平衡树

替罪羊树

#include <bits/stdc++.h>using namespace std;const double alpha = 0.725;
const int N = 2e6 + 10;struct Spgtree {int ls[N], rs[N], val[N], num[N], fac[N], sz[N], sum[N], cnt, root;int top, stk[N];void update(int rt) {fac[rt] = fac[ls[rt]] + fac[rs[rt]] + (num[rt] ? 1 : 0);sz[rt] = sz[ls[rt]] + sz[rs[rt]] + 1;sum[rt] = sum[ls[rt]] + sum[rs[rt]] + num[rt];}void dfs(int rt) {if (!rt) {return ;}dfs(ls[rt]);if (num[rt]) {stk[++top] = rt;}dfs(rs[rt]);}int build(int l, int r) {if (l > r) {return 0;}if (l == r) {ls[stk[l]] = rs[stk[l]] = 0;update(stk[l]);return stk[l];}int mid = l + r >> 1;ls[stk[mid]] = build(l, mid - 1), rs[stk[mid]] = build(mid + 1, r);update(stk[mid]);return stk[mid];}void rebuild(int &rt) {top = 0;dfs(rt);rt = build(1, top);}bool imbalence(int rt) {return sum[rt] && (alpha * sz[rt] <= max(sz[ls[rt]], sz[rs[rt]]) || alpha * sz[rt] >= fac[rt]);}void insert(int &rt, int value) {if (!rt) {rt = ++cnt, val[rt] = value, num[rt] = 1;update(rt);return ;}if (val[rt] == value) {num[rt]++;}else if (value < val[rt]) {insert(ls[rt], value);}else {insert(rs[rt], value);}update(rt);if (imbalence(rt)) {rebuild(rt);}}void insert(int value) {insert(root, value);}void erase(int &rt, int value) {if (!rt) {return ;}if (val[rt] == value) {num[rt]--;}else if (value < val[rt]) {erase(ls[rt], value);}else {erase(rs[rt], value);}update(rt);if (imbalence(rt)) {rebuild(rt);}}void erase(int value) {erase(root, value);}int get_rank(int value) {int rt = root, rank = 1;while (rt) {if (value <= val[rt]) {rt = ls[rt];}else {rank += num[rt] + sum[ls[rt]];rt = rs[rt];}}return rank;}int get_num(int rank) {int rt = root;while (rt) {if (num[rt] && sum[ls[rt]] < rank && sum[ls[rt]] + num[rt] >= rank) {break;}if (sum[ls[rt]] >= rank) {rt = ls[rt];}else {rank -= sum[ls[rt]] + num[rt];rt = rs[rt];}}return val[rt];}
}tree;int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);return 0;
}

fhq treap

维护值

#include <bits/stdc++.h>using namespace std;const int N = 2e6 + 10;mt19937 rnd(233);struct fhqtreap {int ls[N], rs[N], val[N], key[N], sz[N], root, cnt;inline int new_node(int value) {cnt++;val[cnt] = value, sz[cnt] = 1, key[cnt] = rnd();return cnt;}void update(int rt) {sz[rt] = sz[ls[rt]] + sz[rs[rt]] + 1;}void split(int rt, int value, int &x, int &y) {if (!rt) {x = y = 0;return ;}if (val[rt] <= value) {x = rt;split(rs[rt], value, rs[rt], y);}else {y = rt;split(ls[rt], value, x, ls[rt]);}update(rt);}int merge(int x, int y) {if (!x || !y) {return x | y;}if (key[x] < key[y]) {ls[y] = merge(x, ls[y]);update(y);return y;}else {rs[x] = merge(rs[x], y);update(x);return x;}}void insert(int value) {int x, y;split(root, value, x, y);root = merge(merge(x, new_node(value)), y);}void erase(int value) {int x, y, z;split(root, value, x, z);split(x, value - 1, x, y);y = merge(ls[y], rs[y]);root = merge(merge(x, y), z);}int get_num(int rank) {int rt = root;while (rt) {if (sz[ls[rt]] + 1 == rank) {break;}else if (sz[ls[rt]] >= rank) {rt = ls[rt];}else {rank -= sz[ls[rt]] + 1;rt = rs[rt];}}return val[rt];}int get_rank(int value) {int x, y, rank;split(root, value - 1, x, y);rank = sz[x] + 1;root = merge(x, y);return rank;}int pre(int value) {int x, y, rt;split(root, value - 1, x, y);rt = x;while (rs[rt]) {rt = rs[rt];}root = merge(x, y);return val[rt];}int suc(int value) {int x, y, rt;split(root, value, x, y);rt = y;while (ls[rt]) {rt = ls[rt];}root = merge(x, y);return val[rt];}
}tree;int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);return 0;
}

