文章目录

  • 模板
  • P6136 【模板】普通平衡树（数据加强版）
  • 文艺平衡树
  • 可持久化平衡树
  • 书架
  • P3850 [TJOI2007]书架

模板

自己用的可持久化Treap的板子， 改掉split的可持久化就可以当成普通的来用了。

// 使用前插入-INF, 和INF。若不需插入，涉及的排名的地方有加一减一的问题 普通版fhq-treap在split中去掉可持久化就可以。
struct fhq_Treap{ struct { int val, siz, l, r, rnd;}T[N*60]; int cnt, x, y, z;void up(int rt) { T[rt].siz = 1 + T[T[rt].l].siz + T[T[rt].r].siz;} int new_node(int x) { T[++cnt].val = x;T[cnt].rnd = rand();T[cnt].siz = 1;return cnt;} void split(int rt, int k, int &x, int &y) { if(!rt) return x = y = 0, void(0);if(T[rt].val <= k) {x = ++cnt; T[x] = T[rt];split(T[x].r, k, T[x].r, y);up(x);} else { y = ++cnt; T[y] = T[rt];split(T[y].l, k, x, T[y].l);up(y);} } int merge(int x, int y) { if(!x || !y) return x^y;if(T[x].rnd < T[y].rnd) { T[x].r = merge(T[x].r, y);up(x); return x;} T[y].l = merge(x, T[y].l);up(y); return y;}void insert(int &rt, int val) {split(rt, val-1, x, y);rt = merge(merge(x, new_node(val)), y);}void del(int &rt, int val) {split(rt, val-1, x, y);split(y, val, z, y);z = merge(T[z].l, T[z].r);rt = merge(merge(x, z), y);}int _rank(int rt, int val) {int ans = 0;while(rt) {if(val < T[rt].val) rt = T[rt].l;else if(val == T[rt].val) {while(T[T[rt].l].val == val) cout << T[rt].val << endl,  rt = T[rt].l;return ans + T[T[rt].l].siz;}else ans += T[T[rt].l].siz + 1, rt = T[rt].r;}return ans;}// 注意k要加1 int _kth(int rt, int k) {while(rt) {if(T[T[rt].l].siz >= k) rt = T[rt].l;else if (T[T[rt].l].siz + 1 == k) return T[rt].val;else k -= T[T[rt].l].siz + 1, rt = T[rt].r;}return INF;}int pre(int rt, int val) {int ans = -INF;while(rt) { if(val == T[rt].val) {if(T[rt].l) {rt = T[rt].l;while(T[rt].r) rt = T[rt].r;ans = T[rt].val;} break;}if(T[rt].val < val && ans < T[rt].val) ans = T[rt].val;rt = val < T[rt].val ? T[rt].l : T[rt].r;} return ans;}  int nxt(int rt, int val) {int ans = INF;while(rt) { if(val == T[rt].val) {if(T[rt].r) {rt = T[rt].r;while(T[rt].l) rt = T[rt].l;ans = T[rt].val;} break;}if(T[rt].val > val && ans > T[rt].val) ans = T[rt].val;rt = val > T[rt].val ? T[rt].r : T[rt].l;} return ans;}
}Tr;

