<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(vector<int>& parent,int a){
    return parent[a]=(parent[a]==a)?a:Find(parent,parent[a]);
}
void Union(vector<int> &parent,vector<int>&rank,int a,int b){
    int x=Find(parent,a);
    int y=Find(parent,b);
    if(x==y) return;
    if(rank[x]>=rank[y]){
        rank[x]++;
        parent[y]=x;
    }
    else{
        rank[y]++;
        parent[x]=y;
    }
}
struct edge{
    int src;
    int des;
    int w;
};
static bool cmp(edge w1,edge w2){
    return w1.w<w2.w;
}
int krushkals(vector<edge> &v,int e,int n){
    vector<int> parent(n+1,0);
    vector<int> rank(n+1,1);
    sort(v.begin(),v.end(),cmp);
    for(int i=0;i<=n;i++){
        parent[i]=i;
    }
    int ans=0;
    int i=0;
    int edgelen=0;
    while(edgelen<n-1&&v.size()>i){
    int srcpar=Find(parent,v[i].src);
    int despar=Find(parent,v[i].des);
    if(srcpar!=despar){
        Union(parent ,rank,srcpar,despar);
        edgelen++;
        ans+=v[i].w;
    }
    i++;
    }
    return ans;
}
int minCostConnectPoints(vector<vector<int>>& points) {
        int n=points.size();
        int e=(n*(n-1))/2;
        vector<edge> v(e);
        int k=0;
        for(int i=0;i<n;i++){
            int j=i+1;
           while(j<n){
                v[k].src=i;
                v[k].des=j;
                v[k].w=abs(points[i][0]-points[j][0])+abs(points[i][1]-points[j][1]);
                k++;
                j++;
            }
        }
        return krushkals(v,e,n);
    }
};
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