洛谷 - P4219 [BJOI]大融合（维护子树大小）

传送门：洛谷 - P4219

思路分析

答案很显然为断开这条边两个连通块的乘积，要动态加边的话用LCT比较好实现
如果维护子树大小呢，只需要维护虚儿子个数就行了，在$link$，$acess$和$pushup$的时候加上虚儿子的贡献就可以了

AC代码

#include <bits/stdc++.h>
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define fun function
#define sz(x) (x).size()
#define lowbit(x) (x)&(-x)
#define all(x) (x).begin(),(x).end()
#define mem(a,b) memset(a,b,sizeof(a))

namespace FastIO {
#define BUF_SIZE 100000
#define OUT_SIZE 100000
    bool IOerror=0;
    inline char nc() {
        static char buf[BUF_SIZE],*p1=buf+BUF_SIZE,*pend=buf+BUF_SIZE;
        if(p1==pend) {
            p1=buf;
            pend=buf+fread(buf,1,BUF_SIZE,stdin);
            if(pend==p1) {
                IOerror=1;
                return -1;
            }
        }
        return *p1++;
    }
    inline bool blank(char ch) {
        return ch==' '||ch=='\n'||ch=='\r'||ch=='\t';
    }
    template<class T> inline bool read(T &x) {
        bool sign=0;
        char ch=nc();
        x=0;
        for(; blank(ch); ch=nc());
        if(IOerror)return false;
        if(ch=='-')sign=1,ch=nc();
        for(; ch>='0'&&ch<='9'; ch=nc())x=x*10+ch-'0';
        if(sign)x=-x;
        return true;
    }
    template<class T,class... U>bool read(T& h,U&... t) {
        return read(h)&&read(t...);
    }
#undef OUT_SIZE
#undef BUF_SIZE
};
using namespace std;
using namespace FastIO;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

typedef long long ll;
typedef pair<int,int> pii;
typedef unsigned long long ull;

const int INF = 0x3f3f3f3f;
const int N = 2e5+10;

namespace LCT {
#define fa(x) (tree[x].fa)
#define ls(x) (tree[x].ch[0])
#define rs(x) (tree[x].ch[1])
#define ident(x,f) (rs(f)==x)
#define reverse(x) swap(ls(x),rs(x)),tree[x].tag^=1
#define notroot(x) (ls(fa(x)) == x || rs(fa(x)) == x)

    struct node {
        int fa,ch[2],val,siz,vsiz;
        bool tag;
    } tree[N];

    inline void connect(int x,int f,int s) {
        tree[f].ch[s]=x;
        tree[x].fa=f;
    }

    inline void pp(int x) {
        tree[x].siz = tree[ls(x)].siz+tree[rs(x)].siz+tree[x].vsiz+1;
    }

    inline void pushdown(int x) {
        if(tree[x].tag) {
            if(ls(x)) reverse(ls(x));
            if(rs(x)) reverse(rs(x));
        }
        tree[x].tag=0;
    }

    inline void pushall(int x) {
        if(notroot(x)) pushall(fa(x));
        pushdown(x);
    }

    inline void rotate(int x) {
        int f = fa(x),ff=fa(f),fs=ident(x,f),ffs=ident(f,ff);
        connect(tree[x].ch[fs^1],f,fs);
        fa(x) = ff;
        if(notroot(f)) tree[ff].ch[ffs] = x;
        connect(f,x,fs^1);
        pp(f),pp(x);
    }

    inline void splaying(int x) {
        pushall(x);
        while(notroot(x)) {
            int f=fa(x),ff=fa(f);
            if(notroot(f)) ident(f,ff)^ident(x,f) ? rotate(x):rotate(f);
            rotate(x);
        }
    }

    inline void access(int x) {
        for(int y=0; x; x=fa(x)) {
            splaying(x);
            tree[x].vsiz+=tree[rs(x)].siz;
            rs(x)=y;
            tree[x].vsiz-=tree[rs(x)].siz;
            pp(x);
            y=x;
        }
    }

    inline void mkroot(int x) {
        access(x);
        splaying(x);
        reverse(x);
    }

    inline int findroot(int x) {
        access(x);
        splaying(x);
        while(ls(x)) {
            pushdown(x);
            x=ls(x);
        }
        splaying(x);
        return x;
    }

    inline void link(int x,int y) {
        mkroot(x);
        if(findroot(y)==x) return;
        mkroot(y);
        fa(x)=y;
        tree[y].vsiz+=tree[x].siz;
        pp(y);
    }

    inline void cut(int x,int y) {
        mkroot(x);
        if(findroot(y)!=x||fa(y)!=x||ls(y)) return;
        fa(y)=rs(x)=0;
        pp(x);
    }

    inline void split(int x,int y) {
        mkroot(x);
        access(y);
        splaying(y);
    }
#undef fa
#undef ls
#undef rs
#undef ident
#undef reverse
#undef notroot
};

int main() {

#ifdef xiaofan
    freopen("1.in","r",stdin);
    freopen("1.out","w",stdout);
#endif

    int n,q;
    cin>>n>>q;
    for(int i=1;i<=n;i++) LCT::tree[i].siz = 1;
    for(int i=1;i<=q;i++){
        char op;
        int x,y;
        cin>>op>>x>>y;
        if(op=='A'){
            LCT::link(x,y);
        }else{
            LCT::split(x,y);
            cout<<1LL*(LCT::tree[x].vsiz+1)*(LCT::tree[y].vsiz+1)<<endl;
        }
    }




    return 0;
}