<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
class Solution:
    def minCostConnectPoints(self, points: List[List[int]]) -> int:
        """
        THe ask is to find the MST with these points
        lets try using Prims and 
        also write the same using Kruskal's
        """
        def get_manhattan_dist(p1, p2):
            x1, y1 = p1
            x2, y2 = p2
            return abs(x2 - x1) + abs(y2 - y1)

        # list of edges
        total_cost = 0
        min_heap = []
        visit = set()
        visit.add(tuple(points[0]))
        for p in points[1:]:
            d = get_manhattan_dist(points[0], p)
            heapq.heappush(min_heap, (d, points[0], p))

        while min_heap:
            d, n1, n2 = heapq.heappop(min_heap)
            if tuple(n2) in visit:
                continue
            
            total_cost += d
            print("point=, cost", (n1,n2), total_cost, d)
            visit.add(tuple(n2))
            # get neihbours of d
            for p in points:
                if p == n2:
                    continue
                if tuple(p) in visit:
                    continue
                heapq.heappush(min_heap, (get_manhattan_dist(n2, p), n2, p))
        print("visit=", visit)
        return total_cost


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