<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>

#define OO (int)1e7

    struct edge{
        int to ;
        int cost ;
        edge( int to , int cost ) : cost(cost) , to(to){}
        bool operator <( const edge& e ) const {
            return cost > e.cost ;
        }
    };


class Solution {
public:



    int MST( vector<vector<edge>> g ){
        int n = g.size() ;
        vector<int> vis( n , 0 ) , dist( n , OO ) ;
        priority_queue<edge> q ;
        dist[0] = 0 ;
        q.push( {0 , 0} ) ;

        int ans = 0 ;

        while( !q.empty() ){

            int minidx = q.top().to ;
            q.pop() ;

            if( vis[minidx] )
                continue ;

            ans += dist[minidx] ;
            

            for( auto e : g[minidx] ){
                
                if( !vis[e.to] && e.cost < dist[e.to] ){
                    dist[e.to] = e.cost ;
                    q.push(e) ;
                }

            }
            vis[minidx] = true ;
        }
        return ans ;
    }

    int minCostConnectPoints(vector<vector<int>>& points) {
        int n = points.size() ;
        vector<vector<edge>> g( n ) ;
        for( int i = 0 ; i < n ; ++i ){
            for( int j = 0 ; j < n ; ++j ){
                if( j == i )
                    continue ;
                int dist = abs( points[j][0] - points[i][0] ) + abs( points[j][1] - points[i][1] ) ;  
                g[i].push_back( { j , dist } ) ;
            }
        }
        return MST(g) ;
    }
};
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