<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 n = points.size();
        unordered_map<int, vector<pair<int,int>>>mp;//node-> {wt,node}
        for(int i=0; i<points.size(); i++)
        {
            vector<int>p1 = points[i];
            for(int j=0; j<points.size(); j++)
            {
                if(i == j)
                    continue;
                
                else
                {
                    vector<int>p2 = points[j];
                    int x = abs(p2[0] - p1[0]);
                    int y = abs(p2[1] - p1[1]);
                    mp[i].push_back({x+y, j});
                    mp[j].push_back({x+y, i});
                }
            }
        }
        
        
        priority_queue<pair<int,int>, vector<pair<int,int>>, greater<pair<int,int>>>pq;
        
        
        pq.push({0,0});//wt,node
        
        vector<bool>inMST(n, false);
        
        int sum = 0;
        
        while(!pq.empty())
        {
            int node = pq.top().second;
            int wt = pq.top().first;
            
            pq.pop();
            
            if(inMST[node])
                continue;
            
            inMST[node] = true;
            sum += wt;
            
            for(auto n:mp[node])
            {
                int nbr = n.second;
                int nbrwt = n.first;
                
                if(inMST[nbr] == false)
                    pq.push({nbrwt,nbr});
            }
        }
        return sum;
        
    }
};
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