Splay树
P3369 【模板】普通平衡树
#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 100010, INF = 1e9;
struct Node {
int ch[2];
int p, v;
int size;
int cnt;
}tr[N];
int root, idx;
void pushup(int u) {
tr[u].size = tr[tr[u].ch[0]].size + tr[tr[u].ch[1]].size + tr[u].cnt;
}
void rotate(int x) {
int y = tr[x].p;
int z = tr[y].p;
int k = (tr[y].ch[1] == x);
tr[y].ch[k] = tr[x].ch[k ^ 1], tr[tr[x].ch[k ^ 1]].p = y;
tr[x].ch[k ^ 1] = y, tr[y].p = x;
tr[z].ch[tr[z].ch[1] == y] = x, tr[x].p = z;
pushup(y);
pushup(x);
}
void splay(int x, int k) {
while (tr[x].p != k) {
int y = tr[x].p;
int z = tr[y].p;
if (z != k) {
if ((tr[z].ch[1] == y) ^ (tr[y].ch[1] == x)) rotate(x);
else rotate(y);
}
rotate(x);
}
if (!k) root = x;
}
void insert(int x) {
int u = root, p = 0;
while (u && tr[u].v != x) {
p = u;
u = tr[u].ch[x > tr[u].v];
}
if (u) tr[u].cnt++;
else {
u = ++idx;
if (p) tr[p].ch[x > tr[p].v] = u;
tr[u].p = p;
tr[u].v = x;
tr[u].size = 1;
tr[u].cnt = 1;
}
splay(u, 0);
}
void find(int x) {
int u = root;
while (tr[u].ch[x > tr[u].v] && tr[u].v != x) u = tr[u].ch[x > tr[u].v];
splay(u, 0);
}
int get_pre(int x) {
find(x);
if (tr[root].v < x) return root;
int u = tr[root].ch[0];
while (tr[u].ch[1]) u = tr[u].ch[1];
splay(u, 0);
return u;
}
int get_suc(int x) {
find(x);
if (tr[root].v > x) return root;
int u = tr[root].ch[1];
while (tr[u].ch[0]) u = tr[u].ch[0];
splay(u, 0);
return u;
}
void remove(int x) {
int pre = get_pre(x);
int suc = get_suc(x);
splay(pre, 0);
splay(suc, pre);
int del = tr[suc].ch[0];
if (tr[del].cnt > 1) tr[del].cnt--, splay(del, 0);
else tr[suc].ch[0] = 0, splay(suc, 0);
}
int get_rank_by_key(int x) {
insert(x);
int res = tr[tr[root].ch[0]].size;
remove(x);
return res;
}
int get_key_by_rank(int k) {
int u = root;
while (true) {
if (k <= tr[tr[u].ch[0]].size) u = tr[u].ch[0];
else if (k <= tr[tr[u].ch[0]].size + tr[u].cnt) break;
else k -= tr[tr[u].ch[0]].size + tr[u].cnt, u = tr[u].ch[1];
}
splay(u, 0);
return tr[u].v;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
insert(-INF);
insert(INF);
int T;
cin >> T;
while (T--) {
int opt, x;
cin >> opt >> x;
if (opt == 1) insert(x);
else if (opt == 2) remove(x);
else if (opt == 3) cout << get_rank_by_key(x) << '\n';
else if (opt == 4) cout << get_key_by_rank(x + 1) << '\n';
else if (opt == 5) cout << tr[get_pre(x)].v << '\n';
else cout << tr[get_suc(x)].v << '\n';
}
return 0;
}
P6136 【模板】普通平衡树（数据加强版）
注意数组要开到 \(1.1 \times 10 ^ 6\)。
#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 1100010, INF = (1 << 30) + 1;
struct Node {
int ch[2];
int p, v;
int size;
int cnt;
}tr[N];
int root, idx;
void pushup(int u) {
