<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 compare{
    public:
    const bool operator()(const pair<int,vector<int>>& a, const pair<int,vector<int>>& b)
    {
        if (a.first > b.first)
        return true;
        return false;
    }
};
class Solution {
    vector<int>par;
    vector<int>size;

public:

    int find(int node)
    {
        // if(par[node]==node)
        // return node;
        // else
        // {
        //     par[node] = find(par[node]);
        //     
        //     return par[node];
        // }
        
        while(node!=par[node])
        {
            par[node] = par[par[node]];
            node = par[node];
        }
        return node;
    }

    void unio(int node1, int node2)
    {
        int par1 = find(node1);
        int par2 = find(node2);
        if (size[par1] < size[par2])
        {
            par[par1] = par2;
            size[par2] += size[par1];
        }
        else
        {
            par[par2] = par1;
            size[par1] += size[par2];
        }
        return;
    }

    

    int minCostConnectPoints(vector<vector<int>>& points) {
        int nb_points = points.size();
        par.resize(nb_points);
        size.resize(nb_points);
        priority_queue<pair<int,vector<int>>, vector<pair<int,vector<int>>>,compare> weights;
        // vector<vector<int>>cost(nb_points,vector<int>(nb_points));
        for(int i=0;i<nb_points;i++)
        {
            par[i] = i;
            size[i] = 1;
            for (int j = i+1;j<nb_points;j++)
            {
                int cost = abs(points[i][0] - points[j][0]) + abs(points[i][1] - points[j][1]);
                weights.push({cost,{i,j}});
                
            }
            
        }
        

        //find min spanning tree using UF
        int ans=0;
        while(!weights.empty())
        {
            pair<int,vector<int>>cur = weights.top();
            weights.pop();
            if(find(cur.second[0])!=find(cur.second[1]))
            {
                //they are not connected yet
                unio(cur.second[0],cur.second[1]);
                ans += cur.first;
            }

        }


        return ans;
        
    }
};
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