Splay
参考：https://tiger0132.blog.luogu.org/slay-notes
普通模板：
const int N = 1e5 + 10; int ch[N][2], val[N], cnt[N], fa[N], sz[N], lazy[N], ncnt = 0, rt = 0; int n, m; inline int ck(int x) { return ch[fa[x]][1] == x; } inline void push_up(int x) { sz[x] = sz[ch[x][0]] + sz[ch[x][1]] + cnt[x]; } ///区间反转 inline void push_down(int x) { if(lazy[x]) { swap(ch[x][0], ch[x][1]); lazy[ch[x][0]] ^= 1; lazy[ch[x][1]] ^= 1; lazy[x] = 0; } } void Rotate(int x) { int y = fa[x], z = fa[y]; push_down(y), push_down(x);///区间反转 int k = ck(x), w = ch[x][k^1]; ch[y][k] = w, fa[w] = y; ch[z][ck(y)] = x, fa[x] = z; ch[x][k^1] = y, fa[y] = x; push_up(y), push_up(x); } void Splay(int x, int goal = 0) { push_down(x);///区间反转 while(fa[x] != goal) { int y = fa[x], z = fa[y]; if(z != goal) { if(ck(x) == ck(y)) Rotate(y); else Rotate(x); } Rotate(x); } if(!goal) rt = x; } void Find(int x) { if(!rt) return ; int cur = rt; while(ch[cur][x>val[cur]] && x != val[cur]) cur = ch[cur][x>val[cur]]; Splay(cur); } void Insert(int x) { int cur = rt, p = 0; while(cur && val[cur] != x) { p = cur; cur = ch[cur][x>val[cur]]; } if(cur) cnt[cur]++; else { cur = ++ncnt; if(p) ch[p][x>val[p]] = cur; fa[cur] = p; ch[cur][0] = ch[cur][1] = 0; val[cur] = x; cnt[cur] = sz[cur] = 1; } Splay(cur); } int Kth(int k) { int cur = rt; while(true) { push_down(cur); ///区间反转 if(ch[cur][0] && k <= sz[ch[cur][0]]) cur = ch[cur][0]; else if(k > sz[ch[cur][0]] + cnt[cur]) k -=sz[ch[cur][0]] + cnt[cur], cur = ch[cur][1]; else return cur; } } inline int get_min(int x) { while(x && ch[x][0]) x = ch[x][0]; return x; } inline int get_max(int x) { while(x && ch[x][1]) x = ch[x][1]; return x; } int Pre(int x) { Find(x); if(val[rt] < x) return rt; int cur = ch[rt][0]; while(ch[cur][1]) cur = ch[cur][1]; return cur; } int Succ(int x) { Find(x); if(val[rt] > x) return rt; int cur = ch[rt][1]; while(ch[cur][0]) cur = ch[cur][0]; return cur; } void Remove(int x) { int last = Pre(x), next = Succ(x); Splay(last), Splay(next, last); int del = ch[next][0]; if(cnt[del] > 1) cnt[del]--, Splay(del); else ch[next][0] = 0, push_up(next), push_up(last); } ///区间反转 void Reverse(int l, int r) { int x = Kth(l), y = Kth(r+2); Splay(x), Splay(y, x); lazy[ch[y][0]] ^= 1; } void Output(int x) { push_down(x); if(ch[x][0]) Output(ch[x][0]); if(1 <= val[x] && val[x] <= n) printf("%d ", val[x]); if(ch[x][1]) Output(ch[x][1]); } void delete_root() { if(ch[rt][1]) { int cur = ch[rt][1]; while(cur && ch[cur][0]) cur = ch[cur][0]; Splay(cur, rt); ch[cur][0] = ch[rt][0]; fa[ch[cur][0]] = cur; rt = cur; } else rt = ch[rt][0]; fa[rt] = 0; if(rt) push_up(rt); } inline int NewNode(int x) { int cur; if(q.empty()) cur = ++ncnt; else cur = q.front(), q.pop(); ///初始化 ch[cur][0] = ch[cur][1] = fa[cur] = lazy[cur] = 0; val[cur] = x; sz[cur] = cnt[cur] = 1; return cur; } void Recycle(int x) { if(ch[x][0]) Recycle(ch[x][0]); if(ch[x][1]) Recycle(ch[x][1]); if(x) q.push(x); } int build(int l, int r, int *a) { if(l > r) return 0; int mid = l+r >> 1, cur = NewNode(a[mid]); if(l == r) return cur; if(ch[cur][0] = build(l, mid-1, a)) fa[ch[cur][0]] = cur; if(ch[cur][1] = build(mid+1, r, a)) fa[ch[cur][1]] = cur; push_up(cur); return cur; } inline void init() { ncnt = rt = ch[0][0] = ch[0][1] = fa[0] = sz[0] = cnt[0] = val[0] = lazy[0] = 0; }
按排名插入模板（常数较小？？？也许以前的方法写搓了）：
inline void Newnode(int &cur, int f, int a) { cur = ++ncnt; fa[cur] = f; val[cur] = a; ch[cur][0] = ch[cur][1] = 0; sz[cur] = cnt[cur] = 1; } void Insert(int x, int y) { int p = 0; if(!rt) { Newnode(rt, 0, y); return ; } if(!x) { p = rt; sz[p]++; while(ch[p][0]) p = ch[p][0], sz[p]++; Newnode(ch[p][0], p, y); Splay(ch[p][0]); return ; } int u = Kth(x); Splay(u); Newnode(rt, 0, y); ch[rt][1] = ch[u][1]; fa[ch[rt][1]] = rt; ch[u][1] = 0; ch[rt][0] = u; fa[u] = rt; push_up(u), push_up(rt); }
例题：
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 2e5 + 10; int ch[N][2], val[N], cnt[N], fa[N], sz[N], ncnt = 0, rt = 0; inline int ck(int x) { return ch[fa[x]][1] == x; } inline void push_up(int x) { sz[x] = sz[ch[x][0]] + sz[ch[x][1]] + cnt[x]; } void Rotate(int x) { int y = fa[x], z = fa[y], k = ck(x), w = ch[x][k^1]; ch[y][k] = w, fa[w] = y; ch[z][ck(y)] = x, fa[x] = z; ch[x][k^1] = y, fa[y] = x; push_up(y), push_up(x); } void Splay(int x, int goal = 0) { while(fa[x] != goal) { int y = fa[x], z = fa[y]; if(z != goal) { if(ck(x) == ck(y)) Rotate(y); else Rotate(x); } Rotate(x); } if(!goal) rt = x; } void Find(int x) { if(!rt) return ; int cur = rt; while(ch[cur][x>val[cur]] && x != val[cur]) cur = ch[cur][x>val[cur]]; Splay(cur); } void Insert(int x) { int cur = rt, p = 0; while(cur && val[cur] != x) { p = cur; cur = ch[cur][x>val[cur]]; } if(cur) cnt[cur]++; else { cur = ++ncnt; if(p) ch[p][x>val[p]] = cur; fa[cur] = p; ch[cur][0] = ch[cur][1] = 0; val[cur] = x; cnt[cur] = sz[cur] = 1; } Splay(cur); } int Kth(int k) { int cur = rt; while(true) { if(ch[cur][0] && k <= sz[ch[cur][0]]) cur = ch[cur][0]; else if(k > sz[ch[cur][0]] + cnt[cur]) k -=sz[ch[cur][0]] + cnt[cur], cur = ch[cur][1]; else return cur; } } int Pre(int x) { Find(x); if(val[rt] < x) return rt; int cur = ch[rt][0]; while(ch[cur][1]) cur = ch[cur][1]; return cur; } int Succ(int x) { Find(x); if(val[rt] > x) return rt; int cur = ch[rt][1]; while(ch[cur][0]) cur = ch[cur][0]; return cur; } void Remove(int x) { int last = Pre(x), next = Succ(x); Splay(last), Splay(next, last); int del = ch[next][0]; if(cnt[del] > 1) cnt[del]--, Splay(del); else ch[next][0] = 0/*, push_up(next), push_up(last)*/; } int n, opt, x; int main() { Insert(INT_MIN); Insert(INT_MAX); scanf("%d", &n); for (int i = 1; i <= n; ++i) { scanf("%d %d", &opt, &x); if(opt == 1) Insert(x); else if(opt == 2) Remove(x); else if(opt == 3) Find(x), printf("%d ", sz[ch[rt][0]]); else if(opt == 4) printf("%d ", val[Kth(x+1)]); else if(opt == 5) printf("%d ", val[Pre(x)]); else printf("%d ", val[Succ(x)]); } return 0; }
思路：跟区间反转相关的Splay维护的都是下标
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 1e5 + 10; int ch[N][2], val[N], cnt[N], fa[N], sz[N], lazy[N], ncnt = 0, rt = 0; int n, m; inline int ck(int x) { return ch[fa[x]][1] == x; } inline void push_up(int x) { sz[x] = sz[ch[x][0]] + sz[ch[x][1]] + cnt[x]; } ///区间反转 inline void push_down(int x) { if(lazy[x]) { swap(ch[x][0], ch[x][1]); lazy[ch[x][0]] ^= 1; lazy[ch[x][1]] ^= 1; lazy[x] = 0; } } void Rotate(int x) { int y = fa[x], z = fa[y], k = ck(x), w = ch[x][k^1]; ch[y][k] = w, fa[w] = y; ch[z][ck(y)] = x, fa[x] = z; ch[x][k^1] = y, fa[y] = x; push_up(y), push_up(x); } void Splay(int x, int goal = 0) { while(fa[x] != goal) { int y = fa[x], z = fa[y]; if(z != goal) { if(ck(x) == ck(y)) Rotate(y); else Rotate(x); } Rotate(x); } if(!goal) rt = x; } void Find(int x) { if(!rt) return ; int cur = rt; while(ch[cur][x>val[cur]] && x != val[cur]) cur = ch[cur][x>val[cur]]; Splay(cur); } void Insert(int x) { int cur = rt, p = 0; while(cur && val[cur] != x) { p = cur; cur = ch[cur][x>val[cur]]; } if(cur) cnt[cur]++; else { cur = ++ncnt; if(p) ch[p][x>val[p]] = cur; fa[cur] = p; ch[cur][0] = ch[cur][1] = 0; val[cur] = x; cnt[cur] = sz[cur] = 1; } Splay(cur); } int Kth(int k) { int cur = rt; while(true) { push_down(cur); ///区间反转 if(ch[cur][0] && k <= sz[ch[cur][0]]) cur = ch[cur][0]; else if(k > sz[ch[cur][0]] + cnt[cur]) k -=sz[ch[cur][0]] + cnt[cur], cur = ch[cur][1]; else return cur; } } int Pre(int x) { Find(x); if(val[rt] < x) return rt; int cur = ch[rt][0]; while(ch[cur][1]) cur = ch[cur][1]; return cur; } int Succ(int x) { Find(x); if(val[rt] > x) return rt; int cur = ch[rt][1]; while(ch[cur][0]) cur = ch[cur][0]; return cur; } void Remove(int x) { int last = Pre(x), next = Succ(x); Splay(last), Splay(next, last); int del = ch[next][0]; if(cnt[del] > 1) cnt[del]--, Splay(del); else ch[next][0] = 0, push_up(next), push_up(last); } ///区间反转 void Reverse(int l, int r) { int x = Kth(l), y = Kth(r+2); Splay(x), Splay(y, x); lazy[ch[y][0]] ^= 1; } void Output(int x) { push_down(x); if(ch[x][0]) Output(ch[x][0]); if(1 <= val[x] && val[x] <= n) printf("%d ", val[x]); if(ch[x][1]) Output(ch[x][1]); } int l, r; int main() { scanf("%d %d", &n, &m); for (int i = 0; i <= n+1; ++i) Insert(i); while(m--) { scanf("%d %d", &l, &r); Reverse(l, r); } Output(rt); return 0; }
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 1e6 + 10; int ch[N][2], val[N], cnt[N], fa[N], sz[N], rev[N], lazy[N], ncnt = 0, rt = 0; int n, m, a[N], lmx[N], rmx[N], mx[N], sm[N]; queue<int> q; inline int NewNode(int x) { int cur; if(q.empty()) cur = ++ncnt; else cur = q.front(), q.pop(); ch[cur][0] = ch[cur][1] = fa[cur] = 0; rev[cur] = lazy[cur] = 0; sz[cur] = cnt[cur] = 1; mx[cur] = sm[cur] = val[cur] = x; lmx[cur] = rmx[cur] = max(0, x); return cur; } void Recycle(int x) { if(ch[x][0]) Recycle(ch[x][0]); if(ch[x][1]) Recycle(ch[x][1]); if(x) q.push(x); } inline void push_up(int x) { int l = ch[x][0], r = ch[x][1]; sz[x] = sz[l] + cnt[x] + sz[r]; sm[x] = sm[l] + val[x] + sm[r]; lmx[x] = max(lmx[l], sm[l] + val[x] + lmx[r]); rmx[x] = max(rmx[r], sm[r] + val[x] + rmx[l]); mx[x] = max(rmx[l] + val[x] + lmx[r], max(mx[l], mx[r])); } inline void push_down(int x) { int l = ch[x][0], r = ch[x][1]; if(lazy[x]) { lazy[x] = rev[x] = 0; if(l) { lazy[l] = 1; val[l] = val[x]; sm[l] = val[l] * sz[l]; lmx[l] = rmx[l] = max(0, sm[l]); mx[l] = sm[l] > 0 ? sm[l] : val[l]; } if(r) { lazy[r] = 1; val[r] = val[x]; sm[r] = val[r] * sz[r]; lmx[r] = rmx[r] = max(0, sm[r]); mx[r] = sm[r] > 0 ? sm[r] : val[r]; } } if(rev[x]) { rev[l] ^= 1, rev[r] ^= 1, rev[x] = 0; swap(lmx[l], rmx[l]); swap(lmx[r], rmx[r]); swap(ch[l][0], ch[l][1]); swap(ch[r][0], ch[r][1]); } } int build(int l, int r, int *a) { if(l > r) return 0; int mid = l+r >> 1, cur = NewNode(a[mid]); if(l == r) return cur; if(ch[cur][0] = build(l, mid-1, a)) fa[ch[cur][0]] = cur; if(ch[cur][1] = build(mid+1, r, a)) fa[ch[cur][1]] = cur; push_up(cur); return cur; } inline int ck(int x) { return ch[fa[x]][1] == x; } void Rotate(int x) { int y = fa[x], z = fa[y], k = ck(x), w = ch[x][k^1]; ch[y][k] = w, fa[w] = y; ch[z][ck(y)] = x, fa[x] = z; ch[x][k^1] = y, fa[y] = x; push_up(y), push_up(x); } void Splay(int x, int goal = 0) { while(fa[x] != goal) { int y = fa[x], z = fa[y]; if(z != goal) { if(ck(x) == ck(y)) Rotate(y); else Rotate(x); } Rotate(x); } if(!goal) rt = x; } int Kth(int k) { int cur = rt; while(true) { push_down(cur); ///区间反转 if(ch[cur][0] && k <= sz[ch[cur][0]]) cur = ch[cur][0]; else if(k > sz[ch[cur][0]] + cnt[cur]) k -=sz[ch[cur][0]] + cnt[cur], cur = ch[cur][1]; else return cur; } } ///区间反转 void Reverse(int x, int y) { int u = Kth(x), v = Kth(x+y+1); Splay(u), Splay(v, u); int son = ch[v][0]; if(!lazy[son]) { rev[son] ^= 1; swap(ch[son][0], ch[son][1]); swap(lmx[son], rmx[son]); } push_up(v), push_up(u); } void Insert(int x, int y) { for (int i = 1; i <= y; ++i) scanf("%d", &a[i]); int u = Kth(x+1), v = Kth(x+2); Splay(u), Splay(v, u); int cur = build(1, y, a); ch[v][0] = cur, fa[cur] = v; push_up(v), push_up(u); } void Delete(int x, int y) { int u = Kth(x), v = Kth(x+y+1); Splay(u), Splay(v, u); Recycle(ch[v][0]); ch[v][0] = 0; push_up(v), push_up(u); } void Make_Same(int x, int y, int z) { int u = Kth(x), v = Kth(x+y+1); Splay(u), Splay(v, u); int son = ch[v][0]; lazy[son] = 1; val[son] = z; sm[son] = z*sz[son]; mx[son] = sm[son] > 0 ? sm[son] : val[son]; lmx[son] = rmx[son] = max(0, sm[son]); push_up(v), push_up(u); } int Get_Sum(int x, int y) { int u = Kth(x), v = Kth(x+y+1); Splay(u), Splay(v, u); push_up(v), push_up(u); return sm[ch[v][0]]; } char opt[20]; int x, y, z; int main() { scanf("%d %d", &n, &m); for (int i = 2; i <= n+1; ++i) scanf("%d", &a[i]); a[1] = a[n+2] = mx[0] = -2000; rt = build(1, n+2, a); for (int i = 0; i < m; ++i) { scanf("%s", opt); if(opt[0] == 'I') { scanf("%d %d", &x, &y); Insert(x, y); } else if(opt[0] == 'D') { scanf("%d %d", &x, &y); Delete(x, y); } else if(opt[0] == 'M' && opt[5] == 'S') { scanf("%d %d %d", &x, &y, &z); Make_Same(x, y, z); } else if(opt[0] == 'R') { scanf("%d %d", &x, &y); Reverse(x, y); } else if(opt[0] == 'G') { scanf("%d %d", &x, &y); printf("%d ", Get_Sum(x, y)); } else printf("%d ", mx[rt]); } return 0; }
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<cstdio> #include<iostream> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; const int N = 1e6 + 10; int ch[N][2], val[N], cnt[N], fa[N], sz[N], lazy[N], ncnt = 0, rt = 0; int a[N]; inline int ck(int x) { return ch[fa[x]][1] == x; } inline void push_up(int x) { sz[x] = sz[ch[x][0]] + sz[ch[x][1]] + cnt[x]; } void Rotate(int x) { int y = fa[x], z = fa[y], k = ck(x), w = ch[x][k^1]; ch[y][k] = w, fa[w] = y; ch[z][ck(y)] = x, fa[x] = z; ch[x][k^1] = y, fa[y] = x; push_up(y), push_up(x); } void Splay(int x, int goal = 0) { while(fa[x] != goal) { int y = fa[x], z = fa[y]; if(z != goal) { if(ck(x) == ck(y)) Rotate(y); else Rotate(x); } Rotate(x); } if(!goal) rt = x; } void Find(int x) { if(!rt) return ; int cur = rt; while(ch[cur][x>val[cur]] && x != val[cur]) cur = ch[cur][x>val[cur]]; Splay(cur); } void Insert(int x, int id) { int cur = rt, p = 0; while(cur && val[cur] != x) { p = cur; cur = ch[cur][x>val[cur]]; } if(cur) cnt[cur]++; else { cur = ++ncnt; if(p) ch[p][x>val[p]] = cur; fa[cur] = p; ch[cur][0] = ch[cur][1] = 0; val[cur] = x; a[cur] = id; cnt[cur] = sz[cur] = 1; } Splay(cur); } int Kth(int k) { int cur = rt; while(true) { if(ch[cur][0] && k <= sz[ch[cur][0]]) cur = ch[cur][0]; else if(k > sz[ch[cur][0]] + cnt[cur]) k -=sz[ch[cur][0]] + cnt[cur], cur = ch[cur][1]; else return cur; } } int Pre(int x) { Find(x); if(val[rt] < x) return rt; int cur = ch[rt][0]; while(ch[cur][1]) cur = ch[cur][1]; return cur; } int Succ(int x) { Find(x); if(val[rt] > x) return rt; int cur = ch[rt][1]; while(ch[cur][0]) cur = ch[cur][0]; return cur; } void Remove(int x) { int last = Pre(x), next = Succ(x); Splay(last), Splay(next, last); int del = ch[next][0]; if(cnt[del] > 1) cnt[del]--, Splay(del); else ch[next][0] = 0, push_up(next), push_up(last); } int ty, k, p; int main() { int now = 0; Insert(-100, 0); Insert(10000010, 0); while(~scanf("%d", &ty) && ty) { if(ty == 1) { scanf("%d %d", &k, &p); Insert(p, k); ++now; } else if(ty == 2) { if(!now) { printf("0 "); continue; } int cur = Kth(now+1); printf("%d ", a[cur]); --now; Remove(val[cur]); } else if(ty == 3) { if(!now) { printf("0 "); continue; } int cur = Kth(2); printf("%d ", a[cur]); --now; Remove(val[cur]); } } return 0; }
