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https://git.sb/baoshuo/OI-codes.git
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commit
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GPG Key ID:
00CB9680AB29F51A
@ -1,172 +1,323 @@
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#include <iostream>
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#include <cstdlib>
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#include <limits>
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using std::cin;
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using std::cout;
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#define endl '\n'
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const char endl = '\n';
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const int N = 1e5 + 5;
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class Treap {
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template <typename T>
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class Splay {
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private:
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struct node {
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node *left, *right;
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int size, val, key;
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T value;
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node *lchild, *rchild, *parent, **root;
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std::size_t size, count;
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node()
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: left(nullptr),
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right(nullptr),
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size(1),
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val(0),
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key(rand()) {}
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: value(0), lchild(nullptr), rchild(nullptr), parent(nullptr), root(nullptr), size(0), count(0) {}
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node(int _val)
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: left(nullptr),
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right(nullptr),
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size(1),
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val(_val),
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key(rand()) {}
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node(const T &_value, node *_parent, node **_root)
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: value(_value), lchild(nullptr), rchild(nullptr), parent(_parent), root(_root), size(1), count(1) {}
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~node() {
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delete left, right;
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if (lchild != nullptr) delete lchild;
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if (rchild != nullptr) delete rchild;
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}
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inline void pushup() {
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this->size = 1;
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if (this->left != nullptr) this->size += this->left->size;
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if (this->right != nullptr) this->size += this->right->size;
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node *&child(unsigned int x) {
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return !x ? lchild : rchild;
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}
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} *root = nullptr;
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int getNodeSize(node *);
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node *find(node *, int);
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std::pair<node *, node *> split(node *, int);
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std::pair<node *, node *> splitByValue(node *, int);
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node *merge(node *, node *);
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int _getRank(node *, int);
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unsigned int relation() const {
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// 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
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return this == parent->lchild ? 0 : 1;
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}
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// 左儿子大小
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std::size_t lsize() const {
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return lchild == nullptr ? 0 : lchild->size;
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}
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// 右儿子大小
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std::size_t rsize() const {
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return rchild == nullptr ? 0 : rchild->size;
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}
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// 上传信息
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void pushup() {
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size = lsize() + count + rsize();
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}
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// 旋转
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void rotate() {
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node *old = parent;
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unsigned int x = relation();
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if (old->parent != nullptr) {
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old->parent->child(old->relation()) = this;
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}
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parent = old->parent;
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old->child(x) = child(x ^ 1);
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if (child(x ^ 1) != nullptr) {
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child(x ^ 1)->parent = old;
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}
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child(x ^ 1) = old;
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old->parent = this;
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old->pushup();
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pushup();
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if (parent == nullptr) *root = this;
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}
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// Splay
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void splay(node *target = nullptr) {
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while (parent != target) {
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if (parent->parent == target) { // 父节点是目标节点
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rotate();
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} else if (relation() == parent->relation()) { // 关系相同
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parent->rotate();
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rotate();
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} else {
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rotate();
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rotate();
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}
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}
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}
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// 前驱：左子树的最右点
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node *predecessor() {
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node *pred = lchild;
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while (pred->rchild != nullptr) {
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pred = pred->rchild;
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}
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return pred;
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}
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// 后继：右子树的最左点
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node *successor() {
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node *succ = rchild;
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while (succ->lchild != nullptr) {
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succ = succ->lchild;
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}
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return succ;
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}
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} * root;
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// 插入（内部函数）
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node *_insert(const T &value) {
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node **target = &root, *parent = nullptr;
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while (*target != nullptr && (*target)->value != value) {
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parent = *target;
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parent->size++;
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// 根据大小向左右子树迭代
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if (value < parent->value) {
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target = &parent->lchild;
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} else {
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target = &parent->rchild;
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}
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}
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if (*target == nullptr) {
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*target = new node(value, parent, &root);
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} else {
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(*target)->count++;
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(*target)->size++;
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}
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(*target)->splay();
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return root;
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}
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// 查找指定的值对应的节点
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node *find(const T &value) {
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node *node = root; // 从根节点开始查找
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while (node != nullptr && value != node->value) {
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if (value < node->value) {
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node = node->lchild;
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} else {
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node = node->rchild;
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}
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}
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if (node != nullptr) {
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node->splay();
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}
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return node;
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}
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// 删除
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void erase(node *u) {
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if (u == nullptr) return;
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if (u->count > 1) { // 存在重复的数
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u->splay();
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u->count--;
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u->size--;
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return;
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}
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node *pred = u->predecessor(),
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*succ = u->successor();
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pred->splay();
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succ->splay(pred);
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delete succ->lchild;
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succ->lchild = nullptr;
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succ->pushup();
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pred->pushup();
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}
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public:
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Treap()
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: root(nullptr) {}
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void insert(int);
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void erase(int);
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int getRank(int);
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int getKth(int);
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} tree;
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inline int Treap::getNodeSize(Treap::node *node) {
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return node == nullptr ? 0 : node->size;
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}
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std::pair<Treap::node *, Treap::node *> Treap::split(Treap::node *p, int k) {
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if (p == nullptr) return std::make_pair(nullptr, nullptr);
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std::pair<Treap::node *, Treap::node *> o;
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if (k <= this->getNodeSize(p->left)) {
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o = this->split(p->left, k);
