Min Cost to Connect All Points

class Solution {
  
  public: int minCostConnectPoints(vector<vector<int>>& points) {
    int n = points.size();
    vector<vector<int>> edges;
    for (int i = 0;
    i < n;
    i++) {
      for (int j = i + 1;
      j < n;
      j++) {
        int dist = abs(points[i][0] - points[j][0]) + abs(points[i][1] - points[j][1]);
        edges.push_back({
          dist, i, j}
        );
      }
    }
    sort(edges.begin(), edges.end(), [](const vector<int>& a, const vector<int>& b) {
      return a[0] < b[0];
    }
  );
  vector<int> parent(n);
  vector<int> rank(n);
  for (int i = 0;
  i < n;
  i++) {
    parent[i] = i;
  }
  int cost = 0;
  for (const auto& edge : edges) {
    int rootU = find(parent, edge[1]);
    int rootV = find(parent, edge[2]);
    if (rootU != rootV) {
      union(parent, rank, rootU, rootV);
      cost += edge[0];
    }
  }
  return cost;
}

private: int find(vector<int>& parent, int x) {
  if (parent[x] != x) {
    parent[x] = find(parent, parent[x]);
  }
  return parent[x];
}
void union(vector<int>& parent, vector<int>& rank, int x, int y) {
  int rootX = find(parent, x);
  int rootY = find(parent, y);
  if (rank[rootX] < rank[rootY]) {
    parent[rootX] = rootY;
  }
  else if (rank[rootX] > rank[rootY]) {
    parent[rootY] = rootX;
  }
  else {
    parent[rootY] = rootX;
    rank[rootX]++;
  }
}
}