<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>

struct union_find {
    using T = unsigned long long;
    std::vector<T> p, r;

    union_find(T n) {
        p.resize(n), r.resize(n);
        std::iota(std::begin(p), std::end(p), 0);
        std::fill(std::begin(r), std::end(r), 1);
    }

    T find(T x) {
        return p[x] = (x == p[x] ? x : find(p[x]));
    }

    bool merge(T x, T y) {
        x = find(x), y = find(y);
        if (x == y) return false;

        if (r[x] < r[y]) std::swap(x, y);
        r[x] += r[y], p[y] = x;
        return true;
    }
};

struct kruskal {
    using T = unsigned long long;
    using C = unsigned long long;
    using edge = std::tuple<T, T, C>;
    static inline auto edge_lt = [](edge const &a, edge const &b) -> bool {
        return get<2>(a) < get<2>(b);
    };

    std::vector<edge> e;
    std::vector<T> v;

    kruskal(std::vector<T>& ve, std::vector<edge>& ed) {
        v = std::vector<T>(ve), e = std::vector<edge>(ed);
    }

    std::vector<edge> mst() {
        union_find uf(v.size());
        std::sort(std::begin(e), std::end(e), edge_lt);

        std::vector<edge> mst;

        for (edge a : e) {
            if (uf.find(get<0>(a)) != uf.find(get<1>(a)))
                uf.merge(get<0>(a), get<1>(a)), mst.push_back(a);
        }

        return mst;
    }

    T mst_cost() {
        std::vector<edge> tree = mst(); T cost = 0;
        for (edge a : tree) cost += get<2>(a);
        return cost;
    }
};

class Solution {
public:
    int minCostConnectPoints(vector<vector<int>>& points) {
        using edge = std::tuple<unsigned long long, unsigned long long, unsigned long long>;
        vector<edge> edge_list(points.size() * points.size() + 1);
        vector<unsigned long long> vertices(points.size());

        for (int i = 0, e = 0; i < points.size(); i++) {
            vertices[i] = i;

            for (int j = 0; j < points.size(); j++) {
                int dist = manhattan(points[i][0], points[i][1], points[j][0], points[j][1]);
                edge_list[e++] = edge(i, j, dist);
            }
        }

        kruskal krus(vertices, edge_list);
        return krus.mst_cost();
        // return 0;
    }

    int manhattan(int x1, int y1, int x2, int y2) {
        return abs(x1 - x2) + abs(y1 - y2);
    }
};
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