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p->left = o.second;
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p->pushup();
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o.second = p;
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} else {
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o = this->split(p->right, k - this->getNodeSize(p->left) - 1);
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p->right = o.first;
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p->pushup();
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o.first = p;
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Splay()
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: root(nullptr) {
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insert(std::numeric_limits<T>::min());
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insert(std::numeric_limits<T>::max());
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}
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return o;
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}
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std::pair<Treap::node *, Treap::node *> Treap::splitByValue(Treap::node *p, int val) {
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if (p == nullptr) return std::make_pair(nullptr, nullptr);
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std::pair<Treap::node *, Treap::node *> o;
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if (p->val < val) {
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o = this->splitByValue(p->right, val);
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p->right = o.first;
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p->pushup();
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o.first = p;
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} else {
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o = this->splitByValue(p->left, val);
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p->left = o.second;
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p->pushup();
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o.second = p;
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~Splay() {
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delete root;
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}
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return o;
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}
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Treap::node *Treap::merge(Treap::node *x, Treap::node *y) {
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if (x == nullptr) return y;
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if (y == nullptr) return x;
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if (x->key > y->key) {
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x->right = this->merge(x->right, y);
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x->pushup();
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return x;
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// 插入
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void insert(const T &value) {
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_insert(value);
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}
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y->left = this->merge(x, y->left);
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y->pushup();
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return y;
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}
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Treap::node *Treap::find(Treap::node *p, int val) {
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if (p == nullptr) return nullptr;
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if (p->val == val) return p;
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if (p->val > val) return this->find(p->left, val);
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return this->find(p->right, val);
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}
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// 删除
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void erase(const T &value) {
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node *node = find(value);
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void Treap::insert(int val) {
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auto o = this->splitByValue(this->root, val);
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o.first = this->merge(o.first, new Treap::node(val));
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this->root = this->merge(o.first, o.second);
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}
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if (node == nullptr) return;
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void Treap::erase(int val) {
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auto o = this->splitByValue(this->root, val);
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auto t = o;
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if (this->find(o.second, val) != nullptr) {
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t = this->split(o.second, 1);
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delete t.first;
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erase(node);
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}
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this->root = this->merge(o.first, t.second);
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}
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int Treap::_getRank(Treap::node *p, int val) {
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if (p == nullptr) return 1;
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if (val <= p->val) return this->_getRank(p->left, val);
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return this->getNodeSize(p->left) + 1 + this->_getRank(p->right, val);
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}
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// 排名
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unsigned int rank(const T &value) {
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node *node = find(value);
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inline int Treap::getRank(int val) {
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return this->_getRank(this->root, val);
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}
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if (node == nullptr) {
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node = _insert(value);
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// 此时 node 已经成为根节点，直接计算即可
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int res = node->lsize(); // 由于「哨兵」的存在，此处无需 -1
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erase(node);
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int Treap::getKth(int k) {
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auto x = this->split(this->root, k - 1);
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auto y = this->split(x.second, 1);
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Treap::node *o = y.first;
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this->root = this->merge(x.first, this->merge(y.first, y.second));
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return o == nullptr ? -1 : o->val;
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}
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return res;
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}
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int n, op, x;
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// 此时 node 已经成为根节点，直接计算即可
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return node->lsize();
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}
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// 选择
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const T &select(int k) {
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node *node = root;
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while (k < node->lsize() || k >= node->lsize() + node->count) {
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if (k < node->lsize()) { // 所需的节点在左子树中
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node = node->lchild;
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} else {
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k -= node->lsize() + node->count;
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node = node->rchild;
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}
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}
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node->splay();
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return node->value;
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}
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// 前驱
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const T &predecessor(const T &value) {
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node *node = find(value);
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if (node == nullptr) {
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node = _insert(value);
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const T &result = node->predecessor()->value;
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erase(node);
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return result;
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}
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return node->predecessor()->value;
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}
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// 后继
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const T &successor(const T &value) {
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node *node = find(value);
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if (node == nullptr) {
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node = _insert(value);
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const T &result = node->successor()->value;
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erase(node);
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return result;
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}
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return node->successor()->value;
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}
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};
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int n;
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Splay<int> tree;
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int main() {
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std::ios::sync_with_stdio(false);
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cin.tie(nullptr);
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cin >> n;
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while (n--) {
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for (int i = 1; i <= n; i++) {
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int op, x;
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cin >> op >> x;
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if (op == 1) {
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tree.insert(x);
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} else if (op == 2) {
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tree.erase(x);
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} else if (op == 3) {
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cout << tree.getRank(x) << endl;
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} else if (op == 4) {
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cout << tree.getKth(x) << endl;
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} else if (op == 5) {
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cout << tree.getKth(tree.getRank(x) - 1) << endl;
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} else {
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cout << tree.getKth(tree.getRank(x + 1) /* + 1*/) << endl;
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switch (op) {
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case 1: {
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tree.insert(x);
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break;
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}
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case 2: {
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tree.erase(x);
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break;
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}
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case 3: {
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cout << tree.rank(x) << endl;
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break;
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}
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case 4: {
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cout << tree.select(x) << endl;
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break;
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}
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case 5: {
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cout << tree.predecessor(x) << endl;
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break;
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}
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case 6: {
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cout << tree.successor(x) << endl;
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break;
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}
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}
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}
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return 0;
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}
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