973. 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. 1 <= K <= points.length <= 10000

2. -10000 < points[i][0] < 10000

3. -10000 < points[i][1] < 10000

// Naive sorting 
vector<vector<int>> kClosest(vector<vector<int>>& points, int K) { // time: O(nlogn); space: O(K)
    vector<vector<int> > res;
    sort(points.begin(), points.end(), [] (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];
    });
    res = vector<vector<int> > (points.begin(), points.begin() + K);
    return res;
}

// Max heap
vector<vector<int>> kClosest(vector<vector<int>>& points, int K) { // time: O(nlogK); space: O(K)
    vector<vector<int> > res;
    if (points.empty() || K == 0) return res;
    auto comp = [] (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];
    };
    priority_queue<vector<int>, vector<vector<int> >, decltype(comp)> pq(comp);
    for (const vector<int>& pt : points) {
        pq.push(pt);
        if (pq.size() > K) pq.pop();
    }
    while (!pq.empty()) {
        res.push_back(pq.top());
        pq.pop();
    }
    return res;
}

// STL nth_element
vector<vector<int>> kClosest(vector<vector<int>>& points, int K) { // time: average O(n); space: O(K)
    nth_element(points.begin(), points.begin() + K, points.end(), [] (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];
    });
    return vector<vector<int> > (points.begin(), points.begin() + K);
}

// Quick select
int compare(vector<int>& a, vector<int>& b) {
    return (a[0] * a[0] + a[1] * a[1]) - (b[0] * b[0] + b[1] * b[1]);
}
int partition(vector<vector<int> >& points, int left, int right) {
    vector<int> pivot = points[right];
    int p_idx = left;
    for (int i = left; i < right; ++i) {
        if (compare(points[i], pivot) <= 0) {
            swap(points[i], points[p_idx++]);
        }
    }
    swap(points[p_idx], points[right]);
    return p_idx;
}
vector<vector<int>> kClosest(vector<vector<int>>& points, int K) { // time: average O(n), worst O(n^2); space: O(K)
    int left = 0, right = points.size() - 1;
    while (left <= right) {
        int mid = partition(points, left, right);
        if (mid == K) break;
        if (mid < K) left = mid + 1;
        else right = mid - 1;
    }
    return vector<vector<int> > (points.begin(), points.begin() + K);
}