<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 minCostConnectPoints(vector<vector<int>>& points) {
        int res = 0;

        vector<vector<int>> edges;
        // identify edges
        for (int i = 0; i < points.size(); i++) {
            for (int j = i + 1; j < points.size(); j++) {
                auto p1 = points[i];
                auto p2 = points[j];
                int weight = abs(p1[0] - p2[0]) + abs(p1[1] - p2[1]);
                edges.push_back({weight, i, j});
            }
        }

        sort(edges.begin(), edges.end(), compareWeights);

        // use kruskal's algorithm to find mst
        struct DSU dsu(points.size());
        for (auto& e : edges) {
            int weight = e[0];
            int node1 = e[1];
            int node2 = e[2];
            if (dsu.find(node1) != dsu.find(node2)) {
                res += weight;
                dsu.unite(node1, node2);
            }
        }
        return res;
    }
private:
    struct DSU {
        DSU(int n) {
            for (int i = 0; i < n; i++) {
                this->parents.push_back(i);
                this->rank.push_back(1);
            }
        }
        int find(int idx) {
            if (idx != parents[idx]) {
                parents[idx] = find(parents[idx]);
            }
            return parents[idx];
        }
        void unite(int a, int b) {
            a = find(a);
            b = find(b);

            if (rank[a] > rank[b]) {
                parents[b] = a;
            } else if (rank[b] > rank[a]) {
                parents[a] = b;
            } else {
                parents[b] = a;
                rank[a]++;
            }
        }
        vector<int> parents;
        vector<int> rank;
    };
    static bool compareWeights(const vector<int>& a, const vector<int>& b) {
        return a[0] < b[0];
    }
};
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