<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<int>> adj;

        for(int i=0;i<points.size();i++)
        {
            for(int j=0;j<points.size();j++)
            {
                if(i!=j)
                {
                    adj[i].push_back(j);
                }
            }
        }

        // for(auto i : adj)
        // {
        //     cout<<i.first<<" ";
        //     for(int j=0;j<i.second.size();j++)
        //     {
        //         cout<<i.second[j]<<" ";
        //     }
        //     cout<<"\n";
        // }

        priority_queue<pair<int,int>, vector<pair<int,int>>, greater<pair<int,int>>> heap;
        set<int> v;

        int cost =0;

        heap.push({0,0}); // in the format {cost, node}

        
        while(v.size()!=n)
        {
            pair<int,int> node = heap.top();
            heap.pop();
            if(v.find(node.second)!=v.end())
            {
                continue;
            }
            
            v.insert(node.second);
            cout<<node.first<<" ";
            cost+=node.first;

            if(v.size()!=n)
            {
                for(int vertex : adj[node.second])
                {
                if(v.find(vertex)==v.end())
                {
                    int dist = abs(points[node.second][0]-points[vertex][0])+ abs(points[node.second][1]-points[vertex][1]);
                    heap.push({dist,vertex});
                }
                }
            }
            

        }

        return cost;
        
    }
};
95815