bzoj1036 [ZJOI2008]树的统计（树链剖分）

树链剖分就是划分轻重链，把每个点映射到线段树上，保证一条重链上的点在线段树中是一段完整的区间。可以由2遍dfs完成。主要还是个线段树。复杂度O(nlogn+mlog2n)

#include <bits/stdc++.h>using namespace std;#define ll long long#define inf 0x3f3f3f3f#define N 30010inline int read(){    int x=0,f=1;char ch=getchar();    while(ch<'0'||ch>'9'){if(ch=='-') f=-1;ch=getchar();}    while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();    return x*f;}int n,a[N],h[N],num=0,fa[N],dep[N],son[N],size[N],top[N],id[N],dfn=0;struct edge{    int to,next;}data[N<<1];struct node{    int mx,sum;}tree[N<<2];void dfs1(int x){    size[x]=1;    for(int i=h[x];i;i=data[i].next){        int y=data[i].to;        if(fa[x]==y) continue;        fa[y]=x;dep[y]=dep[x]+1;dfs1(y);size[x]+=size[y];        if(size[y]>size[son[x]]) son[x]=y;    }}void dfs2(int x,int tp){    id[x]=++dfn;top[x]=tp;    if(son[x]) dfs2(son[x],tp);    for(int i=h[x];i;i=data[i].next){        int y=data[i].to;        if(y==fa[x]||y==son[x]) continue;        dfs2(y,y);    }}void build(int p,int l,int r){    if(l==r) return;    int mid=l+r>>1;    build(p<<1,l,mid);build(p<<1|1,mid+1,r);}inline void pushup(int p){    tree[p].sum=tree[p<<1].sum+tree[p<<1|1].sum;    tree[p].mx=max(tree[p<<1].mx,tree[p<<1|1].mx);}void change(int p,int l,int r,int x,int val){    if(l==r){tree[p].mx=tree[p].sum=val;return;}    int mid=l+r>>1;    if(x<=mid) change(p<<1,l,mid,x,val);    else change(p<<1|1,mid+1,r,x,val);    pushup(p);}int qsum(int p,int l,int r,int x,int y){    if(x<=l&&r<=y) return tree[p].sum;    int mid=l+r>>1,res=0;    if(x<=mid) res+=qsum(p<<1,l,mid,x,y);    if(y>mid) res+=qsum(p<<1|1,mid+1,r,x,y);    return res;}int qmax(int p,int l,int r,int x,int y){    if(x<=l&&r<=y) return tree[p].mx;    int mid=l+r>>1,res=-inf;    if(x<=mid) res=max(res,qmax(p<<1,l,mid,x,y));    if(y>mid) res=max(res,qmax(p<<1|1,mid+1,r,x,y));    return res;}int solvesum(int x,int y){    int res=0;    while(top[x]!=top[y]){        if(dep[top[x]]<dep[top[y]]) swap(x,y);        res+=qsum(1,1,n,id[top[x]],id[x]);        x=fa[top[x]];    }    if(id[x]>id[y]) swap(x,y);    res+=qsum(1,1,n,id[x],id[y]);    return res;}int solvemax(int x,int y){    int res=-inf;    while(top[x]!=top[y]){        if(dep[top[x]]<dep[top[y]]) swap(x,y);        res=max(res,qmax(1,1,n,id[top[x]],id[x]));        x=fa[top[x]];    }    if(id[x]>id[y]) swap(x,y);    res=max(res,qmax(1,1,n,id[x],id[y]));    return res;}int main(){//  freopen("a.in","r",stdin);    n=read();    for(int i=1;i<n;++i){        int x=read(),y=read();        data[++num].to=y;data[num].next=h[x];h[x]=num;        data[++num].to=x;data[num].next=h[y];h[y]=num;    }    dep[1]=1;dfs1(1);dfs2(1,1);build(1,1,n);    for(int i=1;i<=n;++i) change(1,1,n,id[i],read());int q=read();    while(q--){        char op[10];scanf("%s",op+1);int x=read(),y=read();        if(op[2]=='H') change(1,1,n,id[x],y);        if(op[2]=='S') printf("%d\n",solvesum(x,y));        if(op[2]=='M') printf("%d\n",solvemax(x,y));    }    return 0;}