本部落格為本人對樹剖可解決題目的總結。。。
概念
- 1：\(fa[u]\) : \(u\) 的父親
- 2：\(size[u]\) : \(u\) 節點 \(u\) 為子樹的節點個數
- 3：\(dep[u]\) : \(u\) 節點的深度
- 4：\(wson[u]\) : \(u\) 節點的重兒子編號
- 5：\(top[u]\) : \(u\) 節點所在重鏈的頂部端點
- 6：\(dfn[u]\) : \(u\) 節點的 \(dfs\) 序
- 7：\(pre[u]\) : \(dfs\) 序 為 \(u\) 的對應的節點的編號
板子
兩次 $dfs$
void dfs1(int u,int f)
{
size[u]=1;
for (int i=head[u];i;i=e[i].next)
{
int y=e[i].to;
if(y==f)continue;
dep[y]=dep[u]+1;
fa[y]=u;
dfs1(y,u);
size[u]+=size[y];
if(size[y]>size[wson[u]])wson[u]=y;
}
}
void dfs2(int u,int topfa)
{
dfn[u]=++cnt;
pre[cnt]=u;
top[u]=topfa;
if(wson[u]) dfs2(wson[u],topfa);
for (int i=head[u];i;i=e[i].next)
{
int y=e[i].to;
if(y==fa[u]||y==wson[u]) continue;
dfs2(y,y);
}
}
$lca$
int lca(int x,int y)
{
while(top[x]!=top[y])
{
if(dep[top[x]]<dep[top[y]])swap(x,y);
x=fa[top[x]];
}
if(dep[x]>dep[y])swap(x,y);
return x;
}
鏈上修改，其他操作類比
void qup(int x,int y,int z)
{
while(top[x]!=top[y])
{
if(dep[top[x]]<dep[top[y]])swap(x,y);
update(1,dfn[top[x]],dfn[x],z);
x=fa[top[x]];
}
if(dep[x]<dep[y])swap(x,y);
update(1,dfn[y],dfn[x],z);
//update(1,dfn[y]+1,dfn[x],z);如果題目給的是邊權則改為這個
}
線段樹維護的各種操作
常見的操作不過多敘述了
1 換根
題目
正常換就行
#include<bits/stdc++.h>
#define int long long
#define lid id<<1
#define rid id<<1|1
const int maxn=1e6+10;
const int inf=2e9;
using namespace std;
int n,t,a[maxn<<2];
struct node{int to,next;}e[maxn<<2];
struct tree{int l,r,lazy,minn;}m[maxn<<4];
int tot,head[maxn<<1];
int size[maxn],wson[maxn],fa[maxn],dep[maxn],top[maxn];
int dfn[maxn],pre[maxn],cnt=0;
inline void add(int x,int y)
{
e[++tot].to=y;e[tot].next=head[x];head[x]=tot;
}
void addm(int x,int y)
{
add(x,y);add(y,x);
}
void dfs1(int u,int f)
{
size[u]=1;
for (int i=head[u];i;i=e[i].next)
{
int y=e[i].to;
if(y==f)continue;
dep[y]=dep[u]+1;
fa[y]=u;
dfs1(y,u);
size[u]+=size[y];
if(size[y]>size[wson[u]])wson[u]=y;
}
}
void dfs2(int u,int topfa)
{
dfn[u]=++cnt;
pre[cnt]=u;
top[u]=topfa;
if(wson[u]) dfs2(wson[u],topfa);
for (int i=head[u];i;i=e[i].next)
{
int y=e[i].to;
if(y==fa[u]||y==wson[u]) continue;
dfs2(y,y);
}
}
inline void up(int id)
{
m[id].minn=min(m[lid].minn,m[rid].minn);
}
inline void down(int id)
{
if(m[id].lazy==-1||m[id].l==m[id].r)return ;
m[lid].minn=m[lid].lazy=m[id].lazy;
m[rid].minn=m[rid].lazy=m[id].lazy;
m[id].lazy=-1;
}
void build(int id,int l,int r)
{
m[id].l=l;
m[id].r=r;
m[id].lazy=-1;
int mid=(l+r)>>1;
if(l==r)
{
m[id].minn=a[pre[l]];
return;
}
build(lid,l,mid);
build(rid,mid+1,r);
up(id);
}
