三只企鹅 [重链剖分]

$三只企鹅$

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$\color{red}{正解部分}$

若对 $\{p_i\}$ 进行了修改, 总共修改了 $k$ 次, 此时若询问 $x$, 则答案为 $ans = \sum dep_{p_i} + k dep_x - 2\sum dep_{lca(p_i,x)}$ .

考虑维护 $2\sum dep_{lca(p_i,x)}$,

• 修改 $x$, 将 $x$ 到根节点路径上的每个点的标记加上对应的 $dep$ .
• 询问 $x$, 将 $x$ 到根节点路径上的标记求和, 按上式计算即可 .

使用 树剖 维护 .

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$\color{red}{实现部分}$

• 注意树链剖分维护的东西必须以 $dfs$序 为下标 .

#include<bits/stdc++.h>
#define reg register
typedef long long ll;

int read(){
        char c;
        int s = 0, flag = 1;
        while((c=getchar()) && !isdigit(c))
                if(c == '-'){ flag = -1, c = getchar(); break ; }
        while(isdigit(c)) s = s*10 + c-'0', c = getchar();
        return s * flag;
}

const int maxn = 200005;

int N;
int M;
int num0;
int dftim;
int Fa[maxn];
int top[maxn];
int dfn[maxn];
int son[maxn];
int size[maxn];
int head[maxn];

ll Tmp_1;
ll Tmp_2;
ll dis[maxn];
ll fuck[maxn];
ll fa_w[maxn];

struct Edge{ int nxt, to, w; } edge[maxn << 1];

void Add(int from, int to, int w){ edge[++ num0] = (Edge){ head[from], to, w }; head[from] = num0; }

void DFS_1(int k, int fa){
        size[k] = 1, Fa[k] = fa;
        for(reg int i = head[k]; i; i = edge[i].nxt){
                int to = edge[i].to;
                if(to == fa) continue ;
                dis[to] = dis[k] + edge[i].w, fa_w[to] = edge[i].w;
                DFS_1(to, k); size[k] += size[to];
                if(size[son[k]] < size[to]) son[k] = to;
        }
}

void DFS_2(int k, int tp){
        dfn[k] = ++ dftim, top[k] = tp;
        if(son[k]) DFS_2(son[k], tp);
        fuck[dfn[son[k]]] = fa_w[son[k]];
        for(reg int i = head[k]; i; i = edge[i].nxt){
                int to = edge[i].to;
                if(to == son[k] || to == Fa[k]) continue ;
                DFS_2(to, to);
                fuck[dfn[to]] = fa_w[to];
        }
}

struct Segment_Tree{

        struct Node{ int l, r; ll s, w, tg; } T[maxn << 2];

        void Build(int k, int l, int r){
                T[k].l = l, T[k].r = r;
                if(l == r) return T[k].s = fuck[l], void();
                int mid = l+r >> 1;
                Build(k<<1, l, mid), Build(k<<1|1, mid+1, r);
                T[k].s = T[k<<1].s + T[k<<1|1].s;
        }

        void Push_down(const int &k){
                T[k].w += T[k].s * T[k].tg;
                if(T[k].l == T[k].r) return T[k].tg = 0, void();
                T[k<<1].tg += T[k].tg, T[k<<1|1].tg += T[k].tg;
                T[k].tg = 0;
        }

        void Push_up(const int &k){ T[k].w = (T[k<<1].w + T[k<<1|1].w); }

        void Modify(int k, const int &ql, const int &qr, const int &aim){
                int l = T[k].l, r = T[k].r;
                if(T[k].tg) Push_down(k);
                if(r < ql || l > qr) return ;
                if(ql <= l && r <= qr) return T[k].tg += aim, Push_down(k), void();
                Modify(k<<1, ql, qr, aim), Modify(k<<1|1, ql, qr, aim); Push_up(k);
        }

        ll Query(int k, const int &ql, const int &qr){
                int l = T[k].l, r = T[k].r;
                if(T[k].tg) Push_down(k);
                if(r < ql || l > qr) return 0;
                if(ql <= l && r <= qr) return T[k].w;
                return Query(k<<1, ql, qr) + Query(k<<1|1, ql, qr);
        }

} seg_t;

void modify(int k){ while(k) seg_t.Modify(1, dfn[top[k]], dfn[k], 1), k = Fa[top[k]]; }

ll query(int k){ ll s = 0; while(k) s += seg_t.Query(1, dfn[top[k]], dfn[k]), k = Fa[top[k]]; return s; }

int main(){
        N = read(), M = read();
        for(reg int i = 1; i < N; i ++){
                int u = read(), v = read(), w = read();
                Add(u, v, w), Add(v, u, w);   
        }
        DFS_1(1, 0); DFS_2(1, 1), seg_t.Build(1, 1, N);
        while(M --){
                int opt = read(), x = read();
                if(opt == 1) modify(x), Tmp_1 += dis[x], Tmp_2 ++;
                else printf("%lld\n", Tmp_1 + Tmp_2*dis[x] - 2ll*query(x));
        }
        return 0;
}