<p>You are given an array <code>points</code> representing integer coordinates of some points on a 2D-plane, where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>.</p>

<p>The cost of connecting two points <code>[x<sub>i</sub>, y<sub>i</sub>]</code> and <code>[x<sub>j</sub>, y<sub>j</sub>]</code> is the <strong>manhattan distance</strong> between them: <code>|x<sub>i</sub> - x<sub>j</sub>| + |y<sub>i</sub> - y<sub>j</sub>|</code>, where <code>|val|</code> denotes the absolute value of <code>val</code>.</p>

<p>Return <em>the minimum cost to make all points connected.</em> All points are connected if there is <strong>exactly one</strong> simple path between any two points.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/26/d.png" style="width: 214px; height: 268px;" />
<pre>
<strong>Input:</strong> points = [[0,0],[2,2],[3,10],[5,2],[7,0]]
<strong>Output:</strong> 20
<strong>Explanation:</strong> 
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/26/c.png" style="width: 214px; height: 268px;" />
We can connect the points as shown above to get the minimum cost of 20.
Notice that there is a unique path between every pair of points.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> points = [[3,12],[-2,5],[-4,1]]
<strong>Output:</strong> 18
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= points.length &lt;= 1000</code></li>
	<li><code>-10<sup>6</sup> &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>6</sup></code></li>
	<li>All pairs <code>(x<sub>i</sub>, y<sub>i</sub>)</code> are distinct.</li>
</ul>

class Solution {
public:
    int minCostConnectPoints(vector<vector<int>>& points) {
        // for every point, connect it to the cloest point to it?
        // for every point, add an edge to every other point, the weight being manhattan distance
        // find the minimum spanning tree
        auto cmp = [](auto a, auto b){ return a.first > b.first; };
        using MyPriorityQueue = std::priority_queue<std::pair<int, int>, std::vector<std::pair<int, int>>, decltype(cmp)>;
        unordered_map<int, MyPriorityQueue> adj;
        for(int i = 0; i < points.size(); i++){
            adj[i] = MyPriorityQueue(cmp);
            for (int j = 0; j < points.size(); j++){
                if(!adj.count(j)) adj[j] = MyPriorityQueue(cmp);
                adj[i].push({
                    abs(points[i][0] - points[j][0]) + abs(points[i][1] -points[j][1]),
                    j
                });
                adj[j].push({
                    abs(points[i][0] - points[j][0]) + abs(points[i][1] -points[j][1]),
                    i
                });
            }
        }
        vector<bool> visited(points.size(), false);
        MyPriorityQueue q(cmp);
        q.push({0,0});
        int cost = 0;
        while(!q.empty()){
            auto p = q.top();
            q.pop();
            if (visited[p.second]) continue;
            cost += p.first;
            auto idx = p.second;
            visited[idx] = true;
            auto& neis = adj[idx];
            while(!neis.empty()){
                auto nei = neis.top();
                neis.pop();
                if (!visited[nei.second]){
                    q.push(nei);
                }
            }
        }

        return cost;
    }
};
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