[AH/HNOI2017]单旋
这道题可以用LCT做，开set，LCT，二叉树
- 操作1：直接开set，找到它要插入的位置，一定是前驱，后缀中deep最大的（显然
手玩） - 操作2：set+LCT询问路径，直接手动提上去，因为树的形态不变
- 操作3：同2
- 操作4：LCT::Cut，手动删除
- 操作5：同4
- 没了
- 记得手动更新二叉树（这个一定要想清楚
会又WA又TLE又RE n遍）
# include <bits/stdc++.h>
# define RG register
# define IL inline
# define Fill(a, b) memset(a, b, sizeof(a))
using namespace std;
typedef long long ll;
const int _(1e5 + 10);
IL ll Read(){
char c = '%'; ll x = 0, z = 1;
for(; c > '9' || c < '0'; c = getchar()) if(c == '-') z = -1;
for(; c >= '0' && c <= '9'; c = getchar()) x = x * 10 + c - '0';
return x * z;
}
int fa[_], ch[2][_], rev[_], S[_], sz[_], qc[_], qx[_], o[_], rt, spc[2][_], spf[_];
set <int> T;
set <int> :: iterator it;
IL bool Son(RG int x){ return ch[1][fa[x]] == x; }
IL bool Isroot(RG int x){ return ch[0][fa[x]] != x && ch[1][fa[x]] != x; }
IL void Update(RG int x){ sz[x] = sz[ch[0][x]] + sz[ch[1][x]] + 1; }
IL void Reverse(RG int x){ swap(ch[0][x], ch[1][x]); rev[x] ^= 1; }
IL void Pushdown(RG int x){ if(!rev[x]) return; Reverse(ch[0][x]); Reverse(ch[1][x]); rev[x] = 0; }
IL void Rotate(RG int x){
RG int y = fa[x], z = fa[y], c = Son(x);
if(!Isroot(y)) ch[Son(y)][z] = x; fa[x] = z;
ch[c][y] = ch[!c][x]; fa[ch[c][y]] = y;
ch[!c][x] = y; fa[y] = x;
Update(y);
}
IL void Splay(RG int x){
S[++S[0]] = x;
for(RG int y = x; !Isroot(y); y = fa[y]) S[++S[0]] = fa[y];
while(S[0]) Pushdown(S[S[0]--]);
for(RG int y = fa[x]; !Isroot(x); Rotate(x), y = fa[x])
if(!Isroot(y)) Son(x) ^ Son(y) ? Rotate(x) : Rotate(y);
Update(x);
}
IL void Access(RG int x){ for(RG int y = 0; x; y = x, x = fa[x]) Splay(x), ch[1][x] = y, Update(x); }
IL int Findroot(RG int x){ Access(x); Splay(x); while(ch[0][x]) x = ch[0][x]; return x; }
IL void Makeroot(RG int x){ Access(x); Splay(x); Reverse(x); }
IL void Split(RG int x, RG int y){ Makeroot(x); Access(y); Splay(y); }
IL void Link(RG int x, RG int y){ if(!x || !y) return; Makeroot(x); fa[x] = y; }
IL void Cut(RG int x, RG int y){ if(!x || !y) return; Split(x, y); ch[0][y] = fa[x] = 0; }
IL int Query(RG int x){ Makeroot(rt); Access(x); Splay(x); return sz[x]; }
int main(RG int argc, RG char *argv[]){
RG int len = 0, m = Read();
T.insert(-2e9); T.insert(2e9);
for(RG int i = 1; i <= m; ++i){
qc[i] = Read();
if(qc[i] == 1) o[++len] = qx[i] = Read();
}
sort(o + 1, o + len + 1);
for(RG int i = 1; i <= m; ++i)
if(qc[i] == 1) qx[i] = lower_bound(o + 1, o + len + 1, qx[i]) - o;
for(RG int i = 1; i <= m; ++i){
if(qc[i] != 1 && T.size() == 3){
puts("1"); it = T.begin(); ++it;
if(qc[i] >= 3) T.erase(it), rt = 0;
continue;
}
if(qc[i] == 1){
if(T.size() == 2){ T.insert(qx[i]); rt = qx[i]; puts("1"); continue; }
it = T.lower_bound(qx[i]); RG int ans = 0, pos, g;
if(*it != 2e9){ g = Query(*it); if(g > ans) ans = g, pos = *it; }
if(*(--it) != -2e9){ g = Query(*it); if(g > ans) ans = g, pos = *it; }
T.insert(qx[i]); Link(qx[i], pos);
spc[qx[i] > pos][pos] = qx[i]; spf[qx[i]] = pos;
printf("%d\n", ans + 1);
}
else if(qc[i] == 2){
it = T.begin(); ++it;
RG int x = *it, y = spc[1][x], z = spf[x];
printf("%d\n", Query(x));
if(rt != x){
Cut(x, z); Cut(x, y); Link(x, rt); Link(y, z);
spf[rt] = x; spf[x] = 0; spf[y] = z; spc[1][x] = rt; rt = x; spc[0][z] = y;
}
}
else if(qc[i] == 3){
it = T.end(); --it; --it;
RG int x = *it, y = spc[0][x], z = spf[x];
printf("%d\n", Query(x));
if(rt != x){
Cut(x, z); Cut(x, y); Link(x, rt); Link(y, z);
spf[rt] = x; spf[x] = 0; spf[y] = z; spc[0][x] = rt; rt = x; spc[1][z] = y;
}
}
else if(qc[i] == 4){
it = T.begin(); ++it;
RG int x = *it, y = spc[1][x], z = spf[x];
T.erase(it);
printf("%d\n", Query(x));
Cut(x, z); Cut(x, y); Link(y, z);
spf[y] = z; spc[0][x] = spc[1][x] = spf[x] = 0; spc[0][z] = y;
if(rt == x) rt = y;
}
else if(qc[i] == 5){
it = T.end(); --it; --it;
RG int x = *it, y = spc[0][x], z = spf[x];
T.erase(it);
printf("%d\n", Query(x));
Cut(x, z); Cut(x, y); Link(y, z);
spf[y] = z; spc[0][x] = spc[1][x] = spf[x] = 0; spc[1][z] = y;
if(rt == x) rt = y;
}
}
return 0;
}