tr[u].size = tr[tr[u].ch[0]].size + tr[tr[u].ch[1]].size + tr[u].cnt;
}
void rotate(int x) {
int y = tr[x].p;
int z = tr[y].p;
int k = (tr[y].ch[1] == x);
tr[y].ch[k] = tr[x].ch[k ^ 1], tr[tr[x].ch[k ^ 1]].p = y;
tr[x].ch[k ^ 1] = y, tr[y].p = x;
tr[z].ch[tr[z].ch[1] == y] = x, tr[x].p = z;
pushup(y);
pushup(x);
}
void splay(int x, int k) {
while (tr[x].p != k) {
int y = tr[x].p;
int z = tr[y].p;
if (z != k) {
if ((tr[z].ch[1] == y) ^ (tr[y].ch[1] == x)) rotate(x);
else rotate(y);
}
rotate(x);
}
if (!k) root = x;
}
void insert(int x) {
int u = root, p = 0;
while (u && tr[u].v != x) {
p = u;
u = tr[u].ch[x > tr[u].v];
}
if (u) tr[u].cnt++;
else {
u = ++idx;
if (p) tr[p].ch[x > tr[p].v] = u;
tr[u].p = p;
tr[u].v = x;
tr[u].size = 1;
tr[u].cnt = 1;
}
splay(u, 0);
}
void find(int x) {
int u = root;
while (tr[u].ch[x > tr[u].v] && tr[u].v != x) u = tr[u].ch[x > tr[u].v];
splay(u, 0);
}
int get_pre(int x) {
find(x);
if (tr[root].v < x) return root;
int u = tr[root].ch[0];
while (tr[u].ch[1]) u = tr[u].ch[1];
splay(u, 0);
return u;
}
int get_suc(int x) {
find(x);
if (tr[root].v > x) return root;
int u = tr[root].ch[1];
while (tr[u].ch[0]) u = tr[u].ch[0];
splay(u, 0);
return u;
}
void remove(int x) {
int pre = get_pre(x);
int suc = get_suc(x);
splay(pre, 0);
splay(suc, pre);
int del = tr[suc].ch[0];
if (tr[del].cnt > 1) tr[del].cnt--, splay(del, 0);
else tr[suc].ch[0] = 0, splay(suc, 0);
}
int get_rank_by_key(int x) {
insert(x);
int res = tr[tr[root].ch[0]].size;
remove(x);
return res;
}
int get_key_by_rank(int k) {
int u = root;
while (true) {
if (k <= tr[tr[u].ch[0]].size) u = tr[u].ch[0];
else if (k <= tr[tr[u].ch[0]].size + tr[u].cnt) break;
else k -= tr[tr[u].ch[0]].size + tr[u].cnt, u = tr[u].ch[1];
}
splay(u, 0);
return tr[u].v;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
insert(-INF);
insert(INF);
int n, T;
cin >> n >> T;
for (int i = 1; i <= n; i++) {
int x;
cin >> x;
insert(x);
}
int res = 0, last = 0;
while (T--) {
int opt, x;
cin >> opt >> x;
x ^= last;
if (opt == 1) insert(x);
else if (opt == 2) remove(x);
else if (opt == 3) res ^= (last = get_rank_by_key(x));
else if (opt == 4) res ^= (last = get_key_by_rank(x + 1));
else if (opt == 5) res ^= (last = tr[get_pre(x)].v);
else res ^= (last = tr[get_suc(x)].v);
}
cout << res << '\n';
return 0;
}
AcWing 2437 Splay / P3391 【模板】文艺平衡树
以下是代码：
#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 100010;
struct Node {
int ch[2];
int size;
int p, v;
int flag;
}tr[N];
int root, idx;
void pushup(int u) {
tr[u].size = tr[tr[u].ch[0]].size + tr[tr[u].ch[1]].size + 1;
}
void pushdown(int u) {
if (tr[u].flag) {
swap(tr[u].ch[0], tr[u].ch[1]);
