<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:
    class UnionFind {
    public:
        UnionFind(int size) {
            m_data.resize(size);
            std::iota(m_data.begin(), m_data.end(), 0);
            m_ranks.resize(size, 0);
        }

        int find(int node) {
            if (node == m_data[node]) {
                return node;
            }
            return m_data[node] = find(m_data[node]);
        }

        void unionSet(int nodeA, int nodeB) {
            int rootA = find(nodeA);
            int rootB = find(nodeB);

            if (rootA != rootB) {
                if (m_ranks[rootA] > m_ranks[rootB]) {
                    m_data[rootB] = rootA;
                }
                else if (m_ranks[rootA] < m_ranks[rootB]) {
                    m_data[rootA] = rootB;
                }
                else {
                    m_data[rootB] = rootA;
                    ++m_ranks[rootA];
                }
            }
        }

        bool isConnected(int nodeA, int nodeB) {
            return find(nodeA) == find(nodeB);
        }
    private:
        std::vector<int> m_data;
        std::vector<int> m_ranks;
    };
    class Point {
    public:
        Point(int x, int y, int index) : m_x(x), m_y(y), m_index(index) {}
        int m_x, m_y, m_index;
    };
    class Edge {
    public:
        Edge(int len, Point &a, Point &b)
            : m_length(len), m_pointA(a), m_pointB(b) {}
    
        int m_length;
        Point m_pointA, m_pointB;
    };
    int minCostConnectPoints(vector<vector<int>>& points) {
        int n = static_cast<int>(points.size());
        auto comp = [](const Edge &a, const Edge &b) {
            return a.m_length > b.m_length;
        };
        std::priority_queue<Edge, std::vector<Edge>, decltype(comp)> pq(comp);
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                if (i == j) continue;
                int len  = std::abs(points[i][0] - points[j][0]) + std::abs(points[i][1] - points[j][1]);
                Point pointA(points[i][0], points[i][1], i);
                Point pointB(points[j][0], points[j][1], j);
                pq.emplace(len, pointA, pointB);
            }
        }

        UnionFind uf(n);
        int remainEdges = n - 1;
        int cost = 0;
        while (!pq.empty() && remainEdges) {
            auto edge = pq.top();
            pq.pop();

            if (!uf.isConnected(edge.m_pointA.m_index, edge.m_pointB.m_index)) {
                uf.unionSet(edge.m_pointA.m_index, edge.m_pointB.m_index);
                --remainEdges;
                cost += edge.m_length;
            }
        }

        return cost;
    }
};
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