P2590 [ZJOI2008]树的统计

题目链接：https://www.luogu.org/problem/P2590

注意这题有负权。 （不然你就只能跑10分！）

#include <stdio.h>
#include <algorithm>
#include <iostream>
#include <stdbool.h>
#include <stdlib.h>
#include <string>
#include <string.h>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <math.h>

#define INF 0x3f3f3f3f
#define LL long long
using namespace std;

const int maxn = 300100;

struct Edge{
    int to,next;
}edge[maxn*4];

int head[maxn],tot;

void add_edge(int u,int v){
    edge[++tot] = Edge{v,head[u]};
    head[u] = tot;
}

int v[maxn];
int fa[maxn];
int siz[maxn];
int dep[maxn];
int son[maxn];

void dfs1(int u,int f){
    fa[u] = f;
    dep[u] = dep[f] + 1;
    siz[u] = 1;
    int maxsize = -1;
    for (int i=head[u];~i;i=edge[i].next){
        int v = edge[i].to;
        if (v == f){
            continue;
        }
        dfs1(v,u);
        siz[u] += siz[v];
        if (siz[v] > maxsize){
            maxsize = siz[v];
            son[u] = v;
        }
    }
}


int tim;
int dfn[maxn];
int top[maxn];
int w[maxn];

void dfs2(int u,int t){
    dfn[u] = ++tim;
    top[u] = t;
    w[tim] = v[u];
    if (!son[u]){
        return ;
    }
    dfs2(son[u],t);
    for (int i=head[u];~i;i=edge[i].next){
        int v = edge[i].to;
        if (v == fa[u] || v == son[u]){
            continue;
        }
        dfs2(v,v);
    }
}


struct segment_tree{
    int l,r;
    LL val;
    LL maxval;
    int lazy;
}tree[maxn*4];

void pushup(int nod){
    tree[nod].val = (tree[nod<<1].val + tree[(nod<<1)+1].val);
    tree[nod].maxval = max(tree[nod<<1].maxval,tree[(nod<<1)+1].maxval);
}

void build (int l,int r,int nod){
    tree[nod].l = l;
    tree[nod].r = r;
    if (l == r){
        tree[nod].lazy = 0;
        tree[nod].val = w[l];
        tree[nod].maxval = w[l];
        return ;
    }
    int mid = (l + r) >> 1;
    build(l,mid,nod<<1);
    build(mid+1,r,(nod<<1)+1);
    pushup(nod);
}

void modify(int k,int value,int nod=1){
    if (tree[nod].l == k && tree[nod].r == k){
        tree[nod].val = tree[nod].maxval = value;
        return ;
    }
    int mid = (tree[nod].l + tree[nod].r) >> 1;
    if (k <= mid){
        modify(k,value,nod<<1);
    }
    else
        modify(k,value,(nod<<1)+1);
    pushup(nod);
}


LL query(int x,int y,int k){
    int l = tree[k].l,r = tree[k].r;
    if (x <= l && y >= r){
        return tree[k].val;
    }
    int mid = (l + r) >> 1;
    LL sum = 0;
    if (x <= mid){
        sum += query(x,y,k<<1);
    }
    if (y > mid){
        sum += query(x,y,(k<<1)+1);
    }
    return sum;
}

LL query2(int x,int y,int k){
    int l = tree[k].l,r = tree[k].r;
    if (x <= l && y >= r){
        return tree[k].maxval;
    }
    int mid = (l + r) >> 1;
    LL sum = -INF;
    if (x <= mid){
        sum = max(sum,query2(x,y,k<<1));
    }
    if (y > mid){
        sum = max(query2(x,y,(k<<1)+1),sum);
    }
    return sum;
}

LL query_max(int x,int y){
    LL ret = -INF;
    while (top[x] != top[y]){
        if (dep[top[x]] < dep[top[y]])
            swap(x,y);
        ret = max(ret,query2(dfn[top[x]],dfn[x],1));
        x = fa[top[x]];
    }
    if (dep[x] > dep[y])
        swap(x,y);
    ret = max(ret,query2(dfn[x],dfn[y],1));
    return ret;
}

LL query_sum(int x,int y){
    LL ret = 0;
    while (top[x] != top[y]){
        if (dep[top[x]] < dep[top[y]])
            swap(x,y);
        ret += query(dfn[top[x]],dfn[x],1);
        x = fa[top[x]];
    }
    if (dep[x] > dep[y])
        swap(x,y);
    ret += query(dfn[x],dfn[y],1);
    return ret;
}

int main(){
    int n;
    scanf("%d",&n);
    memset(head,-1, sizeof(head));
    for (int i=1;i<=n-1;i++){
        int x,y;
        scanf("%d%d",&x,&y);
        add_edge(x,y);
        add_edge(y,x);
    }
    for (int i=1;i<=n;i++){
        scanf("%d",&v[i]);
    }
    dfs1(1,1);
    dfs2(1,1);
    build(1,n,1);
    int T;
    scanf("%d",&T);
    while (T--){
        char s[10];
        int x,y,z;
        scanf("%s",s);
        if (strcmp(s,"CHANGE") == 0){
            scanf("%d%d",&x,&z);
            modify(dfn[x],z);
        }
        else if (strcmp(s,"QMAX") == 0) {
            scanf("%d%d",&x,&y);
            printf("%lld
",query_max(x,y));
        }
        else if (strcmp(s,"QSUM") == 0){
            scanf("%d%d",&x,&y);
            printf("%lld
",query_sum(x,y));
        }
    }
    return 0;
}