问题描述
题解
边化点权。
超级多操作的树剖板子...
以后就拿这个当树剖板子复习吧...
\(\mathrm{Code}\)
#include<bits/stdc++.h>
using namespace std;
template <typename Tp>
void read(Tp &x){
x=0;char ch=1;int fh;
while(ch!='-'&&(ch>'9'||ch<'0')) ch=getchar();
if(ch=='-') ch=getchar(),fh=-1;
else fh=1;
while(ch>='0'&&ch<='9') x=(x<<1)+(x<<3)+ch-'0',ch=getchar();
x*=fh;
}
template <typename Tp>
void fr(Tp &x){
char ch=1;
while(ch!='C'&&ch!='N'&&ch!='S'&&ch!='M') ch=getchar();
if(ch=='M'){
ch=1;while(ch!='A'&&ch!='I') ch=getchar();
}
if(ch=='C') x=1;
else if(ch=='N') x=2;
else if(ch=='S') x=3;
else if(ch=='A') x=4;
else x=5;
}
const int maxn=40007;
const int INF=0x3f3f3f3f;
int n;
int Head[maxn],to[maxn],Next[maxn],tot=1,w[maxn];
int size[maxn],fa[maxn],dep[maxn];
int New[maxn],pre[maxn],ind,top[maxn];
int son[maxn];
//edge id i -> 2*i-1,2*i
void add(int x,int y,int z){
to[++tot]=y,Next[tot]=Head[x],Head[x]=tot,w[tot]=z;
}
void dfs1(int x,int f,int dp){
size[x]=1,fa[x]=f,dep[x]=dp;
int mxx=-1;
for(int i=Head[x];i;i=Next[i]){
int y=to[i];
if(y==f) continue;
dfs1(y,x,dp+1);
size[x]+=size[y];
if(size[y]>mxx) mxx=size[y],son[x]=y;
}
}
void dfs2(int x,int tp){
New[x]=++ind,pre[ind]=x,top[x]=tp;
if(!son[x]) return;
dfs2(son[x],tp);
for(int i=Head[x];i;i=Next[i]){
int y=to[i];
if(y==fa[x]||y==son[x]) continue;
dfs2(y,y);
}
}
int val[maxn],f[maxn];
void preprocess(){
for(int i=2;i<=tot;i+=2){//错误笔记：tot一开始等于1，则第一条边从2开始
int x=to[i xor 1],y=to[i];
if(dep[x]>dep[y]) val[x]=w[i],f[i]=f[i xor 1]=x;//错误笔记：边化点权，要记录每个边化到哪个点上了。
else val[y]=w[i],f[i]=f[i xor 1]=y;
}
}
#define lfc (x<<1)
#define rgc ((x<<1)|1)
#define mid ((l+r)>>1)
int mx[maxn<<1],mi[maxn<<1],sum[maxn<<1];
int lazy[maxn<<1];
void pushup(int x){
mx[x]=max(mx[lfc],mx[rgc]);
mi[x]=min(mi[lfc],mi[rgc]);
sum[x]=sum[lfc]+sum[rgc];
}
void pushdown(int x){
if(!lazy[x]) return;
lazy[lfc]^=1,lazy[rgc]^=1;
sum[lfc]=-sum[lfc],sum[rgc]=-sum[rgc];
int lf=mx[lfc],rg=mx[rgc];
mx[lfc]=-mi[lfc],mx[rgc]=-mi[rgc];
mi[lfc]=-lf,mi[rgc]=-rg;
lazy[x]=0;//错误笔记：lazy标记有没有清空
}
void build(int x,int l,int r){
if(l==r){
mx[x]=mi[x]=sum[x]=val[pre[l]];
return;
}
build(lfc,l,mid);build(rgc,mid+1,r);
pushup(x);
}
int L,R,need;
void dd_change(int x,int l,int r){
if(l==r&&L==l){
sum[x]=mx[x]=mi[x]=need;return;
}
pushdown(x);
if(L<=mid) dd_change(lfc,l,mid);
else dd_change(rgc,mid+1,r);
pushup(x);
}