Splay代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<iostream> #include<cstdio> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 2e5 + 10; int ch[N][2], val[N], cnt[N], fa[N], sz[N], lazy[N], ncnt = 0, rt = 0; int n, m, a[N]; inline int ck(int x) { return ch[fa[x]][1] == x; } inline void push_up(int x) { sz[x] = sz[ch[x][0]] + sz[ch[x][1]] + cnt[x]; } void Rotate(int x) { int y = fa[x], z = fa[y], k = ck(x), w = ch[x][k^1]; ch[y][k] = w, fa[w] = y; ch[z][ck(y)] = x, fa[x] = z; ch[x][k^1] = y, fa[y] = x; push_up(y), push_up(x); } void Splay(int x, int goal = 0) { while(fa[x] != goal) { int y = fa[x], z = fa[y]; if(z != goal) { if(ck(x) == ck(y)) Rotate(y); else Rotate(x); } Rotate(x); } if(!goal) rt = x; } inline int Kth(int k) { int cur = rt; while(true) { if(ch[cur][0] && k <= sz[ch[cur][0]]) cur = ch[cur][0]; else if(k > sz[ch[cur][0]] + cnt[cur]) k -=sz[ch[cur][0]] + cnt[cur], cur = ch[cur][1]; else return cur; } } inline void Newnode(int &cur, int f, int a) { cur = ++ncnt; fa[cur] = f; val[cur] = a; ch[cur][0] = ch[cur][1] = 0; sz[cur] = cnt[cur] = 1; } void Insert(int x, int y) { int p = 0; if(!rt) { Newnode(rt, 0, y); return ; } if(!x) { p = rt; sz[p]++; while(ch[p][0]) p = ch[p][0], sz[p]++; Newnode(ch[p][0], p, y); Splay(ch[p][0]); return ; } int u = Kth(x); Splay(u); Newnode(rt, 0, y); ch[rt][1] = ch[u][1]; fa[ch[rt][1]] = rt; ch[u][1] = 0; ch[rt][0] = u; fa[u] = rt; push_up(u), push_up(rt); } void Output(int x) { if(ch[x][0]) Output(ch[x][0]); printf("%d ", val[x]); if(ch[x][1]) Output(ch[x][1]); } int x, y; int main() { while(~scanf("%d", &n)) { ncnt = rt = 0; for (int i = 1; i <= n; ++i) { scanf("%d %d", &x, &y); Insert(x, y); } Output(rt); printf(" "); } return 0; }
树状数组代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<iostream> #include<cstdio> #include<cmath> #include<algorithm> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 4e5 + 5; int n, bit[N], res[N]; pii a[N]; void add(int x, int a) { while(x <= n) bit[x] += a, x += x&-x; } int Kth(int k) { int up = log(n)/log(2); int res = 0; for (int i = up; i >= 0; --i) { if(res + (1<<i) > n) continue; if(bit[res+(1<<i)] < k) { res += 1<<i; k -= bit[res]; } } return res+1; } int main() { while(~scanf("%d", &n)) { for (int i = 1; i <= n; ++i) add(i, 1); for (int i = 1; i <= n; ++i) scanf("%d %d", &a[i].fi, &a[i].se); for (int i = n; i >= 1; --i) { int pos = Kth(a[i].fi+1); res[pos] = a[i].se; add(pos, -1); } for (int i = 1; i <= n; ++i) printf("%d%c", res[i], " "[i==n]); for (int i = 0; i <= n; ++i) bit[i] = 0; } return 0; }
思路：按下标建树，每次将要翻转到前面的节点Splay到根上，将它的左儿子打上标记，然后把根删掉。
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdi pair<double, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 1e5 + 5; int ch[N][2], val[N], cnt[N], fa[N], sz[N], lazy[N], ncnt = 0, rt = 0; int n, m, a[N], id[N], node[N], ans[N]; pii t[N]; inline int ck(int x) { return ch[fa[x]][1] == x; } inline void push_up(int x) { sz[x] = sz[ch[x][0]] + sz[ch[x][1]] + cnt[x]; } ///区间反转 inline void push_down(int x) { if(lazy[x]) { swap(ch[x][0], ch[x][1]); lazy[ch[x][0]] ^= 1; lazy[ch[x][1]] ^= 1; lazy[x] = 0; } } void Rotate(int x) { int y = fa[x], z = fa[y]; push_down(y), push_down(x); int k = ck(x), w = ch[x][k^1]; ch[y][k] = w, fa[w] = y; ch[z][ck(y)] = x, fa[x] = z; ch[x][k^1] = y, fa[y] = x; push_up(y), push_up(x); } void Splay(int x, int goal = 0) { push_down(x); while(fa[x] != goal) { int y = fa[x], z = fa[y]; if(z != goal) { if(ck(x) == ck(y)) Rotate(y); else Rotate(x); } Rotate(x); } if(!goal) rt = x; } int Kth(int k) { int cur = rt; while(true) { push_down(cur); ///区间反转 if(ch[cur][0] && k <= sz[ch[cur][0]]) cur = ch[cur][0]; else if(k > sz[ch[cur][0]] + cnt[cur]) k -=sz[ch[cur][0]] + cnt[cur], cur = ch[cur][1]; else return cur; } } int Newnode(int x) { int cur = ++ncnt; ch[cur][0] = ch[cur][1] = fa[cur] = 0; val[cur] = x; cnt[cur] = sz[cur] = 1; lazy[cur] = 0; return cur; } int build(int l, int r, int *a) { if(l > r) return 0; int mid = l+r >> 1, cur = Newnode(a[mid]); node[id[mid]] = cur; if(l == r) return cur; if(ch[cur][0] = build(l, mid-1, a)) fa[ch[cur][0]] = cur; if(ch[cur][1] = build(mid+1, r, a)) fa[ch[cur][1]] = cur; push_up(cur); return cur; } void delete_root() { int old = rt; if(ch[rt][1]) { rt = ch[rt][1]; Splay(Kth(1)); ch[rt][0] = ch[old][0]; fa[ch[rt][0]] = rt; } else rt = ch[rt][0]; fa[rt] = 0; push_up(rt); } int main() { while(~scanf("%d", &n)) { if(n == 0) break; for (int i = 1; i <= n; ++i) { scanf("%d", &a[i]); t[i].fi = a[i]; t[i].se = i; } sort(t+1, t+1+n); for (int i = 1; i <= n; ++i) id[t[i].se] = i; rt = ncnt = 0; sz[0] = cnt[0] = ch[0][0] = ch[0][1] = fa[0] = lazy[0] = 0; rt = build(1, n, a); for (int i = 1; i <= n; ++i) { Splay(node[i]); printf("%d%c", sz[ch[rt][0]]+i, " "[i==n]); lazy[ch[rt][0]] ^= 1; delete_root(); } } return 0; }
思路：先把TOP操作和QUERY操作的值单独扣出来，然后其他的一段区间看成一个节点
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<cstdio> #include<iostream> #include<vector> #include<unordered_map> #include<algorithm> #include<cmath> #include<cstring> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdi pair<double, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 2e5 + 1000; int ch[N][2], st[N], cnt[N], fa[N], sz[N], ncnt = 0, rt = 0; int n, m; int T, op[N/2], a[N/2], node[N], tot, vc[N/2], tmp; pii t[N]; char s[100]; inline int ck(int x) { return ch[fa[x]][1] == x; } inline void push_up(int x) { sz[x] = sz[ch[x][0]] + sz[ch[x][1]] + cnt[x]; } void Rotate(int x) { int y = fa[x], z = fa[y], k = ck(x), w = ch[x][k^1]; ch[y][k] = w, fa[w] = y; ch[z][ck(y)] = x, fa[x] = z; ch[x][k^1] = y, fa[y] = x; push_up(y), push_up(x); } void Splay(int x, int goal = 0) { while(fa[x] != goal) { int y = fa[x], z = fa[y]; if(z != goal) { if(ck(x) == ck(y)) Rotate(y); else Rotate(x); } Rotate(x); } if(!goal) rt = x; } inline int Kth(int k) { int cur = rt; while(true) { if(ch[cur][0] && k <= sz[ch[cur][0]]) cur = ch[cur][0]; else if(k > sz[ch[cur][0]] + cnt[cur]) k -=sz[ch[cur][0]] + cnt[cur], cur = ch[cur][1]; else return cur; } } inline int KTH(int k) { int cur = rt; while(true) { if(ch[cur][0] && k <= sz[ch[cur][0]]) cur = ch[cur][0]; else if(k > sz[ch[cur][0]] + cnt[cur]) k -=sz[ch[cur][0]] + cnt[cur], cur = ch[cur][1]; else return st[cur] + k-sz[ch[cur][0]]-1; } } inline void delete_root() { if(ch[rt][1]) { int cur = ch[rt][1]; while(cur && ch[cur][0]) cur = ch[cur][0]; Splay(cur, rt); ch[cur][0] = ch[rt][0]; fa[ch[cur][0]] = cur; rt = cur; } else rt = ch[rt][0]; fa[rt] = 0; if(rt) push_up(rt); } inline int NewNode(pii x) { int cur = ++ncnt; ch[cur][0] = ch[cur][1] = fa[cur] = 