LuoguP4219 [BJOI2014]大融合(LCT)

早上考试想用\(LCT\)维护联通块\(size\)，现在才发现\(LCT\)的\(size\)有虚实之分
\(Link\)与\(Acess\)中虚实变,干他丫的
\(Splay\)中只是相对关系，没有虚实变，因此不搞它

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#define R(a,b,c) for(register int a = (b); a <= (c); ++a)
#define nR(a,b,c) for(register int a = (b); a >= (c); --a)
#define Fill(a,b) memset(a, b, sizeof(a))
#define Swap(a,b) ((a) ^= (b) ^= (a) ^= (b))

#define ON_DEBUGG

#ifdef ON_DEBUGG

#define D_e_Line printf("-----------\n")
#define D_e(x) std::cout << (#x) << " : " <<x << "\n"
#define FileOpen() freopen("in.txt", "r", stdin)
#define FileSave() freopen("out.txt", "w", stdout)
#define Pause() system("pause")
#include <ctime>
#define TIME() fprintf(stderr, "\nTIME :　%.3lfms\n", clock() * 1000.0 / CLOCKS_PER_SEC)

#else

#define D_e_Line ;
#define D_e(x) ;
#define FileOpen() ;
#define FilSave ;
#define Pause() ;
#define TIME() ;

#endif

struct ios {
    template<typename ATP> ios& operator >> (ATP &x) {
        x = 0; int f = 1; char c;
        for(c = getchar(); c < '0' || c > '9'; c = getchar()) if(c == '-') f = -1;
        while(c >= '0' && c <= '9') x = x * 10 + (c ^ '0'), c = getchar();
        x *= f;
        return *this;
    }
}io;

using namespace std;

template<typename ATP> inline ATP Min(ATP a, ATP b) {
    return a < b ? a : b;
}
template<typename ATP> inline ATP Max(ATP a, ATP b) {
    return a > b ? a : b;
}
template<typename ATP> inline ATP Abs(ATP a) {
    return a < 0 ? -a : a;
}

const int N = 1e5 + 7;

struct LCT {
    int ch[2], fa, siz, sz; // siz : true edge, sz : virtual edge
    bool rev;
} t[N];
#define ls t[u].ch[0]
#define rs t[u].ch[1]
inline int Ident(int &u) {
    return t[t[u].fa].ch[1] == u;
}

inline bool IsRoot(int &u) {
    return t[t[u].fa].ch[0] != u && t[t[u].fa].ch[1] != u;
}

inline void Pushup(int &u) {
    if(u) t[u].siz = t[ls].siz + t[rs].siz + t[u].sz + 1;
    // left + right + virtual + self
}

inline void Pushrev(int u) {
    Swap(ls, rs);
    t[u].rev ^= 1;
}

inline void Pushdown(int u) {
    if(!t[u].rev) return;
    if(ls) Pushrev(ls);
    if(rs) Pushrev(rs);
    t[u].rev = 0;
}

inline void Rotate(int x) {
    int y = t[x].fa, z = t[y].fa, k = Ident(x);
    t[x].fa = z; if(!IsRoot(y)) t[z].ch[Ident(y)] = x;
    t[y].ch[k] = t[x].ch[k ^ 1], t[t[x].ch[k ^ 1]].fa = y;
    t[x].ch[k ^ 1] = y, t[y].fa = x;
    Pushup(y), Pushup(x);
}

int sta[N], top;

inline void Splay(int u) {
    int x = u;
    while(!IsRoot(u)){
        sta[++top] = u;
        u = t[u].fa;
    }
    sta[++top] = u;
    while(top) Pushdown(sta[top--]);
    while(!IsRoot(x)){
        int y = t[x].fa;
        if(!IsRoot(y)){
            Ident(x) == Ident(y) ? Rotate(y) : Rotate(x);
        }
        Rotate(x);
    }
    Pushup(x);
}

inline void Access(int u) {
    for(register int v = 0; u; v = u, u = t[u].fa){
        Splay(u);
        t[u].sz += t[rs].siz - t[v].siz;
        t[u].ch[1] = v;
        Pushup(u);
    }
}

inline void MakeRoot(int u) {
    Access(u);
    Splay(u);
    Pushrev(u);
}

inline void Split(int u, int v) {
    MakeRoot(u);
    Access(v);
    Splay(v);
}

inline void Link(int u, int v) {
    Split(u, v);
    t[u].fa = v;
    t[v].sz += t[u].siz;
}
inline long long Query(int u, int v) {
    Split(u, v);
    return 1ll * (t[u].sz + 1) * (t[v].sz + 1);
}

//inline void Link(int u, int v) {
//  MakeRoot(u);
//  MakeRoot(v);
//  t[u].fa = v;
//  t[v].sz += t[u].siz;
//  Pushup(v);
//}
//inline long long Query(int u, int v) {
//  MakeRoot(u);
//  MakeRoot(v);
//  return 1ll * (t[u].sz + 1) * (t[v].sz + 1);
//}

char opt[13];
int main() {
    int n, m;
    io >> n >> m;
    R(i,1,n){
        t[i].siz = 1;
        t[i].sz = 0;
    }
    while(m--){
        scanf("%s", opt + 1);
        int x, y;
        io >> x >> y;
        if(opt[1] == 'A'){
            Link(x, y);
        }
        else{
            printf("%lld\n", Query(x, y));
        }
    }
    return 0;
}

原文地址：https://www.cnblogs.com/bingoyes/p/11721207.html