class Solution {
public:
    int minCostConnectPoints(vector<vector<int>>& points) {
        int n = points.size();
        vector<vector<pair<int, int>>> adjList(n);

        // Make the graph
        for(int i = 0;i<n;i++){
            for(int j = i+1;j<n;j++){
                int distance = abs(points[i][0]-points[j][0]) + abs(points[i][1]-points[j][1]);
                adjList[i].push_back({j, distance});
                adjList[j].push_back({i, distance});
            }
        }
        // Implement Prim's Algo
        // Priority Queue of (weight, (node, parent))
        priority_queue<pair<int, pair<int, int>>, vector <pair<int, pair<int, int>>>, greater<pair<int, pair<int, int>>>> minHeap;

        // Let's start with 0th vertex - Start with a random node in Graph
        minHeap.push(make_pair(0, make_pair(0, -1)));
        vector<bool> visited(n, false);
        int ans = 0, edges_added = 0;
        while(edges_added < n){
            pair<int, pair<int, int>> curr = minHeap.top();
            minHeap.pop();

            int weight = curr.first;
            int node = curr.second.first;
            int parent = curr.second.second;

            if(visited[node]) continue;
            visited[node] = true;
            for(auto u:adjList[node]){
                if(!visited[u.first]){
                    minHeap.push(make_pair(u.second, make_pair(u.first, node)));
                }
            }

            ans += weight;
            edges_added++;
        }
        return ans;
    }
};