0; st[cur] = x.fi; cnt[cur] = sz[cur] = x.se - x.fi + 1; return cur; } int build(int l, int r) { if(l > r) return 0; int mid = l+r >> 1, cur = NewNode(t[mid]); node[mid] = cur; if(l == r) return cur; ch[cur][0] = build(l, mid-1); if(ch[cur][0]) fa[ch[cur][0]] = cur; ch[cur][1] = build(mid+1, r); if(ch[cur][1]) fa[ch[cur][1]] = cur; push_up(cur); return cur; } inline int get(int x) { int l = 1, r = tot, m = l+r >> 1; while(l <= r) { if(t[m].fi > x) r = m-1; else if(t[m].se < x) l = m+1; else return node[m]; m = l+r >> 1; } } inline void init() { tmp = 1; tot = 0; ncnt = rt = 0; ch[0][0] = ch[0][1] = st[0] = cnt[0] = fa[0] = sz[0] = 0; } int main() { // freopen("in.txt", "r", stdin); // freopen("out.txt", "w", stdout); scanf("%d", &T); for (int cs = 1; cs <= T; ++cs) { init(); scanf("%d %d", &n, &m); for (int i = 1; i <= m; ++i) { scanf("%s%d", s, &a[i]); if(s[0] == 'T') op[i] = 1, vc[tmp++] = a[i]; else if(s[0] == 'Q') op[i] = 2, vc[tmp++] = a[i]; else op[i] = 3; } vc[tmp++] = n; sort(vc, vc+tmp); tmp = unique(vc, vc+tmp) - vc; for (int i = 1; i < tmp; ++i) { if(vc[i]-vc[i-1] > 1) t[++tot].fi = vc[i-1]+1, t[tot].se = vc[i]-1; t[++tot].fi = vc[i], t[tot].se = vc[i]; } rt = build(1, tot); printf("Case %d: ", cs); for (int i = 1; i <= m; ++i) { if(op[i] == 1) { int cur = get(a[i]); Splay(cur); delete_root(); int now = rt; while(now && ch[now][0]) now = ch[now][0]; ch[now][0] = cur; fa[cur] = now; st[cur] = a[i]; sz[cur] = cnt[cur] = 1; ch[cur][0] = ch[cur][1] = 0; Splay(cur); } else if(op[i] == 2) { int cur = get(a[i]); Splay(cur); printf("%d ", sz[ch[cur][0]]+1); } else printf("%d ", KTH(a[i])); } } return 0; }
思路：常规操作
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdi pair<double, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 3e5 + 50; int ch[N][2], val[N], cnt[N], fa[N], sz[N], lazy[N], ncnt = 0, rt = 0; int n, m; int T, a[N], x, y, z, tmp; char s[100]; inline int ck(int x) { return ch[fa[x]][1] == x; } inline void push_up(int x) { sz[x] = sz[ch[x][0]] + sz[ch[x][1]] + cnt[x]; } ///区间反转 inline void push_down(int x) { if(lazy[x]) { swap(ch[x][0], ch[x][1]); lazy[ch[x][0]] ^= 1; lazy[ch[x][1]] ^= 1; lazy[x] = 0; } } void Rotate(int x) { int y = fa[x], z = fa[y]; push_down(y), push_down(x);///区间反转 int k = ck(x), w = ch[x][k^1]; ch[y][k] = w, fa[w] = y; ch[z][ck(y)] = x, fa[x] = z; ch[x][k^1] = y, fa[y] = x; push_up(y), push_up(x); } void Splay(int x, int goal = 0) { push_down(x);///区间反转 while(fa[x] != goal) { int y = fa[x], z = fa[y]; if(z != goal) { if(ck(x) == ck(y)) Rotate(y); else Rotate(x); } Rotate(x); } if(!goal) rt = x; } int Kth(int k) { int cur = rt; while(true) { push_down(cur); ///区间反转 if(ch[cur][0] && k <= sz[ch[cur][0]]) cur = ch[cur][0]; else if(k > sz[ch[cur][0]] + cnt[cur]) k -=sz[ch[cur][0]] + cnt[cur], cur = ch[cur][1]; else return cur; } } ///区间反转 void Reverse(int l, int r) { int x = Kth(l), y = Kth(r+2); Splay(x), Splay(y, x); lazy[ch[y][0]] ^= 1; } void Cut(int l, int r, int c) { int x = Kth(l), y = Kth(r+2); Splay(x), Splay(y, x); int cur = ch[y][0]; fa[cur] = 0; ch[y][0] = 0; x = Kth(c+1), y = Kth(c+2); Splay(x), Splay(y, x); fa[cur] = y; ch[y][0] = cur; Splay(cur); } void Output(int x) { push_down(x); if(ch[x][0]) Output(ch[x][0]); if(1 <= val[x] && val[x] <= n) printf("%d%c", val[x], " "[++tmp == n]); if(ch[x][1]) Output(ch[x][1]); } inline int NewNode(int x) { int cur = ++ncnt; ch[cur][0] = ch[cur][1] = fa[cur] = 0; val[cur] = x; sz[cur] = cnt[cur] = 1; lazy[cur] = 0; return cur; } int build(int l, int r, int *a) { if(l > r) return 0; int mid = l+r >> 1, cur = NewNode(a[mid]); if(l == r) return cur; if(ch[cur][0] = build(l, mid-1, a)) fa[ch[cur][0]] = cur; if(ch[cur][1] = build(mid+1, r, a)) fa[ch[cur][1]] = cur; push_up(cur); return cur; } int main() { for (int i = 0; i < N; ++i) a[i] = i; while(~scanf("%d %d", &n, &m)) { if(n == -1 && m == -1) break; rt = ncnt = ch[0][0] = ch[1][0] = fa[0] = sz[0] = cnt[0] = lazy[0] = 0; rt = build(0, n+1, a); for (int i = 1; i <= m; ++i) { scanf("%s", s); if(s[0] == 'C') { scanf("%d %d %d", &x, &y, &z); Cut(x, y, z); } else { scanf("%d %d", &x, &y); Reverse(x, y); } } tmp = 0; Output(rt); } return 0; }
思路：平衡树
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<iostream> #include<cstdio> #include<cmath> #include<algorithm> #include<cstring> #include<climits> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdi pair<double, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 1e5 + 10; const int MOD = 1e6; struct splay { int ch[N][2], cnt[N], fa[N], sz[N], ncnt, rt; int n, m; LL val[N]; inline int ck(int x) { return ch[fa[x]][1] == x; } inline void push_up(int x) { sz[x] = sz[ch[x][0]] + sz[ch[x][1]] + cnt[x]; } void Rotate(int x) { int y = fa[x], z = fa[y]; int k = ck(x), w = ch[x][k^1]; ch[y][k] = w, fa[w] = y; ch[z][ck(y)] = x, fa[x] = z; ch[x][k^1] = y, fa[y] = x; push_up(y), push_up(x); } void Splay(int x, int goal = 0) { while(fa[x] != goal) { int y = fa[x], z = fa[y]; if(z != goal) { if(ck(x) == ck(y)) Rotate(y); else Rotate(x); } Rotate(x); } if(!goal) rt = x; } void Find(LL x) { if(!rt) return ; int cur = rt; while(ch[cur][x>val[cur]] && x != val[cur]) cur = ch[cur][x>val[cur]]; Splay(cur); } void Insert(LL x) { int cur = rt, p = 0; while(cur && val[cur] != x) { p = cur; cur = ch[cur][x>val[cur]]; } if(cur) cnt[cur]++; else { cur = ++ncnt; if(p) ch[p][x>val[p]] = cur; fa[cur] = p; ch[cur][0] = ch[cur][1] = 0; val[cur] = x; cnt[cur] = sz[cur] = 1; } Splay(cur); } int Kth(int k) { int cur = rt; while(true) { if(ch[cur][0] && k <= sz[ch[cur][0]]) cur = ch[cur][0]; else if(k > sz[ch[cur][0]] + cnt[cur]) k -=sz[ch[cur][0]] + cnt[cur], cur = ch[cur][1]; else return cur; } } int Pre(LL x) { Find(x); if(val[rt] < x) return rt; int cur = ch[rt][0]; while(ch[cur][1]) cur = ch[cur][1]; return cur; } int Succ(LL x) { Find(x); if(val[rt] > x) return rt; int cur = ch[rt][1]; while(ch[cur][0]) cur = ch[cur][0]; return cur; } int pre(LL x) { Find(x); if(val[rt] <= x) return rt; int cur = ch[rt][0]; while(ch[cur][1]) cur = ch[cur][1]; return cur; } int succ(LL x) { Find(x); if(val[rt] >= x) return rt; int cur = ch[rt][1]; while(ch[cur][0]) cur = ch[cur][0]; return cur; } void Remove(LL x) { int last = Pre(x), next = Succ(x); Splay(last), Splay(next, last); int del = ch[next][0]; if(cnt[del] > 1) cnt[del]--, Splay(del); else ch[next][0] = 0, push_up(next), push_up(last); } inline int NewNode(LL x) { int cur = ++ncnt; ch[cur][0] = ch[cur][1] = fa[cur] = 0; val[cur] = x; sz[cur] = cnt[cur] = 1; return cur; } inline void init() { ncnt = rt = ch[0][0] = ch[0][1] = fa[0] = sz[0] = cnt[0] = val[0] = 0; } }t1, t2; int T, a, b; int main() { scanf("%d", &T); t1.init(); t2.init(); t1.Insert(LONG_MIN); t1.Insert(LONG_MAX); t2.Insert(LONG_MIN); t2.Insert(LONG_MAX); LL ans = 0; while(T--) { scanf("%d %d", &a, &b); if(a == 0) { if(t2.sz[t2.rt] == 2) t1.Insert(b); else { LL del, tmp = LONG_MAX; LL pre = t2.val[t2.pre(b)]; if(pre != LONG_MIN && abs(pre - b) < tmp) { tmp = abs(pre-b); del = pre; } LL succ = t2.val[t2.succ(b)]; if(succ != LONG_MAX && abs(succ - b) < tmp) { tmp = abs(succ-b); del = succ; } (ans += tmp) %= MOD; t2.Remove(del); } } else { if(t1.sz[t1.rt] == 2) t2.Insert(b); else { LL del, tmp = LONG_MAX; LL pre = t1.val[t1.pre(b)]; if(pre != LONG_MIN && abs(pre - b) < tmp) { tmp = abs(pre-b); del = pre; } LL succ = t1.val[t1.succ(b)]; if(succ != LONG_MAX && abs(succ - b) < tmp) { tmp = abs(succ-b); del = succ; } (ans += tmp) %= MOD; t1.Remove(del); } } } printf("%lld ", ans); return 0; }