维护区间

#include <bits/stdc++.h>using namespace std;const int N = 1e5 + 10;mt19937 rnd(233);struct fhqtreap {int ls[N], rs[N], val[N], key[N], sz[N], rev[N], cnt, root;int new_node(int value) {cnt++;val[cnt] = value, key[cnt] = rnd(), sz[cnt] = 1;return cnt;}void push_down(int rt) {if (rev[rt]) {swap(ls[rt], rs[rt]);rev[ls[rt]] ^= 1, rev[rs[rt]] ^= 1;rev[rt] = 0;}}void push_up(int rt) {sz[rt] = sz[ls[rt]] + sz[rs[rt]] + 1;}void split(int rt, int siz, int &x, int &y) {if (!rt) {x = y = 0;return ;}push_down(rt);if (sz[ls[rt]] < siz) {x = rt;split(rs[rt], siz - sz[ls[rt]] - 1, rs[rt], y);}else {y = rt;split(ls[rt], siz, x, ls[rt]);}push_up(rt);}int merge(int x, int y) {if (!x || !y) {return x | y;}if (key[x] < key[y]) {push_down(x);rs[x] = merge(rs[x], y);push_up(x);return x;}else {push_down(y);ls[y] = merge(x, ls[y]);push_up(y);return y;}}void reverse(int l, int r) {int x, y, z;split(root, l - 1, x, y);split(y, r - l + 1, y, z);rev[y] ^= 1;root = merge(merge(x, y), z);}void print(int rt) {if (!rt) {return ;}push_down(rt);print(ls[rt]);printf("%d ", val[rt]);print(rs[rt]);}void print() {print(root);}void build(int n) {for (int i = 1; i <= n; i++) {root = merge(root, new_node(i));}}
}tree;int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);int n, m;scanf("%d %d", &n, &m);tree.build(n);for (int i = 1; i <= m; i++) {int l, r;scanf("%d %d", &l, &r);tree.reverse(l, r);}tree.print(), putchar('\n');return 0;
}

P3850 [TJOI2007]书架

#include <bits/stdc++.h>using namespace std;const int N = 2e5 + 10;string str[N];mt19937 rnd(233);struct Treap {int ls[N], rs[N], val[N], sz[N], key[N], root, cnt;void push_up(int rt) {sz[rt] = sz[ls[rt]] + sz[rs[rt]] + 1;}int new_node(int value) {cnt++;val[cnt] = value, sz[cnt] = 1, key[cnt] = rnd();return cnt;}void split(int rt, int maxn, int &x, int &y) {if (!rt) {x = y = 0;return ;}if (sz[ls[rt]] < maxn) {x = rt;split(rs[rt], maxn - sz[ls[rt]] - 1, rs[x], y);}else {y = rt;split(ls[rt], maxn, x, ls[rt]);}push_up(rt);}int merge(int x, int y) {if (!x || !y) {return x | y;}if (key[x] < key[y]) {rs[x] = merge(rs[x], y);push_up(x);return x;}else {ls[y] = merge(x, ls[y]);push_up(y);return y;}}void insert(int pos, int value) {int x, y;split(root, pos, x, y);root = merge(merge(x, new_node(value)), y);}int get_num(int rank) {int x, y, z, ans;split(root, rank, x, y);split(y, 1, y, z);ans = val[y];root = merge(merge(x, y), z);return ans;}void build(int n) {for (int i = 1; i <= n; i++) {root = merge(root, new_node(i));}}
}tree;int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);int n, m, q, cnt = 0;cin >> n;for (int i = 1; i <= n; i++) {cin >> str[++cnt];}tree.build(cnt);cin >> m;for (int i = 1, pos; i <= m; i++) {cin >> str[++cnt] >> pos;tree.insert(pos, cnt);}cin >> q;for (int i = 1, x; i <= q; i++) {cin >> x;cout << str[tree.get_num(x)] << "\n";}return 0;
}