P6136 【模板】普通平衡树（数据加强版）

普通平衡树
其实对于非删除插入操作都可以迭代求答案，不调用split。

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int INF = 0x3f3f3f3f;
const double Pi = acos(-1);
namespace {template <typename T> inline void read(T &x) {x = 0; T f = 1;char s = getchar();for(; !isdigit(s); s = getchar()) if(s == '-') f = -1;for(;  isdigit(s); s = getchar()) x = (x << 3) + (x << 1) + (s ^ 48);x *= f;}
}
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define _for(n,m,i) for (register int i = (n); i <  (m); ++i)
#define _rep(n,m,i) for (register int i = (n); i <= (m); ++i)
#define _srep(n,m,i)for (register int i = (n); i >= (m); i--)
#define _sfor(n,m,i)for (register int i = (n); i >  (m); i--)
#define lson rt << 1, l, mid
#define rson rt << 1 | 1, mid + 1, r
#define lowbit(x) x & (-x)
#define pii pair<int,int>
#define fi first
#define se second
const int N = 2e6+5;
int val[N], ch[N][2], siz[N], rnd[N], q[N];
int root, cnt, x, y, z, an, tot;
void up(int rt) { siz[rt] = 1 + siz[ch[rt][0]] + siz[ch[rt][1]];
}
int new_node(int x) {int new_cnt = tot ? q[tot--] : ++cnt;val[new_cnt] = x;siz[new_cnt] = 1;rnd[new_cnt] = rand();ch[new_cnt][0] = ch[new_cnt][1] = 0;// cout << "debug:  " << new_cnt << endl;return new_cnt;
}
void split(int rt, int a, int &x, int &y) {if(!rt) x = y = 0;else {if(val[rt] <= a) x = rt, split(ch[rt][1], a, ch[rt][1], y);else y = rt, split(ch[rt][0], a, x, ch[rt][0]);up(rt);}
}
int merge(int x, int y) {if(!x || !y) return x + y;if(rnd[x] < rnd[y]) {ch[x][1] = merge(ch[x][1], y);up(x); return x;} else {ch[y][0] = merge(x, ch[y][0]);up(y); return y;}
}
void insert(int a) {split(root, a, x, y);root = merge(merge(x, new_node(a)), y);
}
void del(int a) {split(root, a, x, y);split(x, a-1, x, z);q[++tot] = z;z = merge(ch[z][0], ch[z][1]);root = merge(merge(x, z), y);
}
int _rank(int a) {split(root, a-1, x, y);an = siz[x] + 1;root = merge(x, y);return an;
}
int _kth(int rt, int k) {while(rt) {if(k <= siz[ch[rt][0]]) rt = ch[rt][0];else if(k == siz[ch[rt][0]] + 1) return val[rt];else k -= siz[ch[rt][0]]+1, rt = ch[rt][1];}
}
int pre(int a) {split(root, a-1, x, y);an = _kth(x, siz[x]);root = merge(x, y);return an;
}
int nxt(int a) {split(root, a, x, y);an = _kth(y, 1);root = merge(x, y);return an;
}
int main() { srand(time(0));int n,m, op, a, la = 0, ans = 0; read(n); read(m);while(n--) {read(a); insert(a);}while(m--) { read(op); read(a);a ^= la;if(op == 1) insert(a);else if(op == 2) del(a);else if(op == 3) la = _rank(a),ans ^= la;else if(op == 4) la = _kth(root, a), ans ^= la;else if(op == 5) la = pre(a), ans ^= la;else la = nxt(a), ans ^= la;} printf("%d\n", ans);
}