思路：常规操作，一开始数据范围看错，一直RE
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<iostream> #include<cstdio> #include<cmath> #include<algorithm> #include<cstring> #include<climits> #include<string> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdi pair<double, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 2.2e6; int ch[N][2], cnt[N], fa[N], sz[N], lazy[N], ncnt = 0, rt = 0; char val[N], s[100]; string t; inline int ck(int x) { return ch[fa[x]][1] == x; } inline void push_up(int x) { sz[x] = sz[ch[x][0]] + sz[ch[x][1]] + cnt[x]; } ///区间反转 inline void push_down(int x) { if(lazy[x]) { swap(ch[x][0], ch[x][1]); lazy[ch[x][0]] ^= 1; lazy[ch[x][1]] ^= 1; lazy[x] = 0; } } void Rotate(int x) { int y = fa[x], z = fa[y]; push_down(y), push_down(x);///区间反转 int k = ck(x), w = ch[x][k^1]; ch[y][k] = w, fa[w] = y; ch[z][ck(y)] = x, fa[x] = z; ch[x][k^1] = y, fa[y] = x; push_up(y), push_up(x); } void Splay(int x, int goal = 0) { push_down(x);///区间反转 while(fa[x] != goal) { int y = fa[x], z = fa[y]; if(z != goal) { if(ck(x) == ck(y)) Rotate(y); else Rotate(x); } Rotate(x); } if(!goal) rt = x; } void Insert(char x) { int cur = rt, p = 0; while(cur && val[cur] != x) { p = cur; cur = ch[cur][x>val[cur]]; } if(cur) cnt[cur]++; else { cur = ++ncnt; if(p) ch[p][x>val[p]] = cur; fa[cur] = p; ch[cur][0] = ch[cur][1] = 0; val[cur] = x; cnt[cur] = sz[cur] = 1; } Splay(cur); } int Kth(int k) { int cur = rt; while(true) { push_down(cur); ///区间反转 if(ch[cur][0] && k <= sz[ch[cur][0]]) cur = ch[cur][0]; else if(k > sz[ch[cur][0]] + cnt[cur]) k -=sz[ch[cur][0]] + cnt[cur], cur = ch[cur][1]; else return cur; } } inline int NewNode(char x) { int cur = ++ncnt; ch[cur][0] = ch[cur][1] = fa[cur] = lazy[cur] = 0; val[cur] = x; sz[cur] = cnt[cur] = 1; return cur; } void Reverse(int l, int r) { int x = Kth(l), y = Kth(r+2); Splay(x), Splay(y, x); lazy[ch[y][0]] ^= 1; } void Delete(int l, int r) { int x = Kth(l), y = Kth(r+2); Splay(x), Splay(y, x); ch[y][0] = 0; push_up(y), push_up(x); } int build(int l, int r, string &a) { if(l > r) return 0; int mid = l+r >> 1, cur = NewNode(a[mid]); if(l == r) return cur; if(ch[cur][0] = build(l, mid-1, a)) fa[ch[cur][0]] = cur; if(ch[cur][1] = build(mid+1, r, a)) fa[ch[cur][1]] = cur; push_up(cur); return cur; } void Insert(int x, int n) { int u = Kth(x), v = Kth(x+1); Splay(u), Splay(v, u); int cur = build(0, n-1, t); fa[cur] = v; ch[v][0] = cur; push_up(v), push_up(u); Splay(cur); } inline void init() { ncnt = rt = ch[0][0] = ch[0][1] = fa[0] = sz[0] = cnt[0] = lazy[0] = 0; } int T, n, k, a, b, now = 0; int main() { init(); Insert('#'); Insert('*'); cin >> T; for (int i = 0; i < T; ++i) { cin >> s; if(s[0] == 'M') { cin >> k; now = k; } else if(s[0] == 'I') { cin >> n; cin.ignore(); getline(cin, t); Insert(now+1, n); } else if(s[0] == 'D') { cin >> n; Delete(now+1, now+n); } else if(s[0] == 'R') { cin >> n; Reverse(now+1, now+n); } else if(s[0] == 'G') { char t = val[Kth(now+2)]; if(t != ' ') putchar(t); putchar(' '); } else if(s[0] == 'P') --now; else if(s[0] == 'N') ++now; } return 0; }
思路：常规操作，REVOLVE记得取模，这个很坑
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<iostream> #include<cstdio> #include<cmath> #include<algorithm> #include<cstring> #include<climits> #include<string> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdi pair<double, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 2e5 + 10; int ch[N][2], cnt[N], fa[N], sz[N], lazy[N], ncnt = 0, rt = 0; LL val[N], a[N], tree[N], add[N]; inline int ck(int x) { return ch[fa[x]][1] == x; } inline void push_up(int x) { int l = ch[x][0], r = ch[x][1]; tree[x] = min(val[x], min(tree[l], tree[r])); sz[x] = sz[l] + sz[r] + cnt[x]; } ///区间反转 inline void push_down(int x) { int l = ch[x][0], r = ch[x][1]; if(lazy[x]) { swap(ch[x][0], ch[x][1]); if(l) lazy[l] ^= 1; if(r) lazy[r] ^= 1; lazy[x] = 0; } if(add[x]) { if(l) val[l] += add[x], tree[l] += add[x], add[l] += add[x]; if(r) val[r] += add[x], tree[r] += add[x], add[r] += add[x]; add[x] = 0; } } void Rotate(int x) { int y = fa[x], z = fa[y]; push_down(y), push_down(x);///区间反转 int k = ck(x), w = ch[x][k^1]; ch[y][k] = w, fa[w] = y; ch[z][ck(y)] = x, fa[x] = z; ch[x][k^1] = y, fa[y] = x; push_up(y), push_up(x); } void Splay(int x, int goal = 0) { push_down(x);///区间反转 while(fa[x] != goal) { int y = fa[x], z = fa[y]; if(z != goal) { if(ck(x) == ck(y)) Rotate(y); else Rotate(x); } Rotate(x); } if(!goal) rt = x; } int Kth(int k) { int cur = rt; while(true) { push_down(cur); ///区间反转 if(ch[cur][0] && k <= sz[ch[cur][0]]) cur = ch[cur][0]; else if(k > sz[ch[cur][0]] + cnt[cur]) k -=sz[ch[cur][0]] + cnt[cur], cur = ch[cur][1]; else return cur; } } inline int NewNode(LL x) { int cur = ++ncnt; ch[cur][0] = ch[cur][1] = fa[cur] = add[cur] = lazy[cur] = 0; val[cur] = x; tree[cur] = x; sz[cur] = cnt[cur] = 1; return cur; } ///区间反转 void REVERSE(int l, int r) { int x = Kth(l), y = Kth(r+2); Splay(x), Splay(y, x); int cur = ch[y][0]; lazy[cur] ^= 1; } void ADD(int l, int r, LL z) { int x = Kth(l), y = Kth(r+2); Splay(x), Splay(y, x); val[ch[y][0]] += z; tree[ch[y][0]] += z; add[ch[y][0]] += z; push_up(y), push_up(x); } void REVOLVE(int l, int r, int z) { int len = r-l+1; z = (z%len + len) % len; if(!z) return ; int ll = r-z+1, rr = r; int x = Kth(ll), y = Kth(rr+2); Splay(x), Splay(y, x); int cur = ch[y][0]; ch[y][0] = 0; push_up(y), push_up(x); x = Kth(l), y = Kth(l+1); Splay(x), Splay(y, x); ch[y][0] = cur; fa[cur] = y; push_up(y), push_up(x); Splay(cur); } LL MIN(int l, int r) { int x = Kth(l), y = Kth(r+2); Splay(x), Splay(y, x); return tree[ch[y][0]]; } void INSERT(int x, LL y) { int u = Kth(x+1), v = Kth(x+2); Splay(u), Splay(v, u); int cur = NewNode(y); fa[cur] = v; ch[v][0] = cur; push_up(v), push_up(u); } void DELETE(int x) { int u = Kth(x), v = Kth(x+2); Splay(u), Splay(v, u); ch[v][0] = 0; push_up(v), push_up(u); } int build(int l, int r, LL *a) { if(l > r) return 0; int mid = l+r >> 1, cur = NewNode(a[mid]); if(l == r) return cur; if(ch[cur][0] = build(l, mid-1, a)) fa[ch[cur][0]] = cur; if(ch[cur][1] = build(mid+1, r, a)) fa[ch[cur][1]] = cur; push_up(cur); return cur; } inline void init() { ncnt = rt = ch[0][0] = ch[0][1] = fa[0] = sz[0] = cnt[0] = val[0] = add[0] = lazy[0] = 0; tree[0] = LONG_MAX; } int n, m, x, y; LL z; char s[100]; int main() { init(); scanf("%d", &n); for (int i = 1; i <= n; ++i) scanf("%lld", &a[i]); a[0] = a[n+1] = LONG_MAX; rt = build(0, n+1, a); scanf("%d", &m); for (int i = 1; i <= m; ++i) { scanf("%s", s); if(s[0] == 'A') { scanf("%d %d %lld", &x, &y, &z); ADD(x, y, z); } else if(s[0] == 'R' && s[3] == 'E') { scanf("%d %d", &x, &y); REVERSE(x, y); } else if(s[0] == 'R' && s[3] == 'O') { scanf("%d %d %lld", &x, &y, &z); REVOLVE(x, y, z); } else if(s[0] == 'I') { scanf("%d %d", &x, &y); INSERT(x, y); } else if(s[0] == 'D') { scanf("%d", &x); DELETE(x); } else if(s[0] == 'M') { scanf("%d %d", &x, &y); printf("%lld ", MIN(x, y)); } } return 0; }
