LeetCode 973. K Closest Points to Origin

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).

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]]
Explanation: The answer [[-2,4],[3,3]] would also be accepted.

Constraints:

• 1 <= k <= points.length <= 104

• -104 < xi, yi < 104

Solution:

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class Solution {
public:
    vector<vector<int>> kClosest(vector<vector<int>>& points, int K) {
        auto cmp = [&](const vector<int>& a, const vector<int>& b) {
            return a[0] * a[0] + a[1] * a[1] <  b[0] * b[0] + b[1] * b[1]; 
        };
        
        nth_element(points.begin(), points.begin() + K, points.end(), cmp);
        // sort(points.begin(), points.end(), cmp);
        
        vector<vector<int>> ans(points.begin(), points.begin() + K);
        return ans;
    }
};