice instead
• Practice any LeetCode problem as a live mock interview
• The Grind 75 Pathway, a structured study plan with AI practice links
• Browse all walkthroughs on GitHub