树链剖分+线段树 bzoj1036 树的统计Count

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题意：节点更新，路径求最大值以及求和。

思路：树链剖分，要注意单点更新和边更新的区别。然后就是在建线段树的时候，应该是用重新编号的新编号去建立的，刚开始一直没注意这个地方，然后调bug也调不出来，后来看了好久才看出来，以后还真要注意一下。

#include<bits/stdc++.h>
#define fuck(x) cout<<"["<<x<<"]"
#define FIN freopen("input.txt","r",stdin)
#define FOUT freopen("output.txt","w+",stdout)
using namespace std;
typedef long long LL;
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1

const int MX = 3e4 + 5;
const int INF = 0x3f3f3f3f;

struct Edge {
    int v, nxt;
} E[MX << 2];
int Head[MX], h_r;
void edge_init() {
    h_r = 0;
    memset(Head, -1, sizeof(Head));
}
void edge_add(int u, int v) {
    E[h_r].v = v;
    E[h_r].nxt = Head[u];
    Head[u] = h_r++;
}

int SUM[MX << 2];
int MAX[MX << 2], A[MX], B[MX];
void push_up(int rt) {
    SUM[rt] = SUM[rt << 1] + SUM[rt << 1 | 1];
    MAX[rt] = max(MAX[rt << 1], MAX[rt << 1 | 1]);
}
void build(int l, int r, int rt) {
    if(l == r) {
        SUM[rt] = A[l];
        MAX[rt] = A[l];
        return;
    }
    int m = (l + r) >> 1;
    build(lson); build(rson);
    push_up(rt);
}
int query_max(int L, int R, int l, int r, int rt) {
    if(L <= l && r <= R) {
        return MAX[rt];
    }
    int m = (l + r) >> 1, ret = -INF;
    if(L <= m) ret = max(ret, query_max(L, R, lson));
    if(R > m) ret = max(ret, query_max(L, R, rson));
    return ret;
}
int query_sum(int L, int R, int l, int r, int rt) {
    if(L <= l && r <= R) {
        return SUM[rt];
    }
    int m = (l + r) >> 1; LL ret = 0;
    if(L <= m) ret += query_sum(L, R, lson);
    if(R > m) ret += query_sum(L, R, rson);
    return ret;
}
void update(int x, int d, int l, int r, int rt) {
    if(l == r) {
        SUM[rt] = d;
        MAX[rt] = d;
        return;
    }
    int m = (l + r) >> 1;
    if(x <= m) update(x, d, lson);
    else update(x, d, rson);
    push_up(rt);
}

int fa[MX], top[MX], siz[MX], son[MX], dep[MX], id[MX], rear;
void DFS1(int u, int f, int d) {
    fa[u] = f; dep[u] = d;
    son[u] = 0; siz[u] = 1;
    for(int i = Head[u]; ~i; i = E[i].nxt) {
        int v = E[i].v;
        if(v == f) continue;
        DFS1(v, u, d + 1);
        siz[u] += siz[v];
        if(siz[son[u]] < siz[v]) {
            son[u] = v;
        }
    }
}
void DFS2(int u, int tp) {
    top[u] = tp;
    id[u] = ++rear;
    if(son[u]) DFS2(son[u], tp);
    for(int i = Head[u]; ~i; i = E[i].nxt) {
        int v = E[i].v;
        if(v == fa[u] || v == son[u]) continue;
        DFS2(v, v);
    }
}
void HLD_presolve() {
    rear = 0;
    DFS1(1, 0, 1);
    DFS2(1, 1);
    for(int i = 1; i <= rear; i++) {
        A[id[i]] = B[i];
    }
    build(1, rear, 1);
}
void HLD_update(int x, int d) {
    update(id[x], d, 1, rear, 1);
}
int HLD_query(int u, int v, bool _max) {
    int tp1 = top[u], tp2 = top[v];
    int Max = -INF, sum = 0;
    while(tp1 != tp2) {
        if(dep[tp1] < dep[tp2]) {
            swap(u, v);
            swap(tp1, tp2);
        }
        if(_max) Max = max(Max, query_max(id[tp1], id[u], 1, rear, 1));
        else sum += query_sum(id[tp1], id[u], 1, rear, 1);
        u = fa[tp1]; tp1 = top[u];
    }

    if(dep[u] > dep[v]) swap(u, v);
    if(_max) {
        Max = max(Max, query_max(id[u], id[v], 1, rear, 1));
        return Max;
    }
    sum += query_sum(id[u], id[v], 1, rear, 1);
    return sum;
}

int main() {
    int n; //FIN;
    while(~scanf("%d", &n)) {
        edge_init();
        for(int i = 1; i <= n - 1; i++) {
            int u, v;
            scanf("%d%d", &u, &v);
            edge_add(u, v);
            edge_add(v, u);
        }
        for(int i = 1; i <= n; i++) {
            scanf("%d", &B[i]);
        }
        HLD_presolve();

        int Q, a, b; char op[10];
        scanf("%d", &Q);
        while(Q--) {
            scanf("%s%d%d", op, &a, &b);

            if(op[0] == 'C') HLD_update(a, b);
            else if(op[0] == 'Q' && op[1] == 'M') printf("%d\n", HLD_query(a, b, true));
            else printf("%d\n", HLD_query(a, b, false));
        }
    }
    return 0;
}