代码：
#include<iostream> #include<cstdio> #include<cmath> #include<algorithm> #include<climits> #include<cstring> using namespace std; #define LL long long const int N = 1e5 + 10; int ch[N][2], cnt[N], fa[N], sz[N], ncnt = 0, rt = 0; LL add[N], tree[N], val[N], a[N]; inline int ck(int x) { return ch[fa[x]][1] == x; } inline void push_up(int x) { sz[x] = sz[ch[x][0]] + sz[ch[x][1]] + cnt[x]; tree[x] = val[x] + tree[ch[x][0]] + tree[ch[x][1]]; } ///区间反转 inline void push_down(int x) { if(add[x]) { int l = ch[x][0], r = ch[x][1]; if(l) add[l] += add[x], val[l] += add[x], tree[l] += sz[l]*1LL*add[x]; if(r) add[r] += add[x], val[r] += add[x], tree[r] += sz[r]*1LL*add[x]; add[x] = 0; } } void Rotate(int x) { int y = fa[x], z = fa[y]; push_down(y), push_down(x);///区间反转 int k = ck(x), w = ch[x][k^1]; ch[y][k] = w, fa[w] = y; ch[z][ck(y)] = x, fa[x] = z; ch[x][k^1] = y, fa[y] = x; push_up(y), push_up(x); } void Splay(int x, int goal = 0) { push_down(x);///区间反转 while(fa[x] != goal) { int y = fa[x], z = fa[y]; if(z != goal) { if(ck(x) == ck(y)) Rotate(y); else Rotate(x); } Rotate(x); } if(!goal) rt = x; } int Kth(int k) { int cur = rt; while(true) { push_down(cur); ///区间反转 if(ch[cur][0] && k <= sz[ch[cur][0]]) cur = ch[cur][0]; else if(k > sz[ch[cur][0]] + cnt[cur]) k -=sz[ch[cur][0]] + cnt[cur], cur = ch[cur][1]; else return cur; } } void ADD(int l, int r, LL c) { int x = Kth(l), y = Kth(r+2); Splay(x), Splay(y, x); add[ch[y][0]] += c; tree[ch[y][0]] += sz[ch[y][0]]*1LL*c; val[ch[y][0]] += c; push_up(y), push_up(x); } LL SUM(int l, int r) { int x = Kth(l), y = Kth(r+2); Splay(x), Splay(y, x); return tree[ch[y][0]]; } inline int NewNode(LL x) { int cur;cur = ++ncnt; ch[cur][0] = ch[cur][1] = fa[cur] = add[cur] = 0; val[cur] = x; tree[cur] = x; sz[cur] = cnt[cur] = 1; return cur; } int build(int l, int r, LL *a) { if(l > r) return 0; int mid = l+r >> 1, cur = NewNode(a[mid]); if(l == r) return cur; if(ch[cur][0] = build(l, mid-1, a)) fa[ch[cur][0]] = cur; if(ch[cur][1] = build(mid+1, r, a)) fa[ch[cur][1]] = cur; push_up(cur); return cur; } inline void init() { ncnt = rt = ch[0][0] = ch[0][1] = fa[0] = sz[0] = cnt[0] = val[0] = add[0] = tree[0] = 0; } int n, m, l, r; LL c; char s[100]; int main() { init(); scanf("%d %d", &n, &m); for (int i = 1; i <= n; ++i) scanf("%lld", &a[i]); rt = build(0, n+1, a); for (int i = 1; i <= m; ++i) { scanf("%s", s); if(s[0] == 'Q') { scanf("%d %d", &l, &r); printf("%lld ", SUM(l, r)); } else if(s[0] == 'C') { scanf("%d %d %lld", &l, &r, &c); ADD(l, r, c); } } return 0; }
将树按入时间戳和出时间戳变成线性结构，然后在这个线性结构上用splay维护
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdi pair<double, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 1e5 + 100; int ch[N][2], val[N], cnt[N], fa[N], sz[N], ncnt = 0, rt = 0; int n, m, a, now = 0; vector<int> g[N]; int L[N], R[N], dfn[N], x, y; char s[100]; inline int ck(int x) { return ch[fa[x]][1] == x; } void Rotate(int x) { int y = fa[x], z = fa[y]; int k = ck(x), w = ch[x][k^1]; ch[y][k] = w, fa[w] = y; ch[z][ck(y)] = x, fa[x] = z; ch[x][k^1] = y, fa[y] = x; } void Splay(int x, int goal = 0) { while(fa[x] != goal) { int y = fa[x], z = fa[y]; if(z != goal) { if(ck(x) == ck(y)) Rotate(y); else Rotate(x); } Rotate(x); } if(!goal) rt = x; } inline int NewNode(int x) { int cur = ++ncnt; ch[cur][0] = ch[cur][1] = fa[cur] = 0; val[cur] = abs(x); if(x > 0) L[x] = cur; else R[-x] = cur; return cur; } int build(int l, int r, int *a) { if(l > r) return 0; int mid = l+r >> 1, cur = NewNode(a[mid]); if(l == r) return cur; if(ch[cur][0] = build(l, mid-1, a)) fa[ch[cur][0]] = cur; if(ch[cur][1] = build(mid+1, r, a)) fa[ch[cur][1]] = cur; return cur; } inline void init() { ncnt = rt = ch[0][0] = ch[0][1] = fa[0] = val[0] = 0; } void dfs(int u) { dfn[++now] = u; for (int v : g[u]) dfs(v); dfn[++now] = -u; } inline int get_min(int x) { while(x && ch[x][0]) x = ch[x][0]; return x; } inline int get_max(int x) { while(x && ch[x][1]) x = ch[x][1]; return x; } int QUERY(int x) { int u = L[x]; Splay(u); return get_min(u); } void MOVE(int X, int Y) { int u = L[X], v = R[X]; Splay(u), Splay(v, u); int x = ch[u][0], y = ch[v][1]; int xx = get_max(x); fa[x] = 0, ch[u][0] = 0; fa[y] = 0, ch[v][1] = 0; if(y && xx) ch[xx][1] = y, fa[y] = xx; if(Y == 0) return ; if(QUERY(Y) == u) { fa[x] = u, ch[u][0] = x; fa[y] = v, ch[v][1] = y; ch[xx][1] = 0; return ; } int uu = L[Y]; Splay(uu); int vv = get_min(ch[uu][1]); Splay(vv, uu); ch[vv][0] = u; fa[u] = vv; } int main() { bool f = false; while(~scanf("%d", &n)) { if(f) printf(" "); else f = true; init(); for (int i = 1; i <= n; ++i) { scanf("%d", &a); g[a].pb(i); } for (int u : g[0]) { now = 0; dfs(u); build(1, now, dfn); } scanf("%d", &m); for (int i = 1; i <= m; ++i) { scanf("%s", s); if(s[0] == 'M') { scanf("%d %d", &x, &y); MOVE(x, y); } else if(s[0] == 'Q') { scanf("%d", &x); printf("%d ", val[QUERY(x)]); } } for (int i = 0; i <= n; ++i) g[i].clear(); } return 0; }
易错点：
1.修改后记得push_up
2.一直往左子树或右子树走时记得第一步判当前节点是不是0
套板子一时爽，一直套一直爽
Link-Cut-Tree
模板：
const int N = 3e5 + 5; int f[N],v[N],s[N],r[N],hep[N],ch[N][2]; inline int get(int x){ return ch[f[x]][0]==x||ch[f[x]][1]==x; } inline void pushup(int x){ s[x]=s[ch[x][1]]^s[ch[x][0]]^v[x]; } inline void filp(int x){ swap(ch[x][0],ch[x][1]);r[x]^=1; } inline void pushdown(int x){ if(!r[x])return;r[x]=0; if(ch[x][0])filp(ch[x][0]); if(ch[x][1])filp(ch[x][1]); } inline void rotate(int x){ int y=f[x],z=f[y],k=ch[y][1]==x,v=ch[x][!k]; if(get(y))ch[z][ch[z][1]==y]=x;ch[x][!k]=y,ch[y][k]=v; if(v)f[v]=y;f[y]=x,f[x]=z;pushup(y),pushup(x); } inline void Splay(int x){ int y=x,top=0;hep[++top]=y; while(get(y))hep[++top]=y=f[y]; while(top)pushdown(hep[top--]); while(get(x)){ y=f[x],top=f[y]; if(get(y)) rotate((ch[y][0]==x)^(ch[top][0]==y)?x:y); rotate(x); }pushup(x);return; } inline void Access(int x){ for(register int y=0;x;x=f[y=x]) Splay(x),ch[x][1]=y,pushup(x); } inline void makeroot(int x){ Access(x);Splay(x);filp(x); } inline int findroot(int x){ Access(x);Splay(x); while(ch[x][0])pushdown(x),x=ch[x][0]; return x; } inline void split(int x,int y){ makeroot(x);Access(y);Splay(y); } inline void link(int x,int y){ makeroot(x);if(findroot(y)!=x)f[x]=y; } inline void cut(int x,int y){ split(x,y); if(findroot(y)==x&&f[x]==y&&!ch[x][1]){ f[x]=ch[y][0]=0;pushup(y); }return; }