文艺平衡树

文艺平衡树

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int INF = 0x3f3f3f3f;
const double Pi = acos(-1);
namespace {template <typename T> inline void read(T &x) {x = 0; T f = 1;char s = getchar();for(; !isdigit(s); s = getchar()) if(s == '-') f = -1;for(;  isdigit(s); s = getchar()) x = (x << 3) + (x << 1) + (s ^ 48);x *= f;}
}
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define _for(n,m,i) for (register int i = (n); i <  (m); ++i)
#define _rep(n,m,i) for (register int i = (n); i <= (m); ++i)
#define _srep(n,m,i)for (register int i = (n); i >= (m); i--)
#define _sfor(n,m,i)for (register int i = (n); i >  (m); i--)
#define lson rt << 1, l, mid
#define rson rt << 1 | 1, mid + 1, r
#define lowbit(x) x & (-x)
#define pii pair<int,int>
#define fi first
#define se second
const int N = 1e5+5;
int ch[N][2], siz[N], val[N], rnd[N], lazy[N];
int cnt, root;
int new_node(int x) {val[++cnt] = x;siz[cnt] = 1;rnd[cnt] = rand();return cnt;
}
void up(int rt) {siz[rt] = 1 + siz[ch[rt][0]] + siz[ch[rt][1]];
}
void down(int rt) {swap(ch[rt][0], ch[rt][1]);if(ch[rt][0]) lazy[ch[rt][0]] ^= 1;if(ch[rt][1]) lazy[ch[rt][1]] ^= 1;lazy[rt] = 0;
}
void split(int rt, int k, int &x, int &y) {if(!rt) return x = y = 0, void (0);if(lazy[rt]) down(rt);if(siz[ch[rt][0]] < k) x = rt, split(ch[rt][1], k - siz[ch[rt][0]]-1, ch[rt][1], y);else y = rt, split(ch[rt][0], k, x, ch[rt][0]);up(rt);
}
int merge(int x, int y) { if(!x || !y) return x + y;if(rnd[x] < rnd[y]) {if(lazy[x]) down(x);ch[x][1] = merge(ch[x][1], y);up(x); return x;}if(lazy[y]) down(y);ch[y][0] = merge(x, ch[y][0]);up(y); return y;
}
void print(int rt) { if(!rt) return ;if(lazy[rt]) down(rt);print(ch[rt][0]);printf("%d ", val[rt]);print(ch[rt][1]);
}
int main() { srand(time(0));int n, m, x, y, z, l, r; read(n); read(m);_rep(1, n, i) root = merge(root, new_node(i));while(m--) { scanf("%d %d", &l, &r);split(root, l-1, x, y);split(y, r-l+1, y, z);lazy[y] ^=  1;root = merge(x, merge(y, z));} print(root);
}

可持久化平衡树

可持久化平衡树。跑完发现比主席树慢。

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int INF = 2147483647;
const double Pi = acos(-1);
namespace {template <typename T> inline void read(T &x) {x = 0; T f = 1;char s = getchar();for(; !isdigit(s); s = getchar()) if(s == '-') f = -1;for(;  isdigit(s); s = getchar()) x = (x << 3) + (x << 1) + (s ^ 48);x *= f;}
}
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define _for(n,m,i) for (register int i = (n); i <  (m); ++i)
#define _rep(n,m,i) for (register int i = (n); i <= (m); ++i)
#define _srep(n,m,i)for (register int i = (n); i >= (m); i--)
#define _sfor(n,m,i)for (register int i = (n); i >  (m); i--)
#define lson rt << 1, l, mid
#define rson rt << 1 | 1, mid + 1, r
#define lowbit(x) x & (-x)
#define pii pair<int,int>
#define fi first
#define se second
const int N = 5e5+5;
struct fhq_Treap{struct { int val, siz, l, r, rnd;}T[N*60]; int cnt, x, y, z;void up(int rt) {T[rt].siz = 1 + T[T[rt].l].siz + T[T[rt].r].siz;}int new_node(int x) {T[++cnt].val = x;T[cnt].rnd = rand();T[cnt].siz = 1;return cnt;}void split(int rt, int k, int &x, int &y) {if(!rt) return x = y = 0, void(0);if(T[rt].val <= k) {x = ++cnt; T[x] = T[rt];split(T[x].r, k, T[x].r, y);up(x);} else { y = ++cnt; T[y] = T[rt];split(T[y].l, k, x, T[y].l);up(y);} } int merge(int x, int y) {if(!x || !y) return x^y;if(T[x].rnd < T[y].rnd) {T[x].r = merge(T[x].r, y);up(x); return x;} T[y].l = merge(x, T[y].l);up(y); return y;}void insert(int &rt, int val) {split(rt, val-1, x, y);rt = merge(merge(x, new_node(val)), y);}void del(int &rt, int val) {split(rt, val-1, x, y);split(y, val, z, y);z = merge(T[z].l, T[z].r);rt = merge(merge(x, z), y);}int _rank(int rt, int val) {int ans = 0;while(rt) {if(val < T[rt].val) rt = T[rt].l;else if(val == T[rt].val) {while(T[T[rt].l].val == val) cout << T[rt].val << endl,  rt = T[rt].l;return ans + T[T[rt].l].siz;}else ans += T[T[rt].l].siz + 1, rt = T[rt].r;}return ans;}int _kth(int rt, int k) {while(rt) {if(T[T[rt].l].siz >= k) rt = T[rt].l;else if (T[T[rt].l].siz + 1 == k) return T[rt].val;else k -= T[T[rt].l].siz + 1, rt = T[rt].r;}return INF;}int pre(int rt, int val) {int ans = -INF;while(rt) {if(val == T[rt].val) {if(T[rt].l) {rt = T[rt].l;while(T[rt].r) rt = T[rt].r;ans = T[rt].val;} break;}if(T[rt].val < val && ans < T[rt].val) ans = T[rt].val;rt = val < T[rt].val ? T[rt].l : T[rt].r;}return ans;}  int nxt(int rt, int val) {int ans = INF;while(rt) {if(val == T[rt].val) {if(T[rt].r) {rt = T[rt].r;while(T[rt].l) rt = T[rt].l;ans = T[rt].val;} break;}if(T[rt].val > val && ans > T[rt].val) ans = T[rt].val;rt = val > T[rt].val ? T[rt].r : T[rt].l;}return ans;}
}Tr;
int root[N];
int main() {int n, vi, op, xi; read(n);Tr.insert(root[0], -INF); Tr.insert(root[0], INF);for(int i = 1; i <= n; i++) {read(vi); read(op); read(xi);root[i] = root[vi];switch(op) { case 1:Tr.insert(root[i], xi);break;case 2:Tr.del(root[i], xi);break;case 3:printf("%d\n", Tr._rank(root[i], xi));break;case 4:printf("%d\n", Tr._kth(root[i], xi+1));break;case 5:printf("%d\n", Tr.pre(root[i], xi));break;case 6:printf("%d\n", Tr.nxt(root[i], xi));break;}}
}

书架

P2596 [ZJOI2006]书架

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int INF = 0x3f3f3f3f;
const double Pi = acos(-1);
namespace {template <typename T> inline void read(T &x) {x = 0; T f = 1;char s = getchar();for(; !isdigit(s); s = getchar()) if(s == '-') f = -1;for(;  isdigit(s); s = getchar()) x = (x << 3) + (x << 1) + (s ^ 48);x *= f;}
}
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define _for(n,m,i) for (register int i = (n); i <  (m); ++i)
#define _rep(n,m,i) for (register int i = (n); i <= (m); ++i)
#define _srep(n,m,i)for (register int i = (n); i >= (m); i--)
#define _sfor(n,m,i)for (register int i = (n); i >  (m); i--)
#define lson rt << 1, l, mid
#define rson rt << 1 | 1, mid + 1, r
#define lowbit(x) x & (-x)
#define pii pair<int,int>
#define fi first
#define se second
const int N = 4e5+5;
int siz[N], ch[N][2], val[N], rnd[N], root;
int new_node(int pos, int va) { val[va] = pos;rnd[va] = rand();siz[va] = 1;return va;
}
void up(int rt) { siz[rt] = 1 + siz[ch[rt][0]] + siz[ch[rt][1]];
}
void split(int rt, int k, int &x, int &y) { if(!rt) return x = y = 0, void(0);if(val[rt] <= k) x = rt, split(ch[rt][1], k, ch[x][1], y);else y = rt, split(ch[rt][0], k, x, ch[rt][0]);up(rt);
}
int merge(int x, int y) { if(!x || !y) return x + y;if(rnd[x] < rnd[y]) { ch[x][1] = merge(ch[x][1], y);up(x);return x; } ch[y][0] = merge(x, ch[y][0]);up(y); return y;
}
char s[10];
int x, y, z, Min, Max;
void insert(int pos, int va) { root = merge(root, new_node(pos, va));
}
void upd(int pos, int va) {split(root, val[pos], x, y);split(x, val[pos]-1, x, z);if(va) val[pos] = --Min, root = merge(merge(z, x), y);else val[pos] = ++Max, root = merge(merge(x, y), z);
}
int _rank(int k) { split(root, val[k]-1, x, y);int ans = siz[x];root = merge(x, y);return ans;
}
int _kth(int rt, int k) { while(rt) { // cout << k << " " << siz[rt] << " " << siz[ch[rt][0]]<< " " << siz[ch[rt][1]] << endl;if(siz[ch[rt][0]] >= k) rt = ch[rt][0];else if(siz[ch[rt][0]] + 1 == k ) return rt;else k -= siz[ch[rt][0]] + 1, rt = ch[rt][1];}
}
void reve(int pos, int t) { if(!t) return ;if(t<0) { // 和前驱交换 split(root, val[pos]-1, x, y);t = _kth(x, siz[x]);split(x, val[t]-1, x, t);split(y, val[pos], pos, y);swap(val[t], val[pos]);root = merge(merge(x, pos), merge(t, y));} else { // 和后继交换 split(root, val[pos], x, y);t = _kth(y, 1);split(y, val[t], t, y);split(x, val[pos]-1, x, pos);swap(val[t], val[pos]);root = merge(merge(x, t), merge(pos, y));}
}
int main() {  srand(time(0));int n, m, k, t; read(n); read(m); Min = 1, Max = n;for(int i = 1; i <= n; i++) { read(k);insert(i, k);} while(m--) { scanf("%s %d", s, &k);if(s[0] == 'T') {upd(k, 1);} else if(s[0] == 'B') { upd(k, 0);} else if(s[0] == 'I') { read(t);reve(k, t);} else if(s[0] == 'A') { printf("%d\n", _rank(k));} else { printf("%d\n", _kth(root, k)); } }
}

