<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:
    void radixsort(vector< pair<long long,int> > & E)
    {
        vector<vector<pair<long long,int>>> B(256);
        
        for(int t=0;t<4;t++)
        {
            for(auto & e : E)
                B[(e.first>>(8*t))&0xFF].push_back(e);
            int j=0;
            for(auto & b : B)
            {
                for(auto & e : b)
                {
                    E[j] = e;
                    j++;
                }
                b.clear();
            }
        }
    }

    int getparent(vector<int> & p, int x)
    {
        if(p[x] != x)
            p[x] = getparent(p,p[x]);
        return p[x];    
    }
    void getunion(vector<int> & p, int x, int y)
    {
        x = getparent(p,x);
        y = getparent(p,y);
        if(x == y)
            return;
        p[y] = x;
    }


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

        vector<pair<long long,int>> edges;
        
        for(int i=0;i+1<N;i++)
        for(int j=i+1;j<N;j++)
        {
            long long d = abs(points[i][0]-points[j][0])+abs(points[i][1]-points[j][1]);
            edges.push_back(pair<long long,int>(d,N*i+j));
        }
        radixsort(edges);
        
        vector<int> parent(N,-1);
        for(int i=0;i<N;i++)
            parent[i] = i;
        
        long long F=0;
        for(auto & e : edges)
        {
            int u = e.second/N;
            int v = e.second%N;
            if(getparent(parent,u)!=getparent(parent,v))
            {
                F += e.first;
                getunion(parent,u,v);
            }
        }
        return F;
    }
};
296995