<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>

import heapq


def calculate_edges(points):
    edges = [[0] * len(points) for _ in range(len(points))]
    for i in range(len(points) - 1):
        for j in range(i + 1, len(points)):
            edges[i][j] = edges[j][i] = abs(points[i][0] - points[j][0]) + abs(points[i][1] - points[j][1])

    return edges


class Solution:
    def minCostConnectPoints(self, points: List[List[int]]) -> int:
        edges = calculate_edges(points)
        
        costs = [float("inf")] * len(points)
        costs[0] = 0
        in_mst = [False] * len(points)
        
        heap = []
        heapq.heappush(heap, (costs[0], 0))

        while heap:
            _, i = heapq.heappop(heap)
            if in_mst[i]:
                continue

            in_mst[i] = True
            for j in range(len(points)):
                if in_mst[j] == False and costs[j] > edges[i][j]:
                    costs[j] = edges[i][j]
                    heapq.heappush(heap, (costs[j], j))
        
        return sum(costs)
42994