Soyo

K Closest Points to Origin

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] < 10000`
• `-10000 < points[i] < 10000`

## Solution

It's similar to find K largest (or smallest) elements in array.

Lazy way: Sort then pick first K elements, `O(nlogn + k)`.
Optimized way: Use Heap, `O(n + klogn)`, `n` for build heap, `klogn` for finding first K elements.

Details

``````class Solution {
func kClosest(_ points: [[Int]], _ K: Int) -> [[Int]] {
let sorted = points.map { Point(\$0) } .sorted(by: <)
return sorted[..<K].map { [\$0.x, \$0.y] }
}

}

struct Point {
var x: Int
var y: Int
let distance: Int
init(_ data: [Int]) {
self.x = data
self.y = data
distance = x * x + y * y
}
}

extension Point: Comparable {
static func <(lhs: Point, rhs: Point) -> Bool {
return lhs.distance < rhs.distance
}
static func ==(lhs: Point, rhs: Point) -> Bool {
return lhs.distance == rhs.distance
}
}
``````