[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;
}