K Closest Points to Origin

May 30, 2020

Introduction

We have a list of points on the plane. Find the K closest points to the origin (0, 0).

(Here, the distance between two points on a plane is the Euclidean distance.)

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

Example 1:

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]].

Example 2:

Input: points = [[3,3],[5,-1],[-2,4]], K = 2
Output: [[3,3],[-2,4]]
(The answer [[-2,4],[3,3]] would also be accepted.)

Note:

1 <= K <= points.length <= 10000
-10000 < points[i][0] < 10000
-10000 < points[i][1] < 10000

Solution

Let’s sort by distance.

import "sort"

type Euclidean  [][]int

func euclideanDistance(p []int)    int { return p[0] * p[0] + p[1] * p[1] }

func (p Euclidean) Len() int           { return len(p) }
func (p Euclidean) Less(i, j int) bool { return euclideanDistance(p[i]) < euclideanDistance(p[j]) }
func (p Euclidean) Swap(i, j int)      { p[i], p[j] = p[j], p[i] }


func kClosest(points [][]int, K int) [][]int {
    sort.Sort(Euclidean(points))
    return points[:K]
}

Performance of this solution is:

Runtime: 116 ms
Memory Usage: 7.5 MB

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