3873. Maximum Points Activated with One Addition

You are given a 2D integer array points, where points[i] = [x_i, y_i] represents the coordinates of the i^th point. All coordinates in points are distinct.

If a point is activated, then all points that have the same x-coordinate or y-coordinate become activated as well.

Activation continues until no additional points can be activated.

You may add one additional point at any integer coordinate (x, y) not already present in points. Activation begins by activating this newly added point.

Return an integer denoting the maximum number of points that can be activated, including the newly added point.

int uf[101010];
int find(int u) {
    return uf[u] == u ? u : uf[u] = find(uf[u]);
}
void uni(int u, int v) {
    int pu = find(u), pv = find(v);
    uf[pu] = uf[pv] = min(pu,pv);
}
class Solution {
public:
    int maxActivated(vector<vector<int>>& points) {
        iota(begin(uf), end(uf), 0);
        unordered_map<int,int> x,y;
        for(int i = 0; i < points.size(); i++) {
            int xx = points[i][0], yy = points[i][1];
            if(x.count(xx)) uni(i,x[xx]);
            else x[xx] = i;
            
            if(y.count(yy)) uni(i, y[yy]);
            else y[yy] = i;
        }
        unordered_map<int,int> cnt;
        for(int i = 0; i < points.size(); i++) cnt[find(i)]++;
        vector<int> S;
        for(auto& [_,v] : cnt) S.push_back(v);
        sort(rbegin(S), rend(S));
        if(S.size() == 1) return S[0] + 1;
        return S[0] + S[1] + 1;
    }
};