<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 Cordinates {
    public:
    int x;
    int y;

    Cordinates(int x, int y){
        this->x = x;
        this->y = y;
    }
};

class Node {
    public:
    Cordinates selfCordinates;
    // Cordinates parentCordinates;
    int weight;

    Node(int weight, Cordinates selfCordinates): selfCordinates(selfCordinates), weight(weight) {}
};

struct Comp {
     bool operator()(const Node &a, const Node &b){
        return a.weight > b.weight;
     }
};

class Solution {
public:
    int manhattanDistance(int xi, int yi, int xj, int yj){
        return abs(xi-yi) + abs(xj-yj);
    }

    int minCostConnectPoints(vector<vector<int>>& points) {

        int totalCost = 0;
        map <pair<int,int>, bool> visitedMap;
        map <pair<int,int>, vector<pair<int, pair<int,int>>>> adjMap;
        priority_queue<Node, vector<Node>, Comp> pq;

        for(int i=0;i<points.size();i++){
            for(int j=0;j<points.size();j++){
                if(i == j)
                    continue;

                int xi = points[i][0];
                int yi = points[j][0];
                int xj = points[i][1];
                int yj = points[j][1];

                int distance = manhattanDistance(xi, yi, xj, yj);
                // cout<<"Distance btw = "<<xi<<","<<xj<<" and "<<yi<<","<<yj<<" is "<<distance<<endl;
                adjMap[{xi,xj}].push_back({distance, {yi,yj}});
                adjMap[{yi,yj}].push_back({distance, {xi,xj}});
            }
        }

        auto point = points[0];
        Node startNode = Node(0, Cordinates(point[0], point[1]));
        pq.push(startNode);

        while(!pq.empty()){
            Node topNode = pq.top();
            pq.pop();

            int weight = topNode.weight;
            int x = topNode.selfCordinates.x;
            int y = topNode.selfCordinates.y;

            if(visitedMap.find({x,y}) != visitedMap.end())
                continue;

            visitedMap[{x,y}] = true;
            totalCost += weight;

            for(auto nbrp : adjMap[{x,y}]){
                int distance = nbrp.first;
                int nbrx = nbrp.second.first;
                int nbry = nbrp.second.second;

                if(visitedMap.find({nbrx,nbry}) == visitedMap.end()){
                    pq.push(Node(distance, Cordinates(nbrx, nbry)));
                }
            }
        }

        return totalCost;
    }
};
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