<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:
        # Number of points in the list
        num_points = len(points)
      
        # Graph represented as an adjacency matrix with initialized distances
        graph = [[0] * num_points for _ in range(num_points)]
      
        # Initialize all distances to infinity
        distances = [float('inf')] * num_points
      
        # Keep track of visited points to avoid cycles
        visited = [False] * num_points
      
        # Calculate the distances between all points and populate the graph
        for i, (x1, y1) in enumerate(points):
            for j in range(i + 1, num_points):
                x2, y2 = points[j]
                distance = abs(x1 - x2) + abs(y1 - y2)
                graph[i][j] = graph[j][i] = distance
      
        # Starting from point 0
        distances[0] = 0
      
        # Variable to store the minimum cost to connect all points
        min_cost = 0
      
        # Prim's algorithm to find the minimum spanning tree (MST)
        for _ in range(num_points):
            # Index for the next point to visit
            next_index = -1
          
            # Find the closest unvisited point
            for j in range(num_points):
                if not visited[j] and (next_index == -1 or distances[j] < distances[next_index]):
                    next_index = j
          
            # Mark this point as visited
            visited[next_index] = True
          
            # Add the distance to the minimum cost
            min_cost += distances[next_index]
          
            # Update distances relative to the current point
            for j in range(num_points):
                if not visited[j]:
                    distances[j] = min(distances[j], graph[next_index][j])
      
        # Return the total cost to connect all points
        return min_cost
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