void update(int id,int s,int tt,int y)
{
int l=m[id].l,r=m[id].r;
if(l>=s&&r<=tt)
{
m[id].lazy=m[id].minn=y;
return;
}
down(id);
int mid=(l+r)>>1;
if(s<=mid)update(lid,s,tt,y);
if(tt>mid) update(rid,s,tt,y);
up(id);
}
void qup(int x,int y,int z)
{
while(top[x]!=top[y])
{
if(dep[top[x]]<dep[top[y]])swap(x,y);
update(1,dfn[top[x]],dfn[x],z);
x=fa[top[x]];
}
if(dep[x]<dep[y])swap(x,y);
update(1,dfn[y],dfn[x],z);
}
int query(int id,int s,int tt)
{
int l=m[id].l,r=m[id].r;
int ans=inf;
if(l>=s&&r<=tt)
{
return m[id].minn;
}
down(id);
int mid=(l+r)>>1;
if(s<=mid)ans=min(ans,query(lid,s,tt));
if(tt>mid)ans=min(ans,query(rid,s,tt));
return ans;
}
int lca(int x,int y)
{
while(top[x]!=top[y])
{
if(dep[top[x]]<dep[top[y]])swap(x,y);
x=fa[top[x]];
}
if(dep[x]>dep[y])swap(x,y);
return x;
}
signed main(){
// freopen("aa.in","r",stdin);
scanf("%lld%lld",&n,&t);
for(int i=1;i<n;i++)
{
int x,y;
scanf("%lld%lld",&x,&y);
addm(x,y);
}
for(int i=1;i<=n;i++)scanf("%lld",&a[i]);
int root=1;
scanf("%lld",&root);
dfs1(1,0);
dfs2(1,1);
build(1,1,n);
while (t--)
{
int x,y,z,k;
scanf("%lld%lld",&z,&x);
if(z==1)root=x;
if(z==2)scanf("%lld%lld",&y,&k),qup(x,y,k);
if(z==3)
{
if(x==root)
{
printf("%lld\n",query(1,1,n));
}
else
{
int w=lca(x,root);
if(w==x)
{
int k;
for(int i=head[x];i;i=e[i].next)
{
int ll=e[i].to;
if(dfn[ll]<=dfn[root]&&dfn[ll]+size[ll]-1>=dfn[root])
{
k=ll;break;
}
}
int ans=min(query(1,1,dfn[k]-1),query(1,dfn[k]+size[k],n));
printf("%lld\n",ans);
}
else printf("%lld\n",query(1,dfn[x],dfn[x]+size[x]-1));
}
}
}
return 0;
}
2 求節點到根的 1 的個數——區間覆蓋
題目
把 += 改為 = 即可
#include<bits/stdc++.h>
#define lid id<<1
#define rid id<<1|1
const int maxn=1e6+10;
const int inf=0x7f7f7f7f;
using namespace std;
int n,t,a[maxn<<2];
struct tree{int l,r,lazy,sum;}m[maxn<<4];
int tot,head[maxn<<1],to[maxn<<2],nxt[maxn<<2];
int size[maxn],wson[maxn],fa[maxn],dep[maxn],top[maxn];
int dfn[maxn],pre[maxn],cnt=0;
int mod,root;
void add(int x,int y)
{
to[++tot]=y;nxt[tot]=head[x];head[x]=tot;
}
void addm(int x,int y)
{
add(x,y),add(y,x);
}
void dfs1(int u,int f)
{
size[u]=1;
for(int i=head[u];i;i=nxt[i])
{
int y=to[i];
if(y==f)continue;
dep[y]=dep[u]+1;
fa[y]=u;
dfs1(y,u);
size[u]+=size[y];
if(size[y]>size[wson[u]])wson[u]=y;
}
}
void dfs2(int u,int topfa)
{
dfn[u]=++cnt;
pre[cnt]=u;
top[u]=topfa;
if(wson[u])dfs2(wson[u],topfa);
for(int i=head[u];i;i=nxt[i])
{
int y=to[i];
if(y==fa[u]||y==wson[u])continue;
dfs2(y,y);
}
}
inline void up(int id)
{
