<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) {
        vector<vector<int>> graph(points.size(),vector<int>(points.size(),0));

        for (int i=0;i<points.size();i++){
            for (int j=i+1;j<points.size();j++){
                int dis = std::abs(points[i][0]-points[j][0])+std::abs(points[i][1]-points[j][1]);
                graph[i][j] = dis;
                graph[j][i] = dis;
            }
        }
        vector<bool> used(points.size(),false);
        used[0] = true;
        std::priority_queue<vector<int>,vector<vector<int>>,Compare> pq;
        for (int i=0;i<points.size();i++){
            pq.push({graph[0][i],0,i});
        }
        int ret = 0;
        while(!pq.empty()){
            vector<int> itm = pq.top();
            pq.pop();
            int new_point = itm[2];
            if (!used[new_point]){
                used[new_point] = true;
                ret += itm[0];
                for (int i=0;i<points.size();i++){
                    if (used[i]) continue;
                    pq.push({graph[new_point][i],new_point,i});
                }
            }
        }
        
        return ret;
    }
    
    struct Compare{
        bool operator()(vector<int>& a, vector<int>& b){
            return a[0]>b[0];
        }  
    };
    
};



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