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OI-codes/LibreOJ/104/104.cpp

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C++
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#include <iostream>
#include <limits>
using std::cin;
using std::cout;
const char endl = '\n';
const int N = 1e5 + 5;
class Splay {
private:
size_t root, cnt;
struct node {
size_t l, r, f, c, s;
int v;
node()
: l(0), r(0), f(0), c(0), s(0), v(0) {}
node(int _v, int _f)
: l(0), r(0), f(_f), c(1), s(1), v(_v) {}
size_t &child(unsigned x) {
return !x ? l : r;
}
} tr[N];
// 上传信息
void pushup(size_t u) {
tr[u].s = tr[tr[u].l].s + tr[tr[u].r].s + tr[u].c;
}
unsigned relation(size_t u) {
// 如果当前节点是其父亲节点的左儿子则返回 0否则返回 1
return u == tr[tr[u].f].l ? 0 : 1;
}
void rotate(size_t u) {
// 旧的父节点
size_t p = tr[u].f;
// 当前节点与父节点之间的关系
unsigned x = relation(u);
// 当前节点 <-> 父节点的父节点
if (tr[p].f) {
tr[tr[p].f].child(relation(p)) = u;
}
tr[u].f = tr[p].f;
// 原先的另一个子节点 <-> 父节点
if (tr[u].child(x ^ 1)) {
tr[tr[u].child(x ^ 1)].f = p;
}
tr[p].child(x) = tr[u].child(x ^ 1);
// 原先的父节点 -> 子节点
tr[u].child(x ^ 1) = p;
tr[p].f = u;
// 更新节点信息
pushup(p);
pushup(u);
}
// Splay
//
// 旋转到给定的位置target默认行为为旋转为根节点
void splay(size_t u, size_t t = 0) {
while (tr[u].f != t) {
if (tr[tr[u].f].f == t) {
rotate(u);
} else if (relation(u) == relation(tr[u].f)) {
rotate(tr[u].f);
rotate(u);
} else {
rotate(u);
rotate(u);
}
}
// 更新根节点
if (!t) root = u;
}
// 前驱
//
// 左子树的最右点
size_t _predecessor(size_t u) {
size_t cur = tr[u].l;
while (tr[cur].r) {
cur = tr[cur].r;
}
return cur;
}
// 后继
//
// 右子树的最左点
size_t _successor(size_t u) {
size_t cur = tr[u].r;
while (tr[cur].l) {
cur = tr[cur].l;
}
return cur;
}
size_t _find(const int &v) {
size_t u = root;
while (u && tr[u].v != v) {
// 根据数值大小向左右子树迭代
u = v < tr[u].v ? tr[u].l : tr[u].r;
}
if (u) splay(u);
return u;
}
size_t _insert(const int &v) {
size_t u = root, f = 0;
while (u && tr[u].v != v) {
f = u;
// 根据数值大小向左右子树迭代
u = v < tr[u].v ? tr[u].l : tr[u].r;
}
if (u) {
tr[u].c++;
tr[u].s++;
} else {
tr[u = ++cnt] = node(v, f);
if (f) tr[f].child(v > tr[f].v) = u;
}
splay(u);
return root;
}
void _erase(size_t u) {
if (!u) return;
if (tr[u].c > 1) { // 存在重复的数
splay(u);
tr[u].c--;
tr[u].s--;
return;
}
size_t pred = _predecessor(u),
succ = _successor(u);
splay(pred); // 将前驱旋转到根节点
splay(succ, pred); // 将后继旋转到根节点的右儿子
tr[succ].l = 0; // 此时要删的节点为根节点的左儿子且为叶子节点
// 更新节点信息
pushup(succ);
pushup(pred);
}
public:
Splay()
: root(0), cnt(0) {
// 插入哨兵节点
insert(std::numeric_limits<int>::min());
insert(std::numeric_limits<int>::max());
}
// 插入
void insert(const int &v) {
_insert(v);
}
// 删除
void erase(const int &v) {
_erase(_find(v));
}
// 排名
unsigned rank(const int &v) {
size_t u = _find(v);
if (!u) { // 不存在则插入一个方便查找
u = _insert(v);
// 此时 u 已经成为根节点,直接取左子树大小即可
unsigned r = tr[tr[u].l].s;
_erase(u);
return r;
}
return tr[tr[u].l].s;
}
// 选择
const int &select(unsigned k) {
size_t u = root;
while (k < tr[tr[u].l].s || k >= tr[tr[u].l].s + tr[u].c) {
if (k < tr[tr[u].l].s) {
u = tr[u].l;
} else {
k -= tr[tr[u].l].s + tr[u].c;
u = tr[u].r;
}
}
splay(u);
return tr[u].v;
}
// 前驱
const int &predecessor(const int &v) {
size_t u = _find(v);
if (!u) { // 不存在则插入一个方便查找
u = _insert(v);
const int &r = tr[_predecessor(u)].v;
_erase(u); // 删除
return r;
}
return tr[_predecessor(u)].v;
}
// 后继
const int &successor(const int &v) {
size_t u = _find(v);
if (!u) { // 不存在则插入一个方便查找
u = _insert(v);
const int &r = tr[_successor(u)].v;
_erase(u); // 删除
return r;
}
return tr[_successor(u)].v;
}
};
int n;
Splay tree;
int main() {
std::ios::sync_with_stdio(false);
cin.tie(nullptr);
cin >> n;
while (n--) {
int op, x;
cin >> op >> x;
if (op == 1) {
tree.insert(x);
} else if (op == 2) {
tree.erase(x);
} else if (op == 3) {
cout << tree.rank(x) << endl;
} else if (op == 4) {
cout << tree.select(x) << endl;
} else if (op == 5) {
cout << tree.predecessor(x) << endl;
} else { // op == 6
cout << tree.successor(x) << endl;
}
}
return 0;
}