m[id].sum=m[lid].sum+m[rid].sum;
}
inline void down(int id,int l,int r,int mid)
{
if(m[id].lazy<0)return ;
m[lid].lazy=m[rid].lazy=m[id].lazy;
if(m[id].lazy==0) m[lid].sum=m[rid].sum=0;
else m[lid].sum=mid-l+1,m[rid].sum=r-mid;
m[id].lazy=-1;
}
void build(int id,int l,int r)
{
m[id].l=l;
m[id].r=r;
if(l==r){m[id].lazy=-1;return;};
int mid=(l+r)>>1;
build(lid,l,mid);
build(rid,mid+1,r);
}
int querysum(int id,int s,int tt,int y)
{
int l=m[id].l,r=m[id].r,ans=0;
// cout<<id<<" "<<l<<" "<<r<<" "<<m[id].sum<<endl;
if(s<=l&&r<=tt)
{
ans=m[id].sum;
m[id].lazy=y;
m[id].sum=(r-l+1)*y;
return ans;
}
int mid=(l+r)>>1;
down(id,l,r,mid);
if(s<=mid)ans+=querysum(lid,s,tt,y);
if(tt>mid)ans+=querysum(rid,s,tt,y);
up(id);
// cout<<"up: "<<id<<" "<<l<<" "<<r<<" "<<m[id].sum<<endl;
return ans;
}
int qsum(int x,int y)
{
int ans=0;
while(top[x]!=top[y])
{
if(dep[top[x]]<dep[top[y]])swap(x,y);
ans+=querysum(1,dfn[top[x]],dfn[x],1);
x=fa[top[x]];
}
if(dep[x]<dep[y])swap(x,y);
ans+=querysum(1,dfn[y],dfn[x],1);
return ans;
}
int main()
{
scanf("%d",&n);
for(int i=2;i<=n;i++)
{
int x;
scanf("%d",&x);
x++;
addm(i,x);
}
dfs1(1,0);
dfs2(1,1);
build(1,1,n);
scanf("%d",&t);
char ss[10];
int x,y,z;
// for(int i=1;i<=n;i++)
// cout<<dfn[i]<<" ";
while(t--)
{
cin>>ss+1;
if(ss[1]=='i')
{
scanf("%d",&x);
x++;
int ans=qsum(1,x);
// cout<<ans<<endl;
printf("%d\n",dep[x]+1-ans);
}
else
{
scanf("%d",&x);
x++;
printf("%d\n",querysum(1,dfn[x],dfn[x]+size[x]-1,0));
}
}
return 0;
}
3 動態開點線段樹維護樹剖
題目
適用於維護多棵線段樹，要加一個 $root$ 陣列存根
#include<bits/stdc++.h>
const int maxn=1e5+10;
using namespace std;
int n,t,a[maxn<<2];
struct node{int to,next;}e[maxn<<4];
struct tree{int maxx,sum,l,r;}m[maxn<<8];
int tot,head[maxn],temp;
int size[maxn],wson[maxn],fa[maxn],dep[maxn],top[maxn];
int root[maxn],zj[maxn];
int dfn[maxn],pre[maxn],cnt;
void add(int x,int y)
{
e[++tot].to=y;
e[tot].next=head[x];
head[x]=tot;
}
void addm(int x,int y)
{
add(x,y),add(y,x);
}
void dfs1(int u,int f)
{
size[u]=1;
for(int i=head[u];i;i=e[i].next)
{
int y=e[i].to;
if(y==f)continue;
dep[y]=dep[u]+1;
fa[y]=u;
dfs1(y,u);
size[u]+=size[y];
if(size[y]>size[wson[u]])wson[u]=y;
}
}
void dfs2(int u,int topfa)
{
dfn[u]=++cnt;
pre[cnt]=u;
top[u]=topfa;
if(wson[u])dfs2(wson[u],topfa);
for(int i=head[u];i;i=e[i].next)
{
int y=e[i].to;
if(y==fa[u]||y==wson[u])continue;
dfs2(y,y);
}
}
void up(int id)
{
int lid=m[id].l,rid=m[id].r;
m[id].maxx=max(m[lid].maxx,m[rid].maxx);
m[id].sum=m[lid].sum+m[rid].sum;
