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;
}