洛谷P2590 [ZJOI2008]树的统计 （树链剖分）

题目链接：

https://www.luogu.com.cn/problem/P2590

思路：

树剖板子

代码：

#include <bits/stdc++.h>
#define ls node<<1
#define rs node<<1|1
#define l_q ls,l,mid
#define r_q rs,mid+1,r
using namespace std;
const int MAXN=1e5+5;
const int INF=0x7fffffff;
typedef long long ll;
ll n;ll val[MAXN];
int head[MAXN],tot;
struct node
{
    int to,nxt;
}e[MAXN<<1];
void add(int x,int y)
{
    e[tot].to=y,e[tot].nxt=head[x],head[x]=tot++;
}
void add_edge(int x,int y)
{
    add(x,y);add(y,x);
}
int dep[MAXN],f[MAXN],son[MAXN],sz[MAXN];
void dfs(int u,int fa)
{
    dep[u]=dep[fa]+1;sz[u]=1;f[u]=fa;
    for(int i=head[u];~i;i=e[i].nxt)
    {
        int v=e[i].to;
        if(v!=fa)
        {
            dfs(v,u);
            sz[u]+=sz[v];
            if(sz[v]>sz[son[u]])
                son[u]=v;
        }
    }
}
ll id[MAXN],cnt,top[MAXN],a[MAXN];
void dfs2(int u,int t)
{
    top[u]=t;id[u]=++cnt;a[cnt]=val[u];
    if(son[u])
        dfs2(son[u],t);
    for(int i=head[u];~i;i=e[i].nxt)
    {
        int v=e[i].to;
        if(v!=f[u]&&v!=son[u])
            dfs2(v,v);
    }
}
ll sum[MAXN<<2],max_[MAXN<<2],lazy[MAXN<<2];
void push_up(int node)
{
    sum[node]=sum[ls]+sum[rs];
    max_[node]=max(max_[ls],max_[rs]);
}
void build(int node,int l,int r)
{
    if(l==r)
    {
        sum[node]=a[l];max_[node]=a[l];return;
    }
    int mid=(l+r)>>1;
    build(node<<1,l,mid);build(node<<1|1,mid+1,r);
    push_up(node);
}
void push_down(int node,int l,int r,int mid)
{
    if(lazy[node])
    {
        lazy[ls]+=lazy[node];lazy[rs]+=lazy[node];
        sum[ls]+=(mid-l+1)*lazy[node];sum[rs]+=(r-mid)*lazy[node];
        max_[ls]+=lazy[node];max_[rs]+=lazy[node];
        lazy[node]=0;
    }
}
void update(int node,int l,int r,int index,int k)
{
    if(l==r)
    {
        lazy[node]+=k;sum[node]+=(r-l+1)*k;max_[node]+=k;return;
    }
    int mid=(l+r)>>1;
    push_down(node,l,r,mid);
    if(index<=mid)
        update(l_q,index,k);
    else
        update(r_q,index,k);
    push_up(node);
}
ll query1(int node,int l,int r,int x,int y)
{
    ll ans=0;
    if(l>=x&&r<=y)
        return sum[node];
    int mid=(l+r)>>1;
    push_down(node,l,r,mid);
    if(x<=mid)
        ans+=query1(l_q,x,y);
    if(y>mid)
        ans+=query1(r_q,x,y);
    return ans;
}
ll query2(int node,int l,int r,int x,int y)
{
    ll max1=-INF;
    if(l>=x&&r<=y)return max_[node];
    int mid=(l+r)>>1;
    push_down(node,l,r,mid);
    if(x<=mid)
        max1=max(max1,query2(l_q,x,y));
    if(y>mid)
        max1=max(max1,query2(r_q,x,y));
    return max1;
}
ll tree_max(int x,int y)
{
    int fx=top[x],fy=top[y];ll max1=-INF;
    while(fx!=fy)
    {
        if(dep[fx]<dep[fy])swap(x,y),swap(fx,fy);
        max1=max(max1,query2(1,1,n,id[fx],id[x]));
        x=f[fx];fx=top[x];
    }
    if(id[x]>id[y])swap(x,y);
    max1=max(max1,query2(1,1,n,id[x],id[y]));
    return max1;
}
ll tree_sum(int x,int y)
{
    int fx=top[x],fy=top[y];ll ans=0;
    while(fx!=fy)
    {
        if(dep[fx]<dep[fy])swap(x,y),swap(fx,fy);
        ans+=query1(1,1,n,id[fx],id[x]);
        x=f[fx];fx=top[x];
    }
    if(id[x]>id[y])swap(x,y);
    ans+=query1(1,1,n,id[x],id[y]);
    return ans;
}
int main()
{
    scanf("%d",&n);memset(head,-1,sizeof(head));
    for(int i=1;i<n;i++)
    {
        int x,y;scanf("%d%d",&x,&y);
        add_edge(x,y);
    }
    for(int i=1;i<=n;i++)
        scanf("%lld",&val[i]);
    dfs(1,0);dfs2(1,1);build(1,1,n);
    int q;scanf("%d",&q);
    while(q--)
    {
        char str[100];
        scanf("%s",str);
        ll x,y;scanf("%lld%lld",&x,&y);
        if(str[0]=='C')
        {
            update(1,1,n,id[x],y-a[id[x]]);a[id[x]]=y;
        }
        else
        {
            if(str[1]=='M')
            {
                printf("%lld\n",tree_max(x,y));
            }
            else
            {
                printf("%lld\n",tree_sum(x,y));
            }

        }
    }
    return 0;
}