}
void update(int &id,int l,int r,int pos,int y)
{
if(!id)id=++temp;
m[id].maxx=max(m[id].maxx,y);
m[id].sum+=y;
if(l==r)return;
int mid=(l+r)>>1;
if(pos<=mid)update(m[id].l,l,mid,pos,y);
else update(m[id].r,mid+1,r,pos,y);
}
void del(int &id,int l,int r,int pos)
{
if(l==r)
{
m[id].maxx=m[id].sum=0;
return ;
}
int mid=(l+r)>>1;
if(mid>=pos)del(m[id].l,l,mid,pos);
else del(m[id].r,mid+1,r,pos);
up(id);
}
int querymax(int id,int l,int r,int x,int y)
{
int mid=(l+r)>>1,ans=0;
if(x<=l&&r<=y)return m[id].maxx;
if(x<=mid)ans=max(ans,querymax(m[id].l,l,mid,x,y));
if(y>mid)ans=max(ans,querymax(m[id].r,mid+1,r,x,y));
return ans;
}
int qmax(int x,int y,int zj)
{
int ans=0;
while(top[x]!=top[y])
{
if(dep[top[x]]<dep[top[y]])swap(x,y);
ans=max(ans,querymax(root[zj],1,n,dfn[top[x]],dfn[x]));
x=fa[top[x]];
}
if(dep[x]<dep[y])swap(x,y);
ans=max(ans,querymax(root[zj],1,n,dfn[y],dfn[x]));
return ans;
}
int querysum(int id,int l,int r,int x,int y)
{
int mid=(l+r)>>1,ans=0;
if(x<=l&&r<=y)return m[id].sum;
if(x<=mid)ans+=querysum(m[id].l,l,mid,x,y);
if(y>mid)ans+=querysum(m[id].r,mid+1,r,x,y);
return ans;
}
int qsum(int x,int y,int zj)
{
int ans=0;
while(top[x]!=top[y])
{
if(dep[top[x]]<dep[top[y]])swap(x,y);
ans+=querysum(root[zj],1,n,dfn[top[x]],dfn[x]);
x=fa[top[x]];
}
if(dep[x]<dep[y])swap(x,y);
ans+=querysum(root[zj],1,n,dfn[y],dfn[x]);
return ans;
}
int main()
{
scanf("%d%d",&n,&t);
for(int i=1;i<=n;i++)scanf("%d%d",&a[i],&zj[i]);
for(int i=1;i<n;i++)
{
int x,y,z;
scanf("%d%d",&x,&y);
addm(x,y);
}
dfs1(1,0);
dfs2(1,1);
for(int i=1;i<=n;i++)
update(root[zj[i]],1,n,dfn[i],a[i]);
char ss[10];
int x,y;
while(t--)
{
scanf("%s",ss);
scanf("%d%d",&x,&y);
if(ss[1]=='C')
{
del(root[zj[x]],1,n,dfn[x]);
update(root[y],1,n,dfn[x],a[x]);
zj[x]=y;
}
else if(ss[1]=='W')
{
del(root[zj[x]],1,n,dfn[x]);
update(root[zj[x]],1,n,dfn[x],y);
a[x]=y;
}
else if(ss[1]=='S')
{
printf("%d\n",qsum(x,y,zj[x]));
}
else printf("%d\n",qmax(x,y,zj[x]));
}
return 0;
}
4 樹上修改值帶增加值
題目
加一個 $flag$ 記錄修改，要把 $lazy$ 清空
#include<bits/stdc++.h>
#define lid id<<1
#define rid id<<1|1
const int maxn=1e5+10;
const int inf=0x7f7f7f7f;
using namespace std;
int n,t,a[maxn<<2];
struct node{int to,next,val,id;}e[maxn<<2];
struct tree{int maxx,lazy,flag,l,r;}m[maxn<<4];
int tot,head[maxn];
int size[maxn],wson[maxn],fa[maxn],dep[maxn],top[maxn],dian[maxn];
int dfn[maxn],pre[maxn],cnt=0;
void add(int x,int y,int z,int i)
{
e[++tot].to=y;
e[tot].val=z;
e[tot].id=i;
e[tot].next=head[x];
head[x]=tot;
}
void addm(int x,int y,int z,int i)
{
add(x,y,z,i),add(y,x,z,i);
}
void dfs1(int u,int f)
{
size[u]=1;
for(int i=head[u];i;i=e[i].next)
{
int y=e[i].to;
if(y==f)continue;
dep[y]=dep[u]+1;
dian[e[i].id]=y;
a[y]=e[i].val;
fa[y]=u;
dfs1(y,u);
size[u]+=size[y];
if(size[y]>size[wson[u]])wson[u]=y;
}
}
void dfs2(int u,int topfa)
{
dfn[u]=++cnt;
pre[cnt]=u;
top[u]=topfa;
if(wson[u])dfs2(wson[u],topfa);
for(int i=head[u];i;i=e[i].next)
{
int y=e[i].to;
if(y==fa[u]||y==wson[u])continue;
dfs2(y,y);
}
}
void up(int id)
{
m[id].maxx=max(m[lid].maxx,m[rid].maxx);
}
inline void down(int id)
{
if(m[id].flag)
{
m[lid].lazy=m[rid].lazy=0;
m[lid].maxx=m[rid].maxx=m[lid].flag=m[rid].flag=m[id].flag;
m[id].flag=0;
}
if(m[id].lazy)
{
m[lid].maxx+=m[id].lazy;
m[rid].maxx+=m[id].lazy;
m[lid].lazy+=m[id].lazy;
m[rid].lazy+=m[id].lazy;
m[id].lazy=0;
}
}
void build(int id,int l,int r)
{
m[id].l=l;
m[id].r=r;
int mid=(l+r)>>1;
if(l==r)
{
m[id].maxx=a[pre[l]];
return ;
}
build(lid,l,mid);
build(rid,mid+1,r);
up(id);
}
void update(int id,int x,int y)
{
int l=m[id].l,r=m[id].r;
if(l==r)
{
m[id].maxx=m[id].flag=y;
m[id].lazy=0;
return ;
}
down(id);
int mid=(l+r)>>1;
if(x<=mid)update(lid,x,y);
else update(rid,x,y);
up(id);
}
void updatex(int id,int s,int tt,int y)
{
int l=m[id].l,r=m[id].r;
if(l>tt||r<s)return;
if(l>=s&&r<=tt)
{
m[id].lazy=0;
m[id].maxx=m[id].flag=y;
return ;
}
down(id);
int mid=(l+r)>>1;
if(s<=mid)updatex(lid,s,tt,y);
if(tt>mid)updatex(rid,s,tt,y);
up(id);
}
void updatey(int id,int s,int tt,int y)
{
int l=m[id].l,r=m[id].r;
if(l>tt||r<s)return;
if(l>=s&&r<=tt)
{
m[id].lazy+=y;
m[id].maxx+=y;
return ;
}
down(id);
int mid=(l+r)>>1;
if(s<=mid)updatey(lid,s,tt,y);
if(tt>mid)updatey(rid,s,tt,y);
up(id);
}
void qup(int x,int y,int z,int f)
{
while(top[x]!=top[y])
{
if(dep[top[x]]<dep[top[y]])swap(x,y);
if(f==1)updatey(1,dfn[top[x]],dfn[x],z);
else updatex(1,dfn[top[x]],dfn[x],z);
x=fa[top[x]];
}
if(dep[x]<dep[y])swap(x,y);
if(f==1)updatey(1,dfn[y]+1,dfn[x],z);
else updatex(1,dfn[y]+1,dfn[x],z);
}
int querymax(int id,int x,int y)
{
int l=m[id].l,r=m[id].r;
int mid=(l+r)>>1,ans=-inf;
if(x<=l&&r<=y)return m[id].maxx;
down(id);
if(x<=mid)ans=max(ans,querymax(lid,x,y));
if(y>mid)ans=max(ans,querymax(rid,x,y));
return ans;
}
int qmax(int x,int y)
{
int ans=-inf;
while(top[x]!=top[y])
{
if(dep[top[x]]<dep[top[y]])swap(x,y);
ans=max(ans,querymax(1,dfn[top[x]],dfn[x]));
x=fa[top[x]];
}
if(dep[x]<dep[y])swap(x,y);
ans=max(ans,querymax(1,dfn[y]+1,dfn[x]));
return ans;
}
int main()
{
// freopen("asa.in","r",stdin);
// freopen("123.out","w",stdout);
scanf("%d",&n);
for(int i=1;i<n;i++)
{
int x,y,z;
scanf("%d%d%d",&x,&y,&z);
addm(x,y,z,i);
}
dfs1(1,0);
dfs2(1,1);
build(1,1,n);
char ss[10];
while(1)
{
int x,y,z;
scanf("%s",ss+1);
if(ss[1]=='S')break;
scanf("%d%d",&x,&y);
if(ss[1]=='M')
{
printf("%d\n",qmax(x,y));
}
else if(ss[2]=='h')
{
update(1,dfn[dian[x]],y);
}
else if(ss[2]=='o')
{
scanf("%d",&z);
qup(x,y,z,0);
}
else
{
scanf("%d",&z);
qup(x,y,z,1);
}
}
return 0;
}
5鏈上權值改為相反數
題目
相反，交換最大值和最小值
#include<bits/stdc++.h>
#define int long long
#define lid id<<1
#define rid id<<1|1
const int maxn=2e5+10;
const int inf=0x7f7f7f7f;
using namespace std;
int n,t,a[maxn];
struct node{int to,next,val,id;}e[maxn<<2];
struct tree{int maxx,minn,sum,lazy,l,r;}m[maxn<<2];
int tot,head[maxn];
int size[maxn],wson[maxn],fa[maxn],dep[maxn],top[maxn],dian[maxn];
int dfn[maxn],pre[maxn],cnt=0;
void add(int x,int y,int z,int i)
{
e[++tot].to=y;
e[tot].val=z;
e[tot].id=i;
e[tot].next=head[x];
head[x]=tot;
}
void addm(int x,int y,int z,int i)
{
add(x,y,z,i),add(y,x,z,i);
}
void dfs1(int u,int f)
{
size[u]=1;
for(int i=head[u];i;i=e[i].next)
{
int y=e[i].to;
if(y==f)continue;
dep[y]=dep[u]+1;
dian[e[i].id]=y;
a[y]=e[i].val;
fa[y]=u;
dfs1(y,u);
size[u]+=size[y];
if(size[y]>size[wson[u]])wson[u]=y;
}
}
void dfs2(int u,int topfa)
{
dfn[u]=++cnt;
pre[cnt]=u;
top[u]=topfa;
if(wson[u])dfs2(wson[u],topfa);
for(int i=head[u];i;i=e[i].next)
{
int y=e[i].to;
if(y==fa[u]||y==wson[u])continue;
dfs2(y,y);
}
}
void up(int id)
{
m[id].maxx=max(m[lid].maxx,m[rid].maxx);
m[id].minn=min(m[lid].minn,m[rid].minn);
m[id].sum=m[lid].sum+m[rid].sum;
}
inline void down(int id)
{
if(!m[id].lazy)return ;
m[lid].maxx=-m[lid].maxx;
m[lid].minn=-m[lid].minn;
m[lid].sum=-m[lid].sum;
swap(m[lid].maxx,m[lid].minn);
m[rid].maxx=-m[rid].maxx;
m[rid].minn=-m[rid].minn;
m[rid].sum=-m[rid].sum;
swap(m[rid].maxx,m[rid].minn);
m[lid].lazy^=1;
m[rid].lazy^=1;
m[id].lazy=0;
}
void build(int id,int l,int r)
{
m[id].l=l;
m[id].r=r;
int mid=(l+r)>>1;
if(l==r)
{
m[id].sum=m[id].minn=m[id].maxx=a[pre[l]];
return ;
}
build(lid,l,mid);
build(rid,mid+1,r);
up(id);
}
void update(int id,int x,int y)
{
int l=m[id].l,r=m[id].r;
if(l==r)
{
m[id].sum=m[id].maxx=m[id].minn=y;
return ;
}
down(id);
int mid=(l+r)>>1;
if(x<=mid)update(lid,x,y);
