<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 n = points.size();
        vector<vector<int>> weights(n, vector<int>(n));
        vector<Element> d;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                int distance = abs(points[i][0] - points[j][0]) + abs(points[i][1] - points[j][1]);
                Element element;
                element.distance = distance;
                element.point1 = i;
                element.point2 = j;
                d.push_back(element);
            }
        }
        sort(d.begin(), d.end(), [](const Element& a, const Element& b) {
            return a.distance < b.distance;
        });
        UF spanning(n);
        int res = 0;
        int index = 0;
        while (spanning.get_count() != 1) {
            Element edge = d[index];
            index ++;
            if (!spanning.connected(edge.point1, edge.point2)) {
                spanning.unite(edge.point1, edge.point2);
                res += edge.distance;
            }
        }
        return res;
    }
private:
    struct Element {
        int distance;
        int point1;
        int point2;
    };
    // struct ElementCompare {
    //     bool operator() (Element element1, Element element2) {
    //         return element1.distance < element2.distance;
    //     }
    // };
    class UF {
    public:
        UF(int n) {
            count = n;
            parent = new vector<int>(n);
            for (int i = 0; i < n; i++) {
                (*parent)[i] = i;
            }
        }

        void unite(int p, int q) {
            int rootP = find(p);
            int rootQ = find(q);
            if (rootP == rootQ) return;
            (*parent)[rootP] = rootQ;
            count--;
        }

        int find(int x) {
            if ((*parent)[x] != x) {
                (*parent)[x] = find((*parent)[x]);
            }
            return (*parent)[x];
        }

        int get_count() {
            return count;
        }

        bool connected(int p, int q) {
            int rootP = find(p);
            int rootQ = find(q);
            return rootP == rootQ;
        }
    private:
        int count;
        vector<int>* parent;

    };
};
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