洛谷 1501 [国家集训队]Tree II BZOJ 2631 Tree

【题解】

　　维护乘法标记和加法标记的LCT

 #include<cstdio>
 #include<algorithm>
 #define Mod (51061)
 #define N 100010
 #define rg register
 #define ls (c[u][0])
 #define rs (c[u][1])
 #define MOD(k) (k-=k>=Mod?Mod:0)
 using namespace std;
 int n,m,top,fa[N],c[N][],rev[N],st[N],size[N];
 unsigned int val[N],del[N],mul[N],sum[N];
 struct edge{
     int u,v;
 }e[N<<];
 inline int read(){
     int k=,f=; char c=getchar();
     while(c<''||c>'')c=='-'&&(f=-),c=getchar();
     while(''<=c&&c<='')k=k*+c-'',c=getchar();
     return k*f;
 }
 inline bool isroot(int u){return c[fa[u]][]!=u&&c[fa[u]][]!=u;}
 inline bool which(int u){return c[fa[u]][]==u;}
 inline void pushup(int u){
     sum[u]=sum[ls]+sum[rs]+val[u]; sum[u]%=Mod;
     size[u]=size[ls]+size[rs]+;
 }
 inline void pushdown(int u){
     if(rev[u]){
         rev[u]=; rev[ls]^=; rev[rs]^=; swap(ls,rs);
     }
     del[ls]*=mul[u]; del[ls]%=Mod;
     del[rs]*=mul[u]; del[rs]%=Mod;
     mul[ls]*=mul[u]; mul[ls]%=Mod;
     mul[rs]*=mul[u]; mul[rs]%=Mod;
     val[ls]*=mul[u]; val[ls]%=Mod;
     val[rs]*=mul[u]; val[rs]%=Mod;
     sum[ls]*=mul[u]; sum[ls]%=Mod;
     sum[rs]*=mul[u]; sum[rs]%=Mod;
     del[ls]+=del[u]; MOD(del[ls]);
     del[rs]+=del[u]; MOD(del[rs]);
     val[ls]+=del[u]; MOD(val[ls]);
     val[rs]+=del[u]; MOD(val[rs]);
     sum[ls]+=del[u]*size[ls]; sum[ls]%=Mod;
     sum[rs]+=del[u]*size[rs]; sum[rs]%=Mod;
     mul[u]=; del[u]=;
 }
 void rotate(int u){
     int f=fa[u],gf=fa[f],wh=which(u);
     if(!isroot(f)) c[gf][which(f)]=u;
     fa[u]=gf; fa[f]=u; fa[c[u][wh^]]=f;
     c[f][wh]=c[u][wh^]; c[u][wh^]=f;
     pushup(f); pushup(u);
 }
 void splay(int u){
     st[top=]=u;
     for(rg int i=u;!isroot(i);i=fa[i]) st[++top]=fa[i];
     for(rg int i=top;i;i--) pushdown(st[i]);
     while(!isroot(u)){
         if(!isroot(fa[u])) rotate(which(u)==which(fa[u])?fa[u]:u);
         rotate(u);
     }
 }
 inline void access(int u){
     for(rg int son=;u;son=u,u=fa[u]) splay(u),c[u][]=son,pushup(u);
 }
 inline void makeroot(int u){access(u); splay(u); rev[u]^=;}
 int find(int u){
     access(u); splay(u);
     while(ls) u=ls; return u;
 }
 void split(int x,int y){makeroot(x); access(y); splay(y);}
 void link(int x,int y){makeroot(x); fa[x]=y;}
 void cut(int x,int y){
     split(x,y); int t=c[y][];
     if(t==x&&!c[t][]) fa[x]=,c[y][]=;
     else{
         while(c[t][]) t=c[t][];
         if(t==x) fa[x]=,c[fa[t]][]=;
     }
 }
 int main(){
     n=read(); m=read();
     for(rg int i=;i<=n;i++) mul[i]=val[i]=;
     for(rg int i=;i<n;i++){
         e[i].u=read(); e[i].v=read();
         link(e[i].u,e[i].v);
     }
     while(m--){
         char c=getchar();
         while(c!='*'&&c!='/'&&c!='+'&&c!='-') c=getchar();
         if(c=='+'){
             int u=read(),v=read(),c=read();
             split(u,v);
             del[v]+=c; MOD(del[v]);
             val[v]+=c; MOD(val[v]);
             sum[v]+=c*size[v]; sum[v]%=Mod;
         }
         else
         if(c=='-'){
             int u1=read(),v1=read(),u2=read(),v2=read();
             cut(u1,v1); link(u2,v2);
         }
         else
         if(c=='/'){
             int u=read(),v=read();
             split(u,v); printf("%d\n",sum[v]%Mod);
         }
         else{
             int u=read(),v=read(),c=read();
             split(u,v);
             val[v]*=c; val[v]%=Mod;
             mul[v]*=c; mul[v]%=Mod;
             del[v]*=c; del[v]%=Mod;
             sum[v]*=c; sum[v]%=Mod;
         }
     }
     return ;
 }