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