verify/LibraryChecker/data-structure/balanced-binary-search-tree/OrderedSet.test.cpp

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Last update: 2025-07-27 00:14:47+09:00
Problem: https://judge.yosupo.jp/problem/ordered_set

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Code

#include "../../../../template/template.hpp"
#define PROBLEM "https://judge.yosupo.jp/problem/ordered_set"
#include "../../../../data-structure/balanced-binary-search-tree/AVLTree.hpp"

int main() {
    cin.tie(0)->sync_with_stdio(0);
    AVLTree avl;
    int n, q;
    in(n, q);
    rep(i, n) {
        int a;
        in(a);
        avl.insert(a);
    }

    rep(i, q) {
        int t, x;
        in(t, x);
        if (t == 0) {
            avl.insert(x);
        } else if (t == 1) {
            avl.erase(x);
        } else if (t == 2) {
            out(avl.kth_element(x - 1));
        } else if (t == 3) {
            out(avl.less_count(x + 1));
        } else if (t == 4) {
            out(avl.upper_bound(x));
        } else if (t == 5) {
            out(avl.lower_bound(x));
        }
    }
}

#line 2 "template/template.hpp"
#pragma region Macros
#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using ull = unsigned long long;
using ld = long double;
using int128 = __int128_t;
#define all(x) (x).begin(), (x).end()
#define uniqv(v) v.erase(unique(all(v)), v.end())
#define OVERLOAD_REP(_1, _2, _3, name, ...) name
#define REP1(i, n) for (auto i = std::decay_t<decltype(n)>{}; (i) != (n); ++(i))
#define REP2(i, l, r) for (auto i = (l); (i) != (r); ++(i))
#define rep(...) OVERLOAD_REP(__VA_ARGS__, REP2, REP1)(__VA_ARGS__)
#define logfixed(x) cout << fixed << setprecision(10) << x << endl;

ostream &operator<<(ostream &dest, __int128_t value) {
  ostream::sentry s(dest);
  if (s) {
    __uint128_t tmp = value < 0 ? -value : value;
    char buffer[128];
    char *d = end(buffer);
    do {
      --d;
      *d = "0123456789"[tmp % 10];
      tmp /= 10;
    } while (tmp != 0);
    if (value < 0) {
      --d;
      *d = '-';
    }
    int len = end(buffer) - d;
    if (dest.rdbuf()->sputn(d, len) != len) {
      dest.setstate(ios_base::badbit);
    }
  }
  return dest;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != (int)v.size() ? " " : "");
  }
  return os;
}

template <typename T>
ostream &operator<<(ostream &os, const set<T> &set_var) {
  for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
    os << *itr;
    ++itr;
    if (itr != set_var.end()) os << " ";
    itr--;
  }
  return os;
}

template <typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &set_var) {
  for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
    os << *itr;
    ++itr;
    if (itr != set_var.end()) os << " ";
    itr--;
  }
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &map_var) {
  for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
    os << itr->first << " -> " << itr->second << "\n";
  }
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const unordered_map<T, U> &map_var) {
  for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
    os << itr->first << " -> " << itr->second << "\n";
  }
  return os;
}

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &pair_var) {
  os << pair_var.first << " " << pair_var.second;
  return os;
}

void out() { cout << '\n'; }
template <class T, class... Ts>
void out(const T &a, const Ts &...b) {
  cout << a;
  (cout << ... << (cout << ' ', b));
  cout << '\n';
}

void outf() { cout << '\n'; }
template <class T, class... Ts>
void outf(const T &a, const Ts &...b) {
  cout << fixed << setprecision(14) << a;
  (cout << ... << (cout << ' ', b));
  cout << '\n';
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

inline void in(void) { return; }
template <typename First, typename... Rest>
void in(First &first, Rest &...rest) {
  cin >> first;
  in(rest...);
  return;
}

template <typename T>
bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}

vector<lint> dx8 = {1, 1, 0, -1, -1, -1, 0, 1};
vector<lint> dy8 = {0, 1, 1, 1, 0, -1, -1, -1};
vector<lint> dx4 = {1, 0, -1, 0};
vector<lint> dy4 = {0, 1, 0, -1};

#pragma endregion
#line 2 "verify/LibraryChecker/data-structure/balanced-binary-search-tree/OrderedSet.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/ordered_set"
#line 1 "data-structure/balanced-binary-search-tree/AVLTree.hpp"
class AVLTree {
   private:
    struct Node {
        Node *p, *left, *right;
        int key, height;
        int subtree_size;

        // Balance Factor
        int bf() {
            return left->height - right->height;
        }
    };
    int siz;
    Node *NIL;
    Node *root;

    // 左回転
    void rotate_left(Node *x) {
        Node *y = x->right;
        x->right = y->left;
        if (y->left != NIL) y->left->p = x;
        y->p = x->p;
        if (x->p == NIL) {
            root = y;
        } else if (x == x->p->left) {
            x->p->left = y;
        } else {
            x->p->right = y;
        }
        y->left = x;
        x->p = y;
        update(x);
        update(y);
    }

    // 右回転
    void rotate_right(Node *y) {
        Node *x = y->left;
        y->left = x->right;
        if (x->right != NIL) x->right->p = y;
        x->p = y->p;
        if (y->p == NIL) {
            root = x;
        } else if (y == y->p->left) {
            y->p->left = x;
        } else {
            y->p->right = x;
        }
        x->right = y;
        y->p = x;
        update(y);
        update(x);
    }

    // 右回転→左回転
    void rotate_RL(Node *x) {
        rotate_right(x->right);
        rotate_left(x);
    }

    // 左回転→右回転
    void rotate_LR(Node *z) {
        rotate_left(z->left);
        rotate_right(z);
    }