tr[tr[u].ch[0]].flag ^= 1;
tr[tr[u].ch[1]].flag ^= 1;
tr[u].flag ^= 1;
}
}
void rotate(int x) {
int y = tr[x].p;
int z = tr[y].p;
int k = tr[y].ch[1] == x;
tr[z].ch[tr[z].ch[1] == y] = x, tr[x].p = z;
tr[y].ch[k] = tr[x].ch[k ^ 1], tr[tr[x].ch[k ^ 1]].p = y;
tr[x].ch[k ^ 1] = y, tr[y].p = x;
pushup(y);
pushup(x);
}
void splay(int x, int k) {
while (tr[x].p != k) {
int y = tr[x].p;
int z = tr[y].p;
if (z != k) {
if ((tr[z].ch[1] == y) ^ (tr[y].ch[1] == x)) rotate(x);
else rotate(y);
}
rotate(x);
}
if (!k) root = x;
}
int n, m;
void insert(int x) {
int u = root, p = 0;
while (u) p = u, u = tr[u].ch[x > tr[u].v];
u = ++idx;
if (p) tr[p].ch[x > tr[p].v] = u;
tr[u].v = x;
tr[u].size = 1;
tr[u].p = p;
tr[u].flag = 0;
splay(u, 0);
}
int get_k(int k) {
int p = root;
while (true) {
pushdown(p);
if (k <= tr[tr[p].ch[0]].size) p = tr[p].ch[0];
else if (k == tr[tr[p].ch[0]].size + 1) {
splay(p, 0);
return p;
}
else k -= tr[tr[p].ch[0]].size + 1, p = tr[p].ch[1];
}
return -1;
}
void output(int u) {
pushdown(u);
if (tr[u].ch[0]) output(tr[u].ch[0]);
if (tr[u].v >= 1 && tr[u].v <= n) cout << tr[u].v << ' ';
if (tr[u].ch[1]) output(tr[u].ch[1]);
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n >> m;
for (int i = 0; i <= n + 1; i++) insert(i);
while (m--) {
int x, y, l, r;
cin >> x >> y;
l = get_k(x), r = get_k(y + 2);
splay(l, 0);
splay(r, l);
tr[tr[r].ch[0]].flag ^= 1;
}
output(root);
return 0;
}
CF675D Tree Construction
实际上，\(x\) 的父结点就是 \(x\) 的前驱和后继中编号较大的那一个。
#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 100010, INF = 1000000000;
struct Node {
int ch[2];
int size;
int p, v;
int cnt;
int kth;
}tr[N];
int root, idx;
void pushup(int u) {
tr[u].size = tr[tr[u].ch[0]].size + tr[tr[u].ch[1]].size + tr[u].cnt;
}
void rotate(int x) {
int y = tr[x].p;
int z = tr[y].p;
int k = tr[y].ch[1] == x;
tr[z].ch[tr[z].ch[1] == y] = x, tr[x].p = z;
tr[y].ch[k] = tr[x].ch[k ^ 1], tr[tr[x].ch[k ^ 1]].p = y;
tr[x].ch[k ^ 1] = y, tr[y].p = x;
pushup(y);
pushup(x);
}
void splay(int x, int k) {
while (tr[x].p != k) {
int y = tr[x].p;
int z = tr[y].p;
if (z != k) {
if ((tr[z].ch[1] == y) ^ (tr[y].ch[1] == x)) rotate(x);
else rotate(y);
}
rotate(x);
}
if (!k) root = x;
}
void find(int x) {
int u = root;
while (tr[u].ch[x > tr[u].v] && tr[u].v != x) {
u = tr[u].ch[x > tr[u].v];
}
splay(u, 0);
}
int get_pre(int x) {
find(x);
if (tr[root].v < x) return root;
int u = tr[root].ch[0];
while (tr[u].ch[1]) u = tr[u].ch[1];
splay(u, 0);
return u;
}
int get_suc(int x) {
find(x);
if (tr[root].v > x) return root;
int u = tr[root].ch[1];
while (tr[u].ch[0]) u = tr[u].ch[0];
splay(u, 0);
return u;
}
void insert(int x, int k) {
