<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:
    typedef pair<int, int> P;
    int primsAlgo(vector<vector<P>> adj, int V)
    {
        priority_queue<P, vector<P>, greater<P>> pq;
        pq.push({0,0});
        vector<bool> inMST(V, false);
        int sum = 0;

        while(!pq.empty())
        {
            auto p = pq.top();
            pq.pop();

            int wt = p.first;
            int node = p.second;

            if(inMST[node] == true)
            {
                continue;
            }

            inMST[node] = true;
            sum += wt;

            for(auto &tmp: adj[node])
            {
                int neighbour = tmp.first;
                int neighbour_wt = tmp.second;

                if(inMST[neighbour] == false)
                {
                    pq.push({neighbour_wt, neighbour});
                }
            }

        }
        return sum;
    }

    int minCostConnectPoints(vector<vector<int>>& points) {
        int V = points.size();

        vector<vector<P>> adj(V);

        for(int i = 0; i<V; i++)
        {
            for(int j = i+1; j<V; j++)
            {
                int x1 = points[i][0];
                int y1 = points[i][1];

                int x2 = points[j][0];
                int y2 = points[j][1];

                int d = abs(x1 - x2) + abs(y1 - y2);

                adj[i].push_back({j, d});
                adj[j].push_back({i, d});
            }
        }
        
        return primsAlgo(adj, V);
    }
};
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