<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 minCostConnectPoints(self, points: List[List[int]]) -> int:
      adj = defaultdict(list)
      for i in range(0, len(points)):
        for j in range(i + 1, len(points)):
          adj[i].append((j, abs(points[i][0] - points[j][0]) + abs(points[i][1] - points[j][1])))
          adj[j].append((i, abs(points[j][0] - points[i][0]) + abs(points[j][1] - points[i][1])))
      # print(adj)
      minHeap = []  
      for neighbor, weight in adj[0]:
        heapq.heappush(minHeap, [weight, 0, neighbor])
      mst = []
      visit = set()
      visit.add(0)
      res = 0
      while len(visit) < len(points):
        weight, n1, n2 = heapq.heappop(minHeap)
        if n2 in visit:
          continue
        mst.append([n1, n2])
        visit.add(n2)
        # print(weight)
        res += weight
        # print(mst)
        for neighbor, weight in adj[n2]:
          if neighbor not in visit:
            heapq.heappush(minHeap, [weight, n2, neighbor])
      return res


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