# K Closest Points to Origin

Published: Sep 10, 2022

Medium Sort Math Geometry Array

## Introduction

This is a geometry problem, yet a simple sorting problem as well. In any case, we should calculate distances to the origin on all points.

## Problem Description

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).

Constraints:

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

https://leetcode.com/problems/k-closest-points-to-origin/

## Examples

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

## Analysis

Sorting is done by an Euclidean distance to the origin `(0, 0)`. We don’t need actual distance, since comparison matters. Instead, sorting key is `x * x + y * y`. After sorting, return first `k` points.

## Solution

``````class KClosestPointsToOrigin:
def kClosest(self, points: List[List[int]], k: int) -> List[List[int]]:
points.sort(key = lambda x: x[0] * x[0] + x[1] * x[1])
return points[:k]
``````

## Complexities

• Time: `O(nlog(n))`
• Space: `O(1)`