<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:
        #create weighted adjacency list
        adjList = defaultdict(list)
        N = len(points)
        for i in range(N):
            x1, y1 = points[i][0], points[i][1]
            for j in range(i+1, N):
                x2, y2 = points[j][0], points[j][1]
                dist = abs(x1-x2) + abs(y1-y2)
                adjList[(x1,y1)].append([dist, x2, y2])
                adjList[(x2,y2)].append([dist, x1, y1])
        #print(adjList)
        
        #prims algo
        minHeap = [[0, points[0][0], points[0][1]]]
        heapq.heapify(minHeap)
        visited = set()
        minCost = 0 
        while len(visited) < N:
            #get min edge
            d, x, y = heapq.heappop(minHeap)
            #print(d,x,y)
            #if point already visited, continue
            if (x,y) in visited:
                continue
            #add point, update cost and add neighbors to heap
            visited.add((x,y))
            minCost += d
            for nei in adjList[(x,y)]:
                heapq.heappush(minHeap, nei)
            #print(minHeap)
        
        return minCost
            


    
        
151085