<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) {
        int i=0;
        map< pair<int,int>,vector< pair<pair<int,int>,int>>> mp;
        for(i=0;i<points.size();i++){
            auto p1=points[i];
            for(int j=i+1;j<points.size();j++){
                auto p2=points[j];
                int x=abs(p1[0]-p2[0])+abs(p1[1]-p2[1]);    
                mp[{p1[0],p1[1]}].push_back({{p2[0],p2[1]},x});
                mp[{p2[0],p2[1]}].push_back({{p1[0],p1[1]},x});
            }
        }
        set<pair<int,int>> visited;
 priority_queue<pair<int,pair<int,int>> ,vector<pair<int,pair<int,int>>> ,greater<pair<int,pair<int,int>>>> pq;
        int ans=0;
         auto x=points[0];
         visited.insert({x[0],x[1]});
         for(auto it : mp[{x[0],x[1]}])
         {
            pq.push({it.second,it.first});
         } 
        while(!pq.empty())
        {
            auto top=pq.top();
            pq.pop();
            if(visited.find(top.second)==visited.end())
            {   ans=ans+top.first;
                visited.insert(top.second);
                auto p=top.second;
                for(auto it : mp[{p.first,p.second}])
                {
                  pq.push({it.second,it.first});
                }   
            }
        }
       return ans;
    }
};
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