<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:
        def findParent(parent_hash_map, point):
            if tuple(point) not in parent_hash_map:
                return tuple(point)
            else:
                if parent_hash_map[tuple(point)] == tuple(point):
                    return tuple(point)
                else:
                    return findParent(parent_hash_map, parent_hash_map[tuple(point)])

        point_hash_map = {}
        distance_array = []
        for i in range(len(points)):
            for j in range(i+1, len(points)):
                distance = abs(points[i][0]-points[j][0]) + abs(points[i][1]-points[j][1])
                distance_array.append(distance)
                try:
                    point_hash_map[distance].append((points[i],points[j]))
                except:
                    point_hash_map[distance] = [(points[i],points[j])]
        
        distance_array.sort()
        
        cost = 0
        edge = 0
        parent_hash_map = {}
        for i in distance_array:
            for point1, point2 in point_hash_map[i]:
                point1_parent = findParent(parent_hash_map, point1)
                point2_parent = findParent(parent_hash_map, point2)
                if point1_parent != point2_parent:
                    parent_hash_map[point1_parent] = point2_parent
                    cost += i
                    edge += 1
                if edge == len(points)-1:
                    return cost

        return cost
        
73159