<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 MST(self, adj, V):


        def get_min_key():

            min_value = float("inf")
            min_index = 0
            for i in range(V):
                if not exist[i] and key[i] < min_value:
                    min_index = i  
                    min_value = key[i]
            return min_index

        key = [float("inf")] * V
        exist = [0] * V
        key[0] = 0

        for _ in range(V-1):
            u = get_min_key()
            exist[u] = 1

            for v in range(V):
                if adj[u][v] and not exist[i] and adj[u][v] < key[v]:
                    key[v] = adj[u][v]

        cost = 0
        for c in key:
            cost += c
        return cost




    def minCostConnectPoints(self, points):
        n = len(points)
        adj = [[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[0] - p2[0]) + abs(p1[1] - p2[1])
                adj[i][j] = md

        return self.MST(adj, n)

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):
        key = [float('inf')] * V
        inMST = [False] * V
        key[0] = 0
        
        for count 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):
        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[0] - p2[0]) + abs(p1[1] - p2[1])
                graph[i][j] = md
                graph[j][i] = md
        
        return self.MST(graph, n)
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