P2596 [ZJOI2006]书架

#include <bits/stdc++.h>using namespace std;const int N = 1e5 + 10;mt19937 rnd(233);int minn, maxn;struct Tree {int ls[N], rs[N], val[N], sz[N], key[N], root, cnt;void push_up(int rt) {sz[rt] = sz[ls[rt]] + sz[rs[rt]] + 1;}int new_node(int value, int pos) {val[value] = pos, sz[value] = 1, key[value] = rnd();return value;}void split(int rt, int value, int &x, int &y) {if (!rt) {x = y = 0;return ;}if (val[rt] <= value) {x = rt;split(rs[rt], value, rs[rt], y);}else {y = rt;split(ls[rt], value, x, ls[rt]);}push_up(rt);}int merge(int x, int y) {if (!x || !y) {return x | y;}if (key[x] < key[y]) {rs[x] = merge(rs[x], y);push_up(x);return x;}else {ls[y] = merge(x, ls[y]);push_up(y);return y;}}int get_num(int rt, int rank) {while (rt) {if (sz[ls[rt]] + 1 == rank) {break;}if (sz[ls[rt]] >= rank) {rt = ls[rt];}else {rank -= sz[ls[rt]] + 1;rt = rs[rt];}}return rt;}int get_num(int rank) {return get_num(root, rank);}void insert(int value, int pos) {int x, y;split(root, pos, x, y);root = merge(merge(x, new_node(value, pos)), y);}void update(int value, int op) {int x, y, z;split(root, val[value], x, z);split(x, val[value] - 1, x, y);if (op) {val[value] = --minn;root = merge(merge(y, x), z);}else {val[value] = ++maxn;root = merge(merge(x, z), y);}}void reverse(int value, int op) {if (!op) {return ;}if (op == 1) {int x, y, z, w;split(root, val[value], x, z);split(x, val[value] - 1, x, y);int t = get_num(z, 1);split(z, val[t], z, w);swap(val[y], val[z]);root = merge(merge(x, z), merge(y, w));}else {int x, y, z, w;split(root, val[value] - 1, x, z);split(z, val[value], z, w);int t = get_num(x, sz[x]);split(x, val[t] - 1, x, y);swap(val[y], val[z]);root = merge(merge(x, z), merge(y, w));}}int get_rank(int value) {int x, y, ans;split(root, val[value] - 1, x, y);ans = sz[x];root = merge(x, y);return ans;}
}tree;int main() {// freopen("in.txt", "r", stdin);// freopen("out.txt", "w", stdout);// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);int n, m;scanf("%d %d", &n, &m);minn = 1, maxn = n;for (int i = 1, x; i <= n; i++) {scanf("%d", &x);tree.insert(x, i);}char op[10];for (int i = 1, s, t; i <= m; i++) {scanf("%s %d", op, &s);if (op[0] == 'T') {tree.update(s, 1);}else if (op[0] == 'B') {tree.update(s, 0);}else if (op[0] == 'I') {scanf("%d", &t);tree.reverse(s, t);}else if (op[0] == 'A') {printf("%d\n", tree.get_rank(s));}else {printf("%d\n", tree.get_num(s));}}return 0;
}