Day 30 K Closest Points to Origin.cpp

PROBLEM:



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. 1 <= K <= points.length <= 10000
2. -10000 < points[i][0] < 10000
3. -10000 < points[i][1] < 10000





SOLUTION:



class Solution {
public:
    vector<vector<int>> kClosest(vector<vector<int>>& points, int K) {
        
        nth_element(points.begin(), points.begin() + K - 1, points.end(), [](vector<int>& p, vector<int>& q) {
            return p[0] * p[0] + p[1] * p[1] < q[0] * q[0] + q[1] * q[1];
        });
        return vector<vector<int>>(points.begin(), points.begin() + K);
    }
};