Published: Sep 10, 2022

## 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`

## 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)`