<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>

struct comparator { 
    int operator() (const pair<int,int> &v1, const pair<int,int> &v2) { 
        return v1.first > v2.first; 
    } 
};

class Solution {
public:
    pair<int,int> distance(int u, int v, vector<vector<int>>& points) {
        vector<int> pu=points[u];
        vector<int> pv=points[v];
        return {abs(pu[0]-pv[0])+abs(pu[1]-pv[1]),v};
    }
    int minCostConnectPoints(vector<vector<int>>& points) {
        priority_queue<pair<int,int>, vector<pair<int,int>>, comparator> pq;
        int n=points.size();
        vector<bool> visited(n,false); 
        unordered_map<int, int> heap_dict;
        for(int i = 0; i < n; ++i) {
            heap_dict[i] = INT_MAX; // Initialize all distances to infinity
        }

        pq.push({0,0});
        int ans=0;
        while(!pq.empty()) {
            auto item = pq.top();
            pq.pop();
            int u=item.second;

            if (visited[u]) continue;

            ans+=item.first;
            visited[u]=true;
            for(int v=0;v<n;v++) {
                if(!visited[v] && distance(u,v,points).first < heap_dict[v]) {
                    pq.push(distance(u,v,points));
                    heap_dict[v]=distance(u,v,points).first;
                }
            }
        }
        return ans;
    }
};
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