Code:

#include <cstdio>
#include <algorithm>
#include <cstring>
#include <string>
using namespace std;
void setIO(string a){freopen((a+".in").c_str(),"r",stdin);}

#define maxn 100009
#define ll long long
int n,q;
struct LCT{
    int ch[maxn][2],f[maxn],siz[maxn],sta[maxn],son[maxn],tag[maxn];
    int lson(int x){ return ch[x][0]; }
    int rson(int x){ return ch[x][1]; }
    int get(int x){ return ch[f[x]][1]==x;}
    int isRoot(int x){ return !(ch[f[x]][0]==x||ch[f[x]][1]==x); }
    void mark(int x){ if(!x)return; swap(ch[x][0],ch[x][1]),tag[x]^=1; }
    void pushdown(int x){ if(tag[x]) mark(lson(x)),mark(rson(x)),tag[x]=0; }
    void pushup(int x){ if(!x) return; siz[x]=siz[lson(x)]+siz[rson(x)]+son[x]+1; }

    void rotate(int x){
        int old=f[x],fold=f[old],which=get(x);
        if(!isRoot(old)) ch[fold][ch[fold][1]==old]=x; 
        ch[old][which]=ch[x][which^1],f[ch[old][which]]=old;
        ch[x][which^1]=old,f[old]=x,f[x]=fold;
        pushup(old),pushup(x); 
    }
    void splay(int x){
        int v=0,u=x;
        sta[++v]=u;
        while(!isRoot(u)) sta[++v]=f[u],u=f[u];
        while(v) pushdown(sta[v--]);
        u=f[u];
        for(int fa;(fa=f[x])!=u;rotate(x))
            if(f[fa]!=u) rotate(get(fa)==get(x)?fa:x);
    }
    void Access(int x){for(int y=0;x;y=x,x=f[x]) splay(x),son[x]=son[x]+siz[ch[x][1]]-siz[y], ch[x][1]=y, pushup(x);  }
    void makeRoot(int x){ Access(x), splay(x), mark(x);}
    void link(int a,int b){ makeRoot(a), makeRoot(b), son[a]+=siz[b], f[b]=a,  pushup(a); }
    ll query(int a,int b){
        makeRoot(a),makeRoot(b); 
        return (long long)siz[a]*(siz[b]-siz[a]);
    }
}tree;
int main(){
    //setIO("input");
    int a,b;
    char opt[5];
    scanf("%d%d",&n,&q);
    while(q--){
        scanf("%s%d%d",opt,&a,&b);
        switch(opt[0]){
            case ‘A‘: {
                tree.link(a,b);
                break;
            }
            case ‘Q‘: {
                printf("%lld\n",tree.query(a,b));
                break;
            }
        }
    }
    return 0;
}

[BJOI2014]大融合 LCT維護子樹信息