GYM 101889I（mst+lca）

最小生成树上倍增询问裸的。

const int maxn = 2e5 + 5;
int n, m, q;
//图
struct Edge {
    int u, v;
    ll cost;

    bool operator < (const Edge &rhs) const {
        return cost < rhs.cost;
    }
}e[maxn];
map<P, ll> mp;
//最小生成树
int fa[maxn];
vector<int> vc[maxn];
ll mst;
//树上倍增
int f[maxn][20], T, d[maxn];
ll dis[maxn][20];

int getf(int v) {
    return v == fa[v] ? v : fa[v] = getf(fa[v]);
}

void kruscal() {
    rep(i, 1, n)    fa[i] = i;
    sort(e + 1, e + 1 + m);

    rep(i, 1, m) {
        int t = getf(e[i].u), p = getf(e[i].v);
        if (t != p) {
            int u = e[i].u, v = e[i].v;
            vc[u].push_back(v);
            vc[v].push_back(u);
            mst += e[i].cost;
            fa[t] = p;
        }
    }
}

void bfs() {
    T = (int)(log(n) / log(2)) + 1;
    queue<int> Q;
    Q.push(1), d[1] = 1;

    while (!Q.empty()) {
        int x = Q.front(); Q.pop();
        for (auto y : vc[x]) {
            if (d[y])   continue;

            Q.push(y);
            f[y][0] = x;
            d[y] = d[x] + 1;
            dis[y][0] = mp[P(y, x)];

            rep(i, 1, T) {
                f[y][i] = f[f[y][i - 1]][i - 1];
                dis[y][i] = max(dis[f[y][i - 1]][i - 1], dis[y][i - 1]);
            }
        }
    }
}

ll lca(int x, int y) {
    ll ret = 0;
    if (d[x] > d[y])    swap(x, y);

    irep(i, T, 0)
        if (d[f[y][i]] >= d[x]) {
            ret = max(ret, dis[y][i]);
            y = f[y][i];
        }

    if (x == y) return ret;

    irep(i, T, 0)
        if (f[y][i] != f[x][i]) {
            ret = max(ret, max(dis[y][i], dis[x][i]));
            y = f[y][i], x = f[x][i];
        }

    return max(ret, max(dis[y][0], dis[x][0]));
}

int main() {
    read(n), read(m);
    rep(i, 1, m) {
        read(e[i].u);
        read(e[i].v);
        read(e[i].cost);
        mp[P(e[i].u, e[i].v)] = mp[P(e[i].v, e[i].u)] = e[i].cost;
    }

    kruscal();
    bfs();
    
    for (read(q); q; q--) {
        int u, v;
        read(u), read(v);
        writeln(mst - lca(u, v) + mp[P(u, v)]);
    }
    return 0;
}

GYM 101889I（mst+lca）

原文：https://www.cnblogs.com/AlphaWA/p/10673943.html