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdi pair<double, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 3e5 + 5; int f[N],v[N],s[N],r[N],hep[N],ch[N][2]; inline int get(int x){ return ch[f[x]][0]==x||ch[f[x]][1]==x; } inline void pushup(int x){ s[x]=s[ch[x][1]]^s[ch[x][0]]^v[x]; } inline void filp(int x){ swap(ch[x][0],ch[x][1]);r[x]^=1; } inline void pushdown(int x){ if(!r[x])return;r[x]=0; if(ch[x][0])filp(ch[x][0]); if(ch[x][1])filp(ch[x][1]); } inline void rotate(int x){ int y=f[x],z=f[y],k=ch[y][1]==x,v=ch[x][!k]; if(get(y))ch[z][ch[z][1]==y]=x;ch[x][!k]=y,ch[y][k]=v; if(v)f[v]=y;f[y]=x,f[x]=z;pushup(y),pushup(x); } inline void Splay(int x){ int y=x,top=0;hep[++top]=y; while(get(y))hep[++top]=y=f[y]; while(top)pushdown(hep[top--]); while(get(x)){ y=f[x],top=f[y]; if(get(y)) rotate((ch[y][0]==x)^(ch[top][0]==y)?x:y); rotate(x); }pushup(x);return; } inline void Access(int x){ for(register int y=0;x;x=f[y=x]) Splay(x),ch[x][1]=y,pushup(x); } inline void makeroot(int x){ Access(x);Splay(x);filp(x); } inline int findroot(int x){ Access(x);Splay(x); while(ch[x][0])pushdown(x),x=ch[x][0]; return x; } inline void split(int x,int y){ makeroot(x);Access(y);Splay(y); } inline void link(int x,int y){ makeroot(x);if(findroot(y)!=x)f[x]=y; } inline void cut(int x,int y){ split(x,y); if(findroot(y)==x&&f[x]==y&&!ch[x][1]){ f[x]=ch[y][0]=0;pushup(y); }return; } int n, m, op, x, y; int main() { scanf("%d %d", &n, &m); for (int i = 1; i <= n; ++i) scanf("%d", &v[i]); for (int i = 1; i <= m; ++i) { scanf("%d %d %d", &op, &x, &y); if(op == 0) split(x, y), printf("%d ", s[y]); else if(op == 1) link(x, y); else if(op == 2) cut(x, y); else Splay(x), v[x] = y; } return 0; }
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdi pair<double, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 1e4 + 10; int f[N], r[N],hep[N],ch[N][2]; inline int get(int x){ return ch[f[x]][0]==x||ch[f[x]][1]==x; } inline void pushup(int x){ return ; } inline void filp(int x){ swap(ch[x][0],ch[x][1]);r[x]^=1; } inline void pushdown(int x){ if(!r[x])return;r[x]=0; if(ch[x][0])filp(ch[x][0]); if(ch[x][1])filp(ch[x][1]); } inline void rotate(int x){ int y=f[x],z=f[y],k=ch[y][1]==x,v=ch[x][!k]; if(get(y))ch[z][ch[z][1]==y]=x;ch[x][!k]=y,ch[y][k]=v; if(v)f[v]=y;f[y]=x,f[x]=z;pushup(y),pushup(x); } inline void Splay(int x){ int y=x,top=0;hep[++top]=y; while(get(y))hep[++top]=y=f[y]; while(top)pushdown(hep[top--]); while(get(x)){ y=f[x],top=f[y]; if(get(y)) rotate((ch[y][0]==x)^(ch[top][0]==y)?x:y); rotate(x); }pushup(x);return; } inline void Access(int x){ for(register int y=0;x;x=f[y=x]) Splay(x),ch[x][1]=y,pushup(x); } inline void makeroot(int x){ Access(x);Splay(x);filp(x); } inline int findroot(int x){ Access(x);Splay(x); while(ch[x][0])pushdown(x),x=ch[x][0]; return x; } inline void split(int x,int y){ makeroot(x);Access(y);Splay(y); } inline void link(int x,int y){ makeroot(x);if(findroot(y)!=x)f[x]=y; } inline void cut(int x,int y){ split(x,y); if(findroot(y)==x&&f[x]==y&&!ch[x][1]){ f[x]=ch[y][0]=0;pushup(y); }return; } char op[100]; int n, m, u, v; int main() { scanf("%d", &n); scanf("%d", &m); for (int i = 1; i <= m; ++i) { scanf("%s %d %d", op, &u, &v); if(op[0] == 'C') link(u, v); else if(op[0] == 'D') cut(u, v); else { makeroot(u); if(findroot(v) != u) printf("No "); else printf("Yes "); } } return 0; }
思路：注意cut和普通的cut不一样
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdi pair<double, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 3e5 + 5; int f[N],v[N],mx[N],r[N],add[N], hep[N],ch[N][2]; inline int get(int x){ return ch[f[x]][0]==x||ch[f[x]][1]==x; } inline void pushup(int x){ mx[x]= max(max(mx[ch[x][1]], mx[ch[x][0]]), v[x]); } inline void filp(int x){ swap(ch[x][0],ch[x][1]);r[x]^=1; } inline void pushdown(int x){ int ls = ch[x][0], rs = ch[x][1]; if(r[x]) { if(ls) filp(ls); if(rs) filp(rs); r[x] = 0; } if(add[x]) { if(ls) add[ls] += add[x], v[ls] += add[x], mx[ls] += add[x]; if(rs) add[rs] += add[x], v[rs] += add[x], mx[rs] += add[x]; add[x] = 0; } } inline void rotate(int x){ int y=f[x],z=f[y],k=ch[y][1]==x,v=ch[x][!k]; if(get(y))ch[z][ch[z][1]==y]=x;ch[x][!k]=y,ch[y][k]=v; if(v)f[v]=y;f[y]=x,f[x]=z;pushup(y),pushup(x); } inline void Splay(int x){ int y=x,top=0;hep[++top]=y; while(get(y))hep[++top]=y=f[y]; while(top)pushdown(hep[top--]); while(get(x)){ y=f[x],top=f[y]; if(get(y)) rotate((ch[y][0]==x)^(ch[top][0]==y)?x:y); rotate(x); }pushup(x);return; } inline void Access(int x){ for(register int y=0;x;x=f[y=x]) Splay(x),ch[x][1]=y,pushup(x); } inline void makeroot(int x){ Access(x);Splay(x);filp(x); } inline int findroot(int x){ Access(x);Splay(x); while(ch[x][0])pushdown(x),x=ch[x][0]; return x; } inline void ADD(int x,int y, int w){ makeroot(x);Access(y);Splay(y); v[y] += w, add[y] += w, mx[y] += w; } inline void split(int x,int y){ makeroot(x);Access(y);Splay(y); } inline void link(int x,int y){ makeroot(x); if(findroot(y)!=x)f[x]=y; } inline void cut(int x,int y) { split(x,y); ch[y][0] = f[ch[y][0]] = 0; } int op, x, y, w, n, m; int U[N], V[N]; int main() { while(~scanf("%d", &n)) { mx[0] = INT_MIN; for (int i = 1; i < n; ++i) scanf("%d %d", &U[i], &V[i]); for (int i = 1; i <= n; ++i) scanf("%d", &v[i]), mx[i] = v[i], add[i] = r[i] = ch[i][0] = ch[i][1] = f[i] = 0; for (int i = 1; i < n; ++i) link(U[i], V[i]); scanf("%d", &m); for (int i = 1; i <= m; ++i) { scanf("%d", &op); if(op == 1) { scanf("%d %d", &x, &y); if(findroot(x) == findroot(y)) printf("-1 "); else link(x, y); } else if(op == 2){ scanf("%d %d", &x, &y); if(findroot(x) != findroot(y) || x == y) printf("-1 "); else cut(x, y); } else if(op == 3) { scanf("%d %d %d", &w, &x, &y); if(findroot(x) != findroot(y)) printf("-1 "); else ADD(x, y, w); } else { scanf("%d %d", &x, &y); if(findroot(x) != findroot(y)) printf("-1 "); else split(x, y), printf("%d ", mx[y]); } } printf(" "); } return 0; }
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdi pair<double, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 1e5 + 5; int f[N],v[N],mx[N],r[N],hep[N],ch[N][2]; inline int get(int x){ return ch[f[x]][0]==x||ch[f[x]][1]==x; } inline void pushup(int x){ mx[x] = max(max(mx[ch[x][0]], mx[ch[x][1]]), v[x]); } inline void filp(int x){ swap(ch[x][0],ch[x][1]);r[x]^=1; } inline void pushdown(int x){ if(!r[x])return;r[x]=0; if(ch[x][0])filp(ch[x][0]); if(ch[x][1])filp(ch[x][1]); } inline void Rotate(int x){ int y=f[x],z=f[y],k=ch[y][1]==x,v=ch[x][!k]; if(get(y))ch[z][ch[z][1]==y]=x;ch[x][!k]=y,ch[y][k]=v; if(v)f[v]=y;f[y]=x,f[x]=z;pushup(y),pushup(x); } inline void Splay(int x){ int y=x,top=0;hep[++top]=y; while(get(y))hep[++top]=y=f[y]; while(top)pushdown(hep[top--]); while(get(x)){ y=f[x],top=f[y]; if(get(y)) Rotate((ch[y][0]==x)^(ch[top][0]==y)?x:y); Rotate(x); }pushup(x);return; } inline void Access(int x){ for(int y=0;x;x=f[y=x]) Splay(x),ch[x][1]=y,pushup(x); } inline void makeroot(int x){ Access(x);Splay(x);filp(x); } inline int findroot(int x){ Access(x);Splay(x); while(ch[x][0])pushdown(x),x=ch[x][0]; return x; } inline void split(int x,int y){ makeroot(x);Access(y);Splay(y); } inline void link(int x,int y){ makeroot(x);if(findroot(y)!=x)f[x]=y; } inline void cut(int x,int y){ split(x,y); if(findroot(y)==x&&f[x]==y&&!ch[x][1]){ f[x]=ch[y][0]=0;pushup(y); }return; } int n, m, x, y; char op[100]; int main() { mx[0] = INT_MIN; scanf("%d", &n); for (int i = 1; i < n; ++i) scanf("%d%d", &x, &y), link(x, y); scanf("%d", &m); for (int i = 1; i <= m; ++i) { scanf("%s%d%d", op, &x, &y); if(op[0] == 'I') Splay(x), v[x] += y; else split(x, y), printf("%d ", mx[y]); } return 0; }
