<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 u,vector<int>& parent)
{
    if(parent[u]<0)
    {
        return u;
    }
    return find(parent[u],parent);
}
void unionbyweight(int u,int v,vector<int>& parent)
{
    int pu=find(u,parent);
    int pv=find(v,parent);
    if(pu!=pv)
    {
        if(abs(parent[pu])>abs(parent[pv]))
        {
             parent[pu]+=parent[pv];
             parent[pv]=pu;
        }
        else
        {
             parent[pv]+=parent[pu];
             parent[pu]=pv;
        }
    }
}
int kruskals(vector<vector<int>>vec,vector<int>& parent)
{
    int E=vec.size();
    int sum=0;
    for(int i=0;i<E;i++)
    {
        int s=vec[i][1];
        int d=vec[i][2];
        int w=vec[i][0];
        if(find(s,parent)!=find(d,parent))
        {
           sum=sum+w;
            unionbyweight(s,d,parent);
        }
    }
    return sum;
}
    int minCostConnectPoints(vector<vector<int>>& points) {
        int V=points.size();
        vector<int>parent(V,-1);
        vector<vector<int>>vec;
        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);
                vec.push_back({d,i,j});
            }
        }
        sort(vec.begin(),vec.end());
        return kruskals(vec,parent);
    }
};
292205