P3850 [TJOI2007]书架

书架

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;
const int INF = 0x3f3f3f3f;
const double Pi = acos(-1);
namespace {template <typename T> inline void read(T &x) {x = 0; T f = 1;char s = getchar();for(; !isdigit(s); s = getchar()) if(s == '-') f = -1;for(;  isdigit(s); s = getchar()) x = (x << 3) + (x << 1) + (s ^ 48);x *= f;}
}
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define _for(n,m,i) for (register int i = (n); i <  (m); ++i)
#define _rep(n,m,i) for (register int i = (n); i <= (m); ++i)
#define _srep(n,m,i)for (register int i = (n); i >= (m); i--)
#define _sfor(n,m,i)for (register int i = (n); i >  (m); i--)
#define lson rt << 1, l, mid
#define rson rt << 1 | 1, mid + 1, r
#define lowbit(x) x & (-x)
#define pii pair<int,int>
#define fi first
#define se second
const int N = 2e5+205;
char s[N][11];
int val[N], ch[N][2], rnd[N], siz[N], cnt, tot, root;
int new_node(int x) {val[++cnt] = x;siz[cnt] = 1;rnd[cnt] = rand();return cnt;
}
void up(int rt) {siz[rt] = 1 + siz[ch[rt][0]] + siz[ch[rt][1]];
}
void split(int rt, int k, int &x, int &y) {if(!rt) return x = y = 0, void (0);if(siz[ch[rt][0]] < k) x = rt, split(ch[x][1], k-siz[ch[rt][0]]-1, ch[x][1], y);else y = rt, split(ch[rt][0], k, x, ch[y][0]);up(rt);
}
int merge(int x, int y) {if(!x || !y) return x + y;if(rnd[x] < rnd[y]) {ch[x][1] = merge(ch[x][1], y);up(x); return x;} ch[y][0] = merge(x, ch[y][0]);up(y); return y;
}
int r1, r2, r3;
void insert(int pos, int va) {split(root, pos, r1, r2);root = merge(merge(r1, new_node(va)), r2);
}
void qry(int pos) {split(root, pos, r1, r2);split(r2, 1, r2, r3);printf("%s\n", s[val[r2]]);root = merge(merge(r1, r2), r3);
}
int main() {srand(time(0));int n, q; read(n);_rep(1, n, i) {scanf("%s", s[++tot]);insert(i-1, tot);}read(n);_rep(1, n, i) {scanf("%s %d", s[++tot], &q);insert(q, tot);}read(n);while(n--) {read(q);qry(q);}
}

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