<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 find(int x,vector<int>& parent){
        if(parent[x]!=x){
            parent[x]=find(parent[x],parent);
        }
        return parent[x];
    }

    bool Union(int x,int y,vector<int>& parent,vector<int>& rank){
        int xp = find(x,parent);
        int yp = find(y,parent);

        if(xp==yp)
            return true;

        if(rank[xp]<rank[yp]){
            parent[xp]=yp;
        }
        else if(rank[yp]<rank[xp])
            parent[yp]=xp;
        else{
            parent[yp]=xp;
            rank[xp]+=1;
        }

        return false;
    }

    int minCostConnectPoints(vector<vector<int>>& points) {
        set<vector<int>> pq;
        vector<int> parent(points.size()),rank(points.size(),1);
        for(int i=0;i<points.size();i++){
            for(int j=i+1;j<points.size();j++){
                if(i==j)
                    continue;
                pq.insert({abs(points[i][0]-points[j][0])+abs(points[i][1]-points[j][1]),i,j});
            }

            parent[i]=i;
        }

        int ans=0;
        while(!pq.empty()){
            auto t = *pq.begin();

            if(!Union(t[1],t[2],parent,rank))
                ans+=t[0];
            pq.erase(t);
        }

        return ans;
    }
};
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