    // 部分木curの情報を更新する（左右の子の情報が最新でないといけない）
    void update(Node *cur) {
        cur->height = max(cur->left->height, cur->right->height) + 1;
        cur->subtree_size = cur->left->subtree_size + cur->right->subtree_size + 1;
    }

    // ノードポインタzをAVL木に挿入する。挿入できた場合true、zのkeyがすでに含まれていた場合falseを返す
    bool insert(Node *z) {
        Node *y = NIL;
        Node *x = root;
        while (x != NIL) {
            y = x;
            if (z->key == x->key) {
                delete z;
                return false;
            }
            if (z->key < x->key) {
                x = x->left;
            } else {
                x = x->right;
            }
        }
        z->p = y;
        if (y == NIL) {
            root = z;
        } else if (z->key < y->key) {
            y->left = z;
        } else {
            y->right = z;
        }
        siz++;
        insert_fixup(z);
        return true;
    }

    // 挿入操作時のAVL木修復処理
    void insert_fixup(Node *z) {
        bool active = true;
        while (z->p != NIL) {
            Node *u = z->p;
            update(u);
            if (!active) {
                z = u;
                continue;
            }
            int bf_u = u->bf();
            if (u->left == z) {
                if (bf_u == 0) {
                    active = false;
                } else if (bf_u == 2) {
                    Node *v = u->left;
                    if (v->bf() == 1) {
                        rotate_right(u);
                        active = false;
                    } else {
                        rotate_LR(u);
                        active = false;
                    }
                }
            } else {
                if (bf_u == 0) {
                    active = false;
                } else if (bf_u == -2) {
                    Node *v = u->right;
                    if (v->bf() == -1) {
                        rotate_left(u);
                        active = false;
                    } else {
                        rotate_RL(u);
                        active = false;
                    }
                }
            }
            z = u;
        }
    }

    // curの部分木内で最小のキーを持つノードポインタを返す
    Node *min_element(Node *cur) {
        while (cur->left != NIL) {
            cur = cur->left;
        }
        return cur;
    }

    // 部分木uの場所に部分木vを植え替える(uの親の子をvにする)
    void transplant(Node *u, Node *v) {
        if (u->p == NIL) {
            root = v;
        } else if (u == u->p->left) {
            u->p->left = v;
        } else {
            u->p->right = v;
        }
        v->p = u->p;
        if (u->p != NIL) update(u->p);
    }

    // ノードポインタzをAVL木から削除する。
    void erase(Node *z) {
        Node *x;
        Node *y = z;
        if (z->left == NIL) {
            x = z->right;
            transplant(z, z->right);
        } else if (z->right == NIL) {
            x = z->left;
            transplant(z, z->left);
        } else {
            y = min_element(z->right);
            x = y->right;
            if (y->p == z) {
                x->p = y;
            } else {
                transplant(y, y->right);
                y->right = z->right;
                y->right->p = y;
            }
            transplant(z, y);
            y->left = z->left;
            y->left->p = y;
        }
        erase_fixup(x);
        siz--;
        delete z;
    }

    // 削除操作時のAVL木修復処理
    void erase_fixup(Node *z) {
        bool active = true;
        while (z->p != NIL) {
            Node *u = z->p;
            update(u);
            if (!active) {
                z = u;
                continue;
            }
            int bf_u = u->bf();
            if (u->right == z) {
                if (bf_u == 1) {
                    active = false;
                } else if (bf_u == 2) {
                    Node *v = u->left;
                    if (v->bf() == 1) {
                        rotate_right(u);
                    } else if (v->bf() == 0) {
                        rotate_right(u);
                        active = false;
                    } else if (v->bf() == -1) {
                        rotate_LR(u);
                    }
                }
            } else {
                if (bf_u == -1) {
                    active = false;
                } else if (bf_u == -2) {
                    Node *v = u->right;
                    if (v->bf() == -1) {
                        rotate_left(u);
                    } else if (v->bf() == 0) {
                        rotate_left(u);
                        active = false;
                    } else if (v->bf() == 1) {
                        rotate_RL(u);
                    }
                }
            }
            z = u;
        }
    }

    // keyのノードポインタを返す。keyが存在しなければNILを返す。
    Node *contains(Node *cur, int key) {
        while (cur != NIL and cur->key != key) {
            if (key < cur->key) {
                cur = cur->left;
            } else {
                cur = cur->right;
            }
        }
        return cur;
    }

    int less_count(Node *cur, int key) {
        int res = 0;
        while (cur != NIL) {
            if (cur->key < key) {
                res += cur->left->subtree_size + 1;
                cur = cur->right;
            } else {
                cur = cur->left;
            }
        }
        return res;
    }

    Node *kth_element(Node *cur, int k) {
        while (cur != NIL and k > 0) {
            if (cur->left->subtree_size < k) {
                k -= cur->left->subtree_size;
                if (k == 1) return cur;
                k--;
                cur = cur->right;
            } else {
                cur = cur->left;
            }
        }
        return cur;
    }

    Node *lower_bound(Node *cur, int key) {
        Node *res = NIL;
        while (cur != NIL) {
            if (key <= cur->key) {
                res = cur;
                cur = cur->left;
            } else {
                cur = cur->right;
            }
        }
        return res;
    }

    Node *upper_bound(Node *cur, int key) {
        Node *res = NIL;
        while (cur != NIL) {
            if (key >= cur->key) {
                res = cur;
                cur = cur->right;
            } else {
                cur = cur->left;
            }
        }
        return res;
    }

   public:
    // コンストラクタ
    AVLTree() {
        NIL = new Node();
        NIL->key = 0;
        NIL->p = NIL->left = NIL->right = NIL;
        NIL->height = 0;
        NIL->subtree_size = 0;
        root = NIL;
        siz = 0;
    }

    // AVