树链剖分【p4114】Qtree-Query on a tree I

裸的树链剖分题.

将边权转为点权要赋给深度较深的点,这样可以保证一个点权对应一个边权.

注意题目中的\(a==b\)的时候输出\(0\)，要不就一遍切了 QAQ.

代码

#include<cstdio>
#include<cstring>
#include<iostream>
#include<cctype>
#define int long long
#define N 100008
#define R register
using namespace std;
inline void in(int &x)
{
int f=1;x=0;char s=getchar();
while(!isdigit(s)){if(s=='-')f=-1;s=getchar();}
while(isdigit(s)){x=x*10+s-'0';s=getchar();}
x*=f;
}
int n,head
,tot;
struct cod{int u,v,w,fr;}edge[N<<2];
inline void add(int x,int y,int z)
{
edge[++tot].u=head[x];
edge[tot].fr=x;
edge[tot].v=y;
edge[tot].w=z;
head[x]=tot;
}
int son
,size
,f
,depth
,val
;
char s[108];
void dfs1(int u,int fa,int dis)
{
f[u]=fa;depth[u]=depth[fa]+1;size[u]=1;val[u]=dis;
for(R int i=head[u];i;i=edge[i].u)
{
if(edge[i].v==fa)continue;
dfs1(edge[i].v,u,edge[i].w);
size[u]+=size[edge[i].v];
if(son[u]==-1 or size[son[u]]<son[edge[i].v])
son[u]=edge[i].v;
}
}
int top
,idx,dfn
,fdfn
;
void dfs2(int u,int t)
{
top[u]=t;dfn[u]=++idx;fdfn[idx]=u;
if(son[u]==-1)return;
dfs2(son[u],t);
for(R int i=head[u];i;i=edge[i].u)
{
if(dfn[edge[i].v])continue;
dfs2(edge[i].v,edge[i].v);
}
}
int tr[N<<2];
#define ls o<<1
#define rs o<<1|1
inline void up(int o){tr[o]=max(tr[ls],tr[rs]);}
void build(int o,int l,int r)
{
if(l==r)
{
tr[o]=val[fdfn[l]];
return;
}
int mid=(l+r)>>1;
build(ls,l,mid);
build(rs,mid+1,r);
up(o);
}
void change(int o,int l,int r,int pos,int z)
{
if(l==r){tr[o]=z;return;}
int mid=(l+r)>>1;
if(pos<=mid)change(ls,l,mid,pos,z);
else change(rs,mid+1,r,pos,z);
up(o);
}
int query(int o,int l,int r,int x,int y)
{
if(x<=l and y>=r)return tr[o];
int mid=(l+r)>>1,res=-214748364766LL;
if(x<=mid)res=max(res,query(ls,l,mid,x,y));
if(y>mid)res=max(res,query(rs,mid+1,r,x,y));
return res;
}
inline int tquery(int x,int y)
{
int fx=top[x],fy=top[y],res=-214748364766LL;
while(fx!=fy)
{
if(depth[fx]>depth[fy])
{
res=max(res,query(1,1,n,dfn[fx],dfn[x]));
x=f[fx];
}
else
{
res=max(res,query(1,1,n,dfn[fy],dfn[y]));
y=f[fy];
}
fx=top[x],fy=top[y];
}
if(x==y)return res;
if(dfn[x]>dfn[y])swap(x,y);
res=max(res,query(1,1,n,dfn[x]+1,dfn[y]));
return res;
}
signed main()
{
in(n);memset(son,-1,sizeof son);
for(R int i=1,x,y,z;i<n;i++)
{
in(x),in(y),in(z);
add(x,y,z);add(y,x,z);
}
dfs1(1,0,0);dfs2(1,1);
build(1,1,n);
for(R int x,y;;)
{
scanf("%s",s+1);
if(s[1]=='D')break;
if(s[1]=='Q')
{
in(x),in(y);
if(x==y)puts("0");
else printf("%lld\n",tquery(x,y));
}
else
{
in(x),in(y);x*=2;
if(depth[edge[x].v]<depth[edge[x].fr])
x=edge[x].fr;
else x=edge[x].v;
change(1,1,n,dfn[x],y);
}
}
}