<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>

def kruskal(WList):
    (edges,component,TE) = ([],{},[])
    for u in WList.keys():
        edges.extend([(d,u,v) for (v,d) in WList[u]])
        component[u] = u
    
    edges.sort()
   
    for (d,u,v) in edges:
        if component[u] != component[v]:
            TE.append((u,v, d))
            c = component[u]
            for w in WList.keys():
                if component[w] == c:
                    component[w] = component[v]
    # Compute the Minimum Cost based on Tree Edges
    min_cost = 0
    for u, v, d in TE:
        min_cost += d
    return(min_cost)

class Solution:
    def minCostConnectPoints(self, points: List[List[int]]) -> int:
        # Init Adjacency Matrix
        AList = { i : [] for i in range(len(points))}
        # Compute distances for each point and store in AMat
        for i in range(len(points)):
            x1, y1 = points[i][0], points[i][1]
            for j in range(i + 1, len(points)):
                x2, y2 = points[j][0], points[j][1]
                dist = abs(x1 - x2) + abs(y1 - y2)
                
                # Distance from point i to j is same as from j to i. So init both entries
                AList[i].append((j, dist))
                AList[j].append((i, dist))
        
        minimum_cost = kruskal(AList)
        return minimum_cost
191305