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容易看出x,y切断后,x的子树大小乘上y的子树大小就是答案

LCT维护子树大小即可

#include<bits/stdc++.h>
#pragma GCC optimize(3)
#define il __inline__ __attribute__ ((always_inline))
namespace IO{const int str=1<<20;static char in_buf[str],*in_s,*in_t;bool __=0;il char gc(){return (in_s==in_t)&&(in_t=(in_s=in_buf)+fread(in_buf,1,str,stdin)),in_s==in_t?EOF:*in_s++;}il void in(char &ch){if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)__=1;else ch=c;}il void in(char *ch){*ch='\0';if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF){__=1;return;}*ch=c;ch++;while((c=gc())!=EOF&&!isspace(c))*ch=c,ch++;if(c==EOF)__=1;*ch='\0';}template<typename T>il void in(T &x){if(__)return;char c=gc();bool f=0;while(c!=EOF&&(c<'0'||c>'9'))f^=(c=='-'),c=gc();if(c==EOF){__=1;return;}x=0;while(c!=EOF&&'0'<=c&&c<='9')x=x*10+c-48,c=gc();if(c==EOF)__=1;if(f)x=-x;}template<typename T,typename ... arr>il void in(T &x,arr & ... y){in(x),in(y...);}const char ln='\n';static char out_buf[str],*out_s=out_buf,*out_t=out_buf+str;il void flush(){fwrite(out_buf,1,out_s-out_buf,stdout);out_s=out_buf;}il void pt(char c){(out_s==out_t)?(fwrite(out_s=out_buf,1,str,stdout),*out_s++=c):(*out_s++=c);}il void out(const char* s){while(*s)pt(*s++);}il void out(char* s){while(*s)pt(*s++);}il void out(char c){pt(c);}template<typename T>il void out(T x){if(!x){pt('0');return;}if(x<0)pt('-'),x=-x;char a[50],t=0;while(x)a[t++]=x%10,x/= 10;while(t--)pt(a[t]+'0');}template<typename T,typename ... arr>il void out(T x,arr & ... y){out(x),out(y...);}}using namespace IO;
const int N=100011;
int n,q,siz[N],siz2[N],c[2][N],f[N];
bool rev[N];
#define ls(x) c[0][x]
#define rs(x) c[1][x]
il void pu(int x){siz[x]=siz[ls(x)]+siz[rs(x)]+1+siz2[x];}
il void pr(int x){rev[x]^=1;int t=ls(x);ls(x)=rs(x),rs(x)=t;}
il void pd(int x){
    if(rev[x]){
        if(ls(x))pr(ls(x));
        if(rs(x))pr(rs(x));
        rev[x]=0;
    }
}
il int g(int x){return rs(f[x])==x;}
il int nrt(int x){return ls(f[x])==x||rs(f[x])==x;}
il void rotate(int x){
    int y=f[x],z=f[y],l=g(x),r=!l,w=c[r][x];
    if(nrt(y))c[g(y)][z]=x;
    c[r][x]=y,c[l][y]=w;
    if(w)f[w]=y;
    f[x]=z,f[y]=x;
    pu(y),pu(x);
}
void pda(int x){
    if(nrt(x))pda(f[x]);
    pd(x);
}
il void splay(int x){
    for(pda(x);nrt(x);rotate(x))if(nrt(f[x]))
        rotate(g(x)^g(f[x])?x:f[x]);
}
il void access(int x){
    for(int y=0;x;x=f[y=x])
        splay(x),siz2[x]+=siz[rs(x)]-siz[rs(x)=y],pu(x);
}
il void mrt(int x){access(x),splay(x),pr(x);}
int main(){
    in(n,q);
    for(int i=1;i<=n;++i)siz[i]=1;
    char opt;int x,y;
    while(q--){
        in(opt,x,y);
        if(opt=='A')
            mrt(x),mrt(y),
            siz2[f[x]=y]+=siz[x];
        else{
            mrt(x),access(y),splay(y);  
            f[x]=ls(y)=0,pu(x);
            mrt(x),mrt(y);
            out((long long)siz[x]*siz[y],ln);
            siz2[f[x]=y]+=siz[x];
        }
    }
    flush();
}
LG 4219 [BJOI2014]大融合
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