else update(rid,x,y);
up(id);
}
void xiangfan(int id,int x,int y)
{
int l=m[id].l,r=m[id].r;
if(l>=x&&r<=y)
{
m[id].maxx=-m[id].maxx;
m[id].minn=-m[id].minn;
m[id].sum=-m[id].sum;
swap(m[id].maxx,m[id].minn);
m[id].lazy^=1;
return;
}
down(id);
int mid=(l+r)>>1;
if(x<=mid)xiangfan(lid,x,y);
if(y>mid)xiangfan(rid,x,y);
up(id);
}
void qfan(int x,int y)
{
while(top[x]!=top[y])
{
if(dep[top[x]]<dep[top[y]])swap(x,y);
xiangfan(1,dfn[top[x]],dfn[x]);
x=fa[top[x]];
}
if(dep[x]<dep[y])swap(x,y);
xiangfan(1,dfn[y]+1,dfn[x]);
}
int querysum(int id,int x,int y)
{
int l=m[id].l,r=m[id].r;
int mid=(l+r)>>1,ans=0;
if(x<=l&&r<=y)return m[id].sum;
down(id);
if(x<=mid)ans+=querysum(lid,x,y);
if(y>mid)ans+=querysum(rid,x,y);
up(id);
return ans;
}
int qsum(int x,int y)
{
int ans=0;
while(top[x]!=top[y])
{
if(dep[top[x]]<dep[top[y]])swap(x,y);
ans+=querysum(1,dfn[top[x]],dfn[x]);
x=fa[top[x]];
}
if(dep[x]<dep[y])swap(x,y);
ans+=querysum(1,dfn[y]+1,dfn[x]);
return ans;
}
int querymax(int id,int x,int y)
{
int l=m[id].l,r=m[id].r;
int mid=(l+r)>>1,ans=-inf;
if(x<=l&&r<=y)return m[id].maxx;
down(id);
if(x<=mid)ans=max(ans,querymax(lid,x,y));
if(y>mid)ans=max(ans,querymax(rid,x,y));
up(id);
return ans;
}
int qmax(int x,int y)
{
int ans=-inf;
while(top[x]!=top[y])
{
if(dep[top[x]]<dep[top[y]])swap(x,y);
ans=max(ans,querymax(1,dfn[top[x]],dfn[x]));
x=fa[top[x]];
}
if(dep[x]<dep[y])swap(x,y);
ans=max(ans,querymax(1,dfn[y]+1,dfn[x]));
return ans;
}
int querymin(int id,int x,int y)
{
int l=m[id].l,r=m[id].r;
int mid=(l+r)>>1,ans=inf;
if(x<=l&&r<=y)return m[id].minn;
down(id);
if(x<=mid)ans=min(ans,querymin(lid,x,y));
if(y>mid)ans=min(ans,querymin(rid,x,y));
up(id);
return ans;
}
int qmin(int x,int y)
{
int ans=inf;
while(top[x]!=top[y])
{
if(dep[top[x]]<dep[top[y]])swap(x,y);
ans=min(ans,querymin(1,dfn[top[x]],dfn[x]));
x=fa[top[x]];
}
if(dep[x]<dep[y])swap(x,y);
ans=min(ans,querymin(1,dfn[y]+1,dfn[x]));
return ans;
}
signed main()
{
scanf("%lld",&n);
for(int i=1;i<n;i++)
{
int x,y,z;
scanf("%lld%lld%lld",&x,&y,&z);
x++,y++;
addm(x,y,z,i);
}
dfs1(1,0);
dfs2(1,1);
build(1,1,n);
char ss[10];
scanf("%lld",&t);
while(t--)
{
int x,y,z;
scanf("%s",ss);
scanf("%lld%lld",&x,&y);
x++,y++;
if(ss[0]=='C')
{
x--,y--;
update(1,dfn[dian[x]],y);
}
else if(ss[0]=='N')
{
qfan(x,y);
}
else if(ss[1]=='U')
{
printf("%lld\n",qsum(x,y));
}
else if(ss[1]=='A')
{
printf("%lld\n",qmax(x,y));
}
else printf("%lld\n",qmin(x,y));
}
return 0;
}