int p = 0, u = root;
while (u && tr[u].v != x)
p = u, u = tr[u].ch[x > tr[u].v];
if (u) tr[u].cnt++;
else {
u = ++idx;
if (p) tr[p].ch[x > tr[p].v] = u;
tr[u].p = p;
tr[u].size = tr[u].cnt = 1;
tr[u].v = x;
tr[u].kth = k;
}
splay(u, 0);
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
insert(-INF, -INF);
insert(INF, -INF);
int T, x;
cin >> T >> x;
insert(x, 1);
for (int i = 2; i <= T; i++) {
int x;
cin >> x;
int pre = get_pre(x);
int suc = get_suc(x);
int node = tr[pre].kth > tr[suc].kth ? pre : suc;
cout << tr[node].v << ' ';
insert(x, i);
}
return 0;
}
P2286 [HNOI2004]宠物收养场
- 只有宠物的时候，拿一个平衡树维护宠物的信息。
- 那么当一个人来的时候，可以找他的特点值 \(x\) 的前驱和后继，看它们谁与 \(x\) 的差距更小就取谁。（如果相同取前驱）
- 只有人的时候，拿一个平衡树维护人的信息。
- 同理，当一只宠物来的时候可以用它的特点值 \(x\) 找出最适合它的主人。
代码：
#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 80010, INF = 1000000000, mod = 1000000;
struct Node {
int ch[2];
int size;
int p, v;
int cnt;
}tr[N];
int root, idx;
void pushup(int u) {
tr[u].size = tr[tr[u].ch[0]].size + tr[tr[u].ch[1]].size + tr[u].cnt;
}
void rotate(int x) {
int y = tr[x].p;
int z = tr[y].p;
int k = tr[y].ch[1] == x;
tr[z].ch[tr[z].ch[1] == y] = x, tr[x].p = z;
tr[y].ch[k] = tr[x].ch[k ^ 1], tr[tr[x].ch[k ^ 1]].p = y;
tr[x].ch[k ^ 1] = y, tr[y].p = x;
pushup(y);
pushup(x);
}
void splay(int x, int k) {
while (tr[x].p != k) {
int y = tr[x].p;
int z = tr[y].p;
if (z != k) {
if ((tr[z].ch[1] == y) ^ (tr[y].ch[1] == x)) rotate(x);
else rotate(y);
}
rotate(x);
}
if (!k) root = x;
}
void find(int x) {
int u = root;
while (tr[u].ch[x > tr[u].v] && tr[u].v != x) {
u = tr[u].ch[x > tr[u].v];
}
splay(u, 0);
}
int get_pre(int x) {
find(x);
if (tr[root].v < x) return root;
int u = tr[root].ch[0];
while (tr[u].ch[1]) u = tr[u].ch[1];
splay(u, 0);
return u;
}
int get_suc(int x) {
find(x);
if (tr[root].v > x) return root;
int u = tr[root].ch[1];
while (tr[u].ch[0]) u = tr[u].ch[0];
splay(u, 0);
return u;
}
int _get_pre(int x) {
find(x);
if (tr[root].v <= x) return root;
int u = tr[root].ch[0];
while (tr[u].ch[1]) u = tr[u].ch[1];
splay(u, 0);
return u;
}
int _get_suc(int x) {
find(x);
if (tr[root].v >= x) return root;
int u = tr[root].ch[1];
while (tr[u].ch[0]) u = tr[u].ch[0];
splay(u, 0);
return u;
}
void insert(int x) {
int p = 0, u = root;
while (u && tr[u].v != x)
p = u, u = tr[u].ch[x > tr[u].v];
if (u) tr[u].cnt++;
else {
u = ++idx;
if (p) tr[p].ch[x > tr[p].v] = u;
tr[u].p = p;
tr[u].size = tr[u].cnt = 1;
tr[u].v = x;
}
splay(u, 0);
}
void del(int x) {
int pre = get_pre(x);
int suc = get_suc(x);
splay(pre, 0);
splay(suc, pre);
int del_v = tr[suc].ch[0];
if (tr[del_v].cnt > 1) tr[del_v].cnt--, splay(del_v, 0);
else tr[suc].ch[0] = 0, splay(suc, 0);