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb push_back #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdi pair<double, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head const int N = 3e4 + 5; int f[N],s[N], v[N],r[N],hep[N],ch[N][2]; inline int get(int x){ return ch[f[x]][0]==x||ch[f[x]][1]==x; } inline void pushup(int x){ s[x] = s[ch[x][0]] + s[ch[x][1]] + v[x]; } inline void filp(int x){ swap(ch[x][0],ch[x][1]);r[x]^=1; } inline void pushdown(int x){ if(!r[x])return;r[x]=0; if(ch[x][0])filp(ch[x][0]); if(ch[x][1])filp(ch[x][1]); } inline void rotate(int x){ int y=f[x],z=f[y],k=ch[y][1]==x,v=ch[x][!k]; if(get(y))ch[z][ch[z][1]==y]=x;ch[x][!k]=y,ch[y][k]=v; if(v)f[v]=y;f[y]=x,f[x]=z;pushup(y),pushup(x); } inline void Splay(int x){ int y=x,top=0;hep[++top]=y; while(get(y))hep[++top]=y=f[y]; while(top)pushdown(hep[top--]); while(get(x)){ y=f[x],top=f[y]; if(get(y)) rotate((ch[y][0]==x)^(ch[top][0]==y)?x:y); rotate(x); }pushup(x);return; } inline void Access(int x){ for(register int y=0;x;x=f[y=x]) Splay(x),ch[x][1]=y,pushup(x); } inline void makeroot(int x){ Access(x);Splay(x);filp(x); } inline int findroot(int x){ Access(x);Splay(x); while(ch[x][0])pushdown(x),x=ch[x][0]; return x; } inline void split(int x,int y){ makeroot(x);Access(y);Splay(y); } inline bool link(int x,int y){ makeroot(x);if(findroot(y)!=x)f[x]=y; else return false; return true; } inline void cut(int x,int y){ split(x,y); if(findroot(y)==x&&f[x]==y&&!ch[x][1]){ f[x]=ch[y][0]=0;pushup(y); }return; } int n, m, x, y; char op[100]; int main() { scanf("%d", &n); for (int i = 1; i <= n; ++i) scanf("%d", &v[i]); scanf("%d", &m); for (int i = 1; i <= m; ++i) { scanf("%s %d %d", op, &x, &y); if(op[0] == 'b') { if(link(x, y)) printf("yes "); else printf("no "); } else if(op[0] == 'p') { Splay(x); v[x] = y; } else { if(findroot(x) != findroot(y)) printf("impossible "); else split(x, y), printf("%d ", s[y]); } } return 0; }
FHQ Treap
参考：https://blog.csdn.net/pengwill97/article/details/82891241
模板：
struct fhq_treap { static const int N = 1e5 + 5; struct Node { int val, key, lc, rc, sz; }tree[N]; int rt, tot; inline void init() { rt = tot = 0; tree[rt].sz = tree[rt].val = tree[rt].lc = tree[rt].rc = 0; srand(time(0)); } inline void update(int rt) { tree[rt].sz = tree[tree[rt].lc].sz + tree[tree[rt].rc].sz + 1; } void split(int rt, int &a, int &b, int val) { if(rt == 0) {a = b = 0; return ;} if(tree[rt].val <= val) { a = rt; split(tree[rt].rc, tree[a].rc, b, val); } else { b = rt; split(tree[rt].lc, a, tree[b].lc, val); } update(rt); } void merge(int &rt, int a, int b) { if(a==0 || b==0) { rt = a+b; return ; } if(tree[a].key < tree[b].key) { rt = a; merge(tree[rt].rc, tree[a].rc, b); } else { rt = b; merge(tree[rt].lc, a, tree[b].lc); } update(rt); } inline int new_node(int val) { tree[++tot].sz = 1; tree[tot].val = val; tree[tot].lc = tree[tot].rc = 0; tree[tot].key = rand()*rand(); return tot; } void ins(int &rt, int val) { int x = 0, y = 0, node = new_node(val); split(rt, x, y, val); merge(x, x, node); merge(rt, x, y); } void delete_node(int &rt, int val) { int x = 0, y = 0, z = 0; split(rt, x, y, val); split(x, x, z, val-1); merge(z, tree[z].lc, tree[z].rc); merge(x, x, z); merge(rt, x, y); } inline int get_kth(int rt, int k) { while(tree[tree[rt].lc].sz+1 != k) { if(tree[tree[rt].lc].sz >= k) rt = tree[rt].lc; else k -= tree[tree[rt].lc].sz+1, rt = tree[rt].rc; } return tree[rt].val; } int get_rnk(int &rt, int val) { int x = 0, y = 0; split(rt, x, y, val-1); int tmp = tree[x].sz+1; merge(rt, x, y); return tmp; } int get_pre(int &rt, int val) { int x = 0, y = 0; split(rt, x, y, val-1); int tmp = get_kth(x, tree[x].sz); merge(rt, x, y); return tmp; } int get_scc(int &rt, int val) { int x = 0, y = 0; split(rt, x, y, val); int tmp = get_kth(y, 1); merge(rt, x, y); return tmp; } }t;
例题：
代码：
#pragma GCC optimize(2) #pragma GCC optimize(3) #pragma GCC optimize(4) #include<bits/stdc++.h> using namespace std; #define y1 y11 #define fi first #define se second #define pi acos(-1.0) #define LL long long //#define mp make_pair #define pb emplace_back #define ls rt<<1, l, m #define rs rt<<1|1, m+1, r #define ULL unsigned LL #define pll pair<LL, LL> #define pli pair<LL, int> #define pii pair<int, int> #define piii pair<pii, int> #define pdd pair<double, double> #define mem(a, b) memset(a, b, sizeof(a)) #define debug(x) cerr << #x << " = " << x << " "; #define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0); //head struct fhq_treap { static const int N = 1e5 + 5; struct Node { int val, key, lc, rc, sz; }tree[N]; int rt, tot; inline void init() { rt = tot = 0; tree[rt].sz = tree[rt].val = tree[rt].lc = tree[rt].rc = 0; srand(time(0)); } inline void update(int rt) { tree[rt].sz = tree[tree[rt].lc].sz + tree[tree[rt].rc].sz + 1; } void split(int rt, int &a, int &b, int val) { if(rt == 0) {a = b = 0; return ;} if(tree[rt].val <= val) { a = rt; split(tree[rt].rc, tree[a].rc, b, val); } else { b = rt; split(tree[rt].lc, a, tree[b].lc, val); } update(rt); } void merge(int &rt, int a, int b) { if(a==0 || b==0) { rt = a+b; return ; } if(tree[a].key < tree[b].key) { rt = a; merge(tree[rt].rc, tree[a].rc, b); } else { rt = b; merge(tree[rt].lc, a, tree[b].lc); } update(rt); } inline int new_node(int val) { tree[++tot].sz = 1; tree[tot].val = val; tree[tot].lc = tree[tot].rc = 0; tree[tot].key = rand()*rand(); return tot; } void ins(int &rt, int val) { int x = 0, y = 0, node = new_node(val); split(rt, x, y, val); merge(x, x, node); merge(rt, x, y); } void delete_node(int &rt, int val) { int x = 0, y = 0, z = 0; split(rt, x, y, val); split(x, x, z, val-1); merge(z, tree[z].lc, tree[z].rc);///??? merge(x, x, z); merge(rt, x, y); } inline int get_kth(int rt, int k) { while(tree[tree[rt].lc].sz+1 != k) { if(tree[tree[rt].lc].sz >= k) rt = tree[rt].lc; else k -= tree[tree[rt].lc].sz+1, rt = tree[rt].rc; } return tree[rt].val; } int get_rnk(int &rt, int val) { int x = 0, y = 0; split(rt, x, y, val-1); int tmp = tree[x].sz+1; merge(rt, x, y); return tmp; } int get_pre(int &rt, int val) { int x = 0, y = 0; split(rt, x, y, val-1); int tmp = get_kth(x, tree[x].sz); merge(rt, x, y); return tmp; } int get_scc(int &rt, int val) { int x = 0, y = 0; split(rt, x, y, val); int tmp = get_kth(y, 1); merge(rt, x, y); return tmp; } }t; int n, op, x; int main() { t.init(); scanf("%d", &n); for (int i = 1; i <= n; ++i) { scanf("%d %d", &op, &x); if(op == 1) t.ins(t.rt, x); else if(op == 2) t.delete_node(t.rt, x); else if(op == 3) printf("%d ", t.get_rnk(t.rt, x)); else if(op == 4) printf("%d ", t.get_kth(t.rt, x)); else if(op == 5) printf("%d ", t.get_pre(t.rt, x)); else printf("%d ", t.get_scc(t.rt, x)); } return 0; }