<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 {
public:
int minCostConnectPoints(vector<vector<int>>& points)
{
	int n = points.size();
	if(n < 2) return 0;
	std::vector<std::vector<std::pair<int, int>>> adjList(n);
	for(int i=0; i<n; i++)
	{
		for(int j = i+1; j<n; j++)
		{
			int distance = std::abs(points[i][0] - points[j][0]) + std::abs(points[i][1] - points[j][1]);
			adjList[i].push_back({j, distance});
			adjList[j].push_back({i, distance});
		}
	}

	int mstSum = 0;
	std::vector<bool> visited(n, false);
	std::vector<int> parents(n, -1);
	std:priority_queue<vector<int>, vector<vector<int>>, greater<vector<int>>> minHeap;

	minHeap.push({0, 0, -1});

	while(!minHeap.empty())
	{
		vector<int> top = minHeap.top();
		minHeap.pop();
		int weight = top[0];
		int node = top[1];
		int parent = top[2];
		if(!visited[node])
		{
			visited[node] = true;
			parents[node] = parent;
			mstSum += weight;
			for(pair<int, int> neighbour : adjList[node])
            {
                if(!visited[neighbour.first])
				    minHeap.push({neighbour.second, neighbour.first, node});
            }
		}
	}
	return mstSum;
}



};
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