void qj_change(int x,int l,int r){
if(l>R||r<L) return;
if(L<=l&&r<=R){
lazy[x]^=1;int temp=mx[x];
sum[x]=-sum[x],mx[x]=-mi[x],mi[x]=-temp;
return;
}
pushdown(x);
qj_change(lfc,l,mid);qj_change(rgc,mid+1,r);
pushup(x);
}
int sum_query(int x,int l,int r){
if(l>R||r<L) return 0;
if(L<=l&&r<=R) return sum[x];
pushdown(x);
return sum_query(lfc,l,mid)+sum_query(rgc,mid+1,r);
}
int max_query(int x,int l,int r){
if(l>R||r<L) return -INF;
if(L<=l&&r<=R) return mx[x];
pushdown(x);
return max(max_query(lfc,l,mid),max_query(rgc,mid+1,r));
}
int min_query(int x,int l,int r){
if(l>R||r<L) return INF;
if(L<=l&&r<=R) return mi[x];
pushdown(x);
return min(min_query(lfc,l,mid),min_query(rgc,mid+1,r));
}
int T,op;
void cz1(){
int x;
read(x);read(need);
x=New[f[x<<1]],L=x;//错误笔记：双向存边，在数组中编号要*2
dd_change(1,1,n);
}
void cz2(){
int x,y;
read(x);read(y);
++x,++y;
while(top[x]!=top[y]){
if(dep[top[x]]<dep[top[y]]) swap(x,y);
L=New[top[x]],R=New[x];//错误笔记：写作L=New[x],R=New[y]
qj_change(1,1,n);
x=fa[top[x]];
}
if(dep[x]>dep[y]) swap(x,y);
L=New[x]+1,R=New[y];
if(L<=R) qj_change(1,1,n);
}
void cz3(){
int x,y,res=0;
read(x);read(y);
++x,++y;
while(top[x]!=top[y]){
if(dep[top[x]]<dep[top[y]]) swap(x,y);
L=New[top[x]],R=New[x];
res+=sum_query(1,1,n);
x=fa[top[x]];
}
if(dep[x]>dep[y]) swap(x,y);
L=New[x]+1,R=New[y];
if(L<=R) res+=sum_query(1,1,n);
printf("%d\n",res);
}
void cz4(){
int x,y,res=-INF;
read(x);read(y);
++x,++y;
while(top[x]!=top[y]){
if(dep[top[x]]<dep[top[y]]) swap(x,y);
L=New[top[x]],R=New[x];
res=max(res,max_query(1,1,n));
x=fa[top[x]];
}
if(dep[x]>dep[y]) swap(x,y);
L=New[x]+1,R=New[y];
if(L<=R) res=max(res,max_query(1,1,n));
printf("%d\n",res);
}
void cz5(){
int x,y,res=INF;
read(x);read(y);
++x,++y;
while(top[x]!=top[y]){
if(dep[top[x]]<dep[top[y]]) swap(x,y);
L=New[top[x]],R=New[x];
res=min(res,min_query(1,1,n));
x=fa[top[x]];
}
if(dep[x]>dep[y]) swap(x,y);
L=New[x]+1,R=New[y];
if(L<=R) res=min(res,min_query(1,1,n));
printf("%d\n",res);
}
int main(){
#ifndef ONLINE_JUDGE
freopen("travel.in","r",stdin);
#endif
read(n);
for(int i=1,x,y,z;i<n;i++){
read(x);read(y);read(z);
++x,++y;
add(x,y,z);add(y,x,z);
}
dfs1(1,0,1);dfs2(1,1);
preprocess();build(1,1,n);
read(T);
while(T--){
fr(op);
if(op==1) cz1();
else if(op==2) cz2();
else if(op==3) cz3();
else if(op==4) cz4();
else cz5();
}
return 0;
}