> ## Documentation Index
> Fetch the complete documentation index at: https://leetcode-py.wisl.dev/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> leetcode-py is a Python LeetCode practice environment generator with one CLI: lcpy. It is not a service or platform.
> Each problem is a directory under leetcode/ with README.md, solution.py, test_solution.py, helpers.py, and playground.ipynb. lcpy gen creates them from JSON templates bundled with the package.
> Examples are backed by tests; copy them verbatim.

# K Closest Points to Origin Python Solution

> Tested Python solution for LeetCode 973 with 12 pytest cases. Generate a practice environment with lcpy.

LeetCode 973, Medium. Topics: Array, Math, Divide and Conquer, Geometry, Sorting, Heap (Priority Queue), Quickselect. [View on LeetCode](https://leetcode.com/problems/k-closest-points-to-origin/description/).

Generate this problem as a practice environment: tested reference solution, 12 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 973   # by problem number
lcpy gen -s k_closest_points_to_origin   # by problem name
```

## Problem

Given an array of `points` where `points[i] = [xi, yi]` represents a point on the **X-Y** plane and an integer `k`, return the `k` closest points to the origin `(0, 0)`.

The distance between two points on the **X-Y** plane is the Euclidean distance (i.e., `√(x1 - x2)² + (y1 - y2)²`).

You may return the answer in **any order**. The answer is **guaranteed** to be **unique** (except for the order that it is in).

### Examples

![Example 1](https://assets.leetcode.com/uploads/2021/03/03/closestplane1.jpg)

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

**Explanation:** The distance between (1, 3) and the origin is sqrt(10). The distance between (-2, 2) and the origin is sqrt(8). Since sqrt(8) \< sqrt(10), (-2, 2) is closer to the origin. We only want the closest k = 1 points from the origin, so the answer is just \[\[-2,2]].

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

**Explanation:** The answer \[\[-2,4],\[3,3]] would also be accepted.

### Constraints

* `1 <= k <= points.length <= 10^4`
* `-10^4 <= xi, yi <= 10^4`

## Solution

Reference implementation from [solution.py on GitHub](https://github.com/wislertt/leetcode-py/blob/main/leetcode/k_closest_points_to_origin/solution.py), full suite in [test\_solution.py](https://github.com/wislertt/leetcode-py/blob/main/leetcode/k_closest_points_to_origin/test_solution.py):

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
import heapq


class Solution:
    # Time: O(n log k)
    # Space: O(k)
    def k_closest(self, points: list[list[int]], k: int) -> list[list[int]]:
        heap: list[tuple[int, list[int]]] = []

        for x, y in points:
            dist = x * x + y * y
            heapq.heappush(heap, (-dist, [x, y]))
            if len(heap) > k:
                heapq.heappop(heap)

        return [point for _, point in heap]
```

## Complexity

| Time       | Space |
| ---------- | ----- |
| O(n log k) | O(k)  |

## Tags

[Grind 75](/catalog/grind-75), [Grind](/catalog/grind), [NeetCode 150](/catalog/neetcode-150), [NeetCode 250](/catalog/neetcode-250), [NeetCode All](/catalog/neetcode).