<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>

#define pii pair<int, int>

class Solution {
public:
    vector<int> parent;
    int minCostConnectPoints(vector<vector<int>>& points) {
        int n = points.size();
        
        parent.resize(n);
        vector<vector<int>> edges;

        for(int i=0; i<n; i++) {
            parent[i] = i;
            for(int j=i+1; j<n; j++) {
                int dist = getDistance(points[i], points[j]);
                edges.push_back({dist, i, j});
            }
        }
        sort(edges.begin(), edges.end());

        int cost = 0, added = 0;
        for(int i=0; i<edges.size() && added != n-1; i++) {
            if(unionFind(edges[i][1], edges[i][2])) {
                cost += edges[i][0];
                added++;
            }
        }
        return cost;
    }
    
    int find(int x) {
        if(x == parent[x]) return x;
        return parent[x] = find(parent[x]);
    }
    
    bool unionFind(int x, int y) {
        int px = find(x), py = find(y);
        if(px == py) return false;
        parent[px] = py;
        return true;
    }

    int getDistance(vector<int>& pointA, vector<int>& pointB) {
        return abs(pointA[0] - pointB[0]) + abs(pointA[1] - pointB[1]);
    }
};
182035