<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:
    struct Edge{
        int from;
        int to;
        int cost;
        Edge(int _from, int _to, int _cost): from(_from), to(_to), cost(_cost){}
    };

    int uf[1000004];
    int depth[1000004];

    int getRoot(int node){
        while(node != uf[node]){
            node = uf[node];
        }
        return node;
    }

    void link(int node1, int node2){
        if(depth[node1] == depth[node2]){
            uf[node2] = node1;
            depth[node1] += 1;
        }
        else if(depth[node1] < depth[node2]){
            uf[node2] = node1;
        }
        else{
            uf[node1] = node2;
        }
    }

    int minCostConnectPoints(vector<vector<int>>& points) {
        int n = points.size();
        vector<Edge> e;
        for(int i = 0; i < n; i++){
            for(int j = i + 1; j < n; j++){
                int c = abs(points[i][0] - points[j][0]) + abs(points[i][1] - points[j][1]);
                e.push_back(Edge(i, j, c));
            }
        }
        sort(e.begin(), e.end(), [](Edge e1, Edge e2){return e1.cost < e2.cost;});
        int m = e.size();
        for(int i = 0; i < n; i++){
            uf[i] = i;
            depth[i] = 0;
        }
        int ans = 0;
        for(int i = 0; i < m; i++){
            //cout<<e[i].from<<" "<<e[i].to<<" "<<e[i].cost<<endl;
            int node1 = getRoot(e[i].from);
            int node2 = getRoot(e[i].to);
            if(node1 != node2){
                link(node1, node2);
                ans += e[i].cost;
            }
        }
        return ans;
    }
};
71865