【图论】KruskalMST算法

适用于无向图。其实找出来的是一片最小生成森林来的，并不一定是树，取决于原图是否连通。

int n, m;

const int MAXM = 200000 + 10;

struct DisjointSet {

    static const int MAXN = 200000 + 10;
    int fnd[MAXN], siz[MAXN];

    void Init(int n) {
        for(int i = 1; i <= n; i++)
            fnd[i] = i, siz[i] = 1;
    }

    int Find(int x) {
        return x == fnd[x] ? x : fnd[x] = Find(fnd[x]);
    }

    bool Merge(int x, int y) {
        x = Find(x), y = Find(y);
        if(x == y)
            return 0;
        if(siz[x] < siz[y])
            swap(x, y);
        fnd[y] = x;
        siz[x] += siz[y];
        return 1;
    }

} dsu;


struct Edge {
    int u, v, w;
    bool operator<(const Edge& edge)const {
        return w < edge.w;
    }
} edge[MAXM];

ll mst() {
    for(int i = 1; i <= m; ++i)
        edge[i] = {u, v, w};
    sort(edge + 1, edge + 1 + m);
    dsu.Init(n);
    ll res = 0;
    for(int i = 1; i <= m; ++i) {
        int u = edge[i].u;
        int v = edge[i].v;
        int w = edge[i].w;
        if(dsu.Merge(u, v))
            res += w;
    }
    return res;
}