}
int get_rank_by_key(int x) {
find(x);
return tr[tr[root].ch[0]].size;
}
int get_key_by_rank(int k) {
int u = root;
while (true) {
if (k <= tr[tr[u].ch[0]].size) u = tr[u].ch[0];
else if (k <= tr[tr[u].ch[0]].size + tr[u].cnt) break;
else k -= tr[tr[u].ch[0]].size + tr[u].cnt, u = tr[u].ch[1];
}
splay(u, 0);
return tr[u].v;
}
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
insert(-INF);
insert(INF);
int n, sum = 0, cnt[3] = {0, 0};
cin >> n;
for (int i = 1; i <= n; i++) {
int opt, x;
cin >> opt >> x;
if (cnt[opt ^ 1] <= 0) {
cnt[opt]++;
insert(x);
continue;
}
cnt[opt ^ 1]--;
int pre = _get_pre(x);
int suc = _get_suc(x);
int a = tr[pre].v;
int b = tr[suc].v;
int c = abs(a - x);
int d = abs(b - x);
if (c <= d) del(a), sum = (sum + c) % mod;
else del(b), sum = (sum + d) % mod;
}
cout << sum << '\n';
return 0;
}
P2234 [HNOI2002]营业额统计
找到前驱和后继，并作差求最小即可。
注意要特殊处理 \(1\) 号结点。
#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
const int N = 40000, INF = 1000000000;
struct Node {
int ch[2];
int size;
int p, v;
int cnt;
}tr[N];
int root, idx;
void pushup(int u) {
tr[u].size = tr[tr[u].ch[0]].size + tr[tr[u].ch[1]].size + tr[u].cnt;
}
void rotate(int x) {
int y = tr[x].p;
int z = tr[y].p;
int k = tr[y].ch[1] == x;
tr[z].ch[tr[z].ch[1] == y] = x, tr[x].p = z;
tr[y].ch[k] = tr[x].ch[k ^ 1], tr[tr[x].ch[k ^ 1]].p = y;
tr[x].ch[k ^ 1] = y, tr[y].p = x;
pushup(y);
pushup(x);
}
void splay(int x, int k) {
while (tr[x].p != k) {
int y = tr[x].p;
int z = tr[y].p;
if (z != k) {
if ((tr[z].ch[1] == y) ^ (tr[y].ch[1] == x)) rotate(x);
else rotate(y);
}
rotate(x);
}
if (!k) root = x;
}
void find(int x) {
int u = root;
while (tr[u].ch[x > tr[u].v] && tr[u].v != x) {
u = tr[u].ch[x > tr[u].v];
}
splay(u, 0);
}
int get_pre(int x) {
find(x);
if (tr[root].v <= x) return root;
int u = tr[root].ch[0];
while (tr[u].ch[1]) u = tr[u].ch[1];
splay(u, 0);
return u;
}
int get_suc(int x) {
find(x);
if (tr[root].v >= x) return root;
int u = tr[root].ch[1];
while (tr[u].ch[0]) u = tr[u].ch[0];
splay(u, 0);
return u;
}
void insert(int x) {
int p = 0, u = root;
while (u && tr[u].v != x)
p = u, u = tr[u].ch[x > tr[u].v];
if (u) tr[u].cnt++;
else {
u = ++idx;
if (p) tr[p].ch[x > tr[p].v] = u;
tr[u].p = p;
tr[u].size = tr[u].cnt = 1;
tr[u].v = x;
}
splay(u, 0);
}
int sum;
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
insert(-INF);
insert(INF);
int n, x;
cin >> n >> x;
sum = x;
insert(x);
for (int i = 2; i <= n; i++) {
int x;
cin >> x;
int pre = get_pre(x);
int suc = get_suc(x);
int c1 = abs(tr[pre].v - x);
int c2 = abs(tr[suc].v - x);
sum += min(c1, c2);
insert(x);
}
cout << sum << '\n';
return 0;
}
