<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:

    def minKey(self,inMST,key):
        minIndex=0
        minVal=float('inf')
        for i in range(len(key)):
            if not inMST[i] and key[i]<minVal:
                minIndex=i
                minVal=key[i]
        return minIndex

    def MST(self,graph,V):
        inMST=[False]*V
        key=[float('inf')]*V
        key[0]=0
        for i in range(1,V):
            u=self.minKey(inMST,key)
            inMST[u]=True
            for v in range(V):
                if graph[u][v] and not inMST[v] and graph[u][v]<key[v]:
                    key[v]=graph[u][v]
        cost=0
        for i in key:
            cost+=i
        return cost

    def minCostConnectPoints(self, points: List[List[int]]) -> int:
        n=len(points)
        graph=[[0]*n for _ in range(n)]
        for i in range(n-1):
            for j in range(i+1,n):
                p1=points[i]
                p2=points[j]
                md=abs(p1[1]-p2[1])+abs(p1[0]-p2[0])
                graph[i][j]=md
                graph[j][i]=md
        return self.MST(graph,n)
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