Loj #139

* 树链剖分模板题
* 由于存在换根操作
* 对所有关于节点 u 的修改和查询操作进行分类讨论
* 若 Root 在 u 的子树中，则不处理 u 所在的 Root 的那颗子树
* 否则不会有影响
* 寻找 Root 所在的那颗子树的根可以用倍增求

#include <bits/stdc++.h>

const int N = 1e5 + 10;

#define LL long long

int topp[N], fa[N], size[N], son[N], deep[N], tree[N], lst[N], rst[N], bef[N], data[N];
int f[N][30];
int Tree;
LL W[N << 2], F[N << 2], S[N << 2];
struct Node {
    int u, v, nxt;
} G[N << 1];
int now, head[N];
int n, m, Root;

int opt, T;

#define gc getchar()

inline int read() {
     int x = 0; char c = gc;
    while(c < '0' || c > '9') c = gc;
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = gc;
    return x;
}

void Add(int u, int v) {G[++ now].v = v; G[now].nxt = head[u]; head[u] = now;}

void Dfs_1(int u, int f_, int dep) {
    fa[u] = f_, deep[u] = dep, size[u] = 1;
    for(int i = head[u]; ~ i; i = G[i].nxt) {
        int v = G[i].v;
        if(v == f_) continue;
        f[v][0] = u;
        Dfs_1(v, u, dep + 1);
        size[u] += size[v];
        if(size[son[u]] < size[v]) son[u] = v;
    }
}

void Dfs_2(int u, int tp) {
    topp[u] = tp, tree[u] = ++ Tree, bef[Tree] = u, lst[u] = Tree;
    if(!son[u]) {
        rst[u] = Tree; return ;
    }
    Dfs_2(son[u], tp);
    for(int i = head[u]; ~ i; i = G[i].nxt) {
        int v = G[i].v;
        if(v != fa[u] && v != son[u]) Dfs_2(v, v);
    }
    rst[u] = Tree;
}

void Before() {
    for(int i = 1; (1 << i) <= n; i ++)
        for(int j = 1; j <= n; j ++)
            if(f[j][i - 1]) f[j][i] = f[f[j][i - 1]][i - 1];
}

#define lson jd << 1
#define rson jd << 1 | 1

void Build_tree(int l, int r, int jd) {
    S[jd] = (r - l + 1);
    if(l == r) {
        W[jd] = data[bef[l]];
        return ;
    }
    int mid = (l + r) >> 1;
    Build_tree(l, mid, lson);
    Build_tree(mid + 1, r, rson);
    W[jd] = W[lson] + W[rson];
}

void Pushdown(int jd) {
    if(!F[jd]) return ;
    F[lson] += F[jd];
    F[rson] += F[jd];
    W[lson] += (S[lson] * F[jd]);
    W[rson] += (S[rson] * F[jd]);
    F[jd] = 0;
} 

void Sec_G(int l, int r, int jd, int x, int y, int num) {
    if(x <= l && r <= y) {
        F[jd] += num;
        W[jd] += (S[jd] * num);
        return ;
    }
    Pushdown(jd);
    int mid = (l + r) >> 1;
    if(x <= mid) Sec_G(l, mid, lson, x, y, num);
    if(y >  mid) Sec_G(mid + 1, r, rson, x, y, num);
    W[jd] = W[lson] + W[rson];
}

void Sec_G_imp(int x, int y, int num) {
    int tpx = topp[x], tpy = topp[y];
    while(tpx != tpy) {
        if(deep[tpx] < deep[tpy]) std:: swap(tpx, tpy), std:: swap(x, y);
        Sec_G(1, n, 1, tree[tpx], tree[x], num);
        x = fa[tpx];
        tpx = topp[x];
    }
    if(deep[x] < deep[y]) std:: swap(x, y);
    Sec_G(1, n, 1, tree[y], tree[x], num);
    return ;
}

inline int Find(int x, int y) {
    int dy = deep[y], dx = deep[x];
    int del = deep[y] - deep[x] - 1;
    for(int i = 0; (1 << i) <= del; i ++)
        if(del & (1 << i)) y = f[y][i];
    return y;
}

LL Answer;

void Sec_A(int l, int r, int jd, int x, int y) {
    if(x <= l && r <= y) {
        Answer += W[jd];
        return ;
    }
    Pushdown(jd);
    int mid = (l + r) >> 1;
    if(x <= mid) Sec_A(l, mid, lson, x, y);
    if(y > mid)  Sec_A(mid + 1, r, rson, x, y);
}

LL Sec_A_imp(int x, int y) {
    int tpx = topp[x], tpy = topp[y];
    LL ret = 0;
    while(tpx != tpy) {
        if(deep[tpx] < deep[tpy]) std:: swap(tpx, tpy), std:: swap(x, y);
        Answer = 0;
        Sec_A(1, n, 1, tree[tpx], tree[x]);
        ret += Answer;
        x = fa[tpx];
        tpx = topp[x];
    }
    if(deep[x] < deep[y]) std:: swap(x, y);
    Answer = 0;
    Sec_A(1, n, 1, tree[y], tree[x]);
    ret += Answer;
    return ret;
}

int main() {
    Root = 1;
    n = read();
    for(int i = 1; i <= n; i ++) head[i] = -1;
    for(int i = 1; i <= n; i ++) data[i] = read();
    for(int i = 1; i < n; i ++) {
        int u = read();
        Add(i + 1, u), Add(u, i + 1);
    }
    Dfs_1(1, 0, 1);
    Dfs_2(1, 1);
    Build_tree(1, n, 1);
    Before();
    int t = read();
    for(T = 1; T <= t; T ++) {
        opt = read();
        if(opt == 1) Root = read();
        else if(opt == 2) {
            int u = read(), v = read(), x = read();
            Sec_G_imp(u, v, x);
        } else if(opt == 3) {
            int u = read(), x = read();
            if(Root == u) {
                Sec_G(1, n, 1, 1, n, x);
                continue;
            }
            if(lst[u] <= tree[Root] && tree[Root] <= rst[u]) {
                Sec_G(1, n, 1, 1, n, x);
                int Use_son = Find(u, Root);
                Sec_G(1, n, 1, lst[Use_son], rst[Use_son], -x);
            } else Sec_G(1, n, 1, lst[u], rst[u], x);
        } else if(opt == 4) {
            int x = read(), y = read();
            printf("%lld\n", Sec_A_imp(x, y));
        } else {
            int u = read();
            if(Root == u) {
                Answer = 0;
                Sec_A(1, n, 1, 1, n);
                printf("%lld\n", Answer);
                continue;
            }
            LL Now_ans = 0;
            if(lst[u] <= tree[Root] && tree[Root] <= rst[u]) {
                Answer = 0;
                Sec_A(1, n, 1, 1, n);
                Now_ans += Answer;
                int Use_son = Find(u, Root);
                Answer = 0;
                Sec_A(1, n, 1, lst[Use_son], rst[Use_son]);
                Now_ans -= Answer;
            } else {
                Answer = 0;
                Sec_A(1, n, 1, lst[u], rst[u]);
                Now_ans += Answer;
            }
            printf("%lld\n", Now_ans);
        }
    }
    return 0;
}