<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 MST(vector<vector<int>> graph){
        int res = 0;
        int V = graph.size();
        vector<int> key(V, INT_MAX);
        vector<bool> mstSet(V, false);
        key[0] = 0;

        for(int count = 0; count < V; count++){
            //Select the minimum Edge
            int  u = -1;
            for(int i = 0; i < V; i++){
                if(!mstSet[i] && (u == -1 || key[i] < key[u]))
                    u = i;
            }
            //Add the edge into the mstSet
            mstSet[u] = true;
            res += key[u];

            //update all the edges
            for(int v = 0; v < V; v++){
                if(graph[u][v] != 0 && mstSet[v] == false)
                    key[v] = min(key[v], graph[u][v]);
            }
        }
        return res;
    }

    int minCostConnectPoints(vector<vector<int>>& points) {
        int V =  points.size();
        vector<vector<int>> graph;
        for(int i = 0; i < V; i++){
            vector<int> temp;
            for(int j = 0; j < V; j++){
                temp.push_back(0);
            }
            graph.push_back(temp);
        }

        for(int i = 0; i < V; i++){
            for(int j = i+1; j < V; j++){
                int x1 = points[i][0], y1 = points[i][1];
                int x2 = points[j][0], y2 = points[j][1];
                int dist = abs(x1 - x2) + abs(y1 - y2);
                graph[i][j] = dist;
                graph[j][i] = dist;
            }
        }

        int res  = MST(graph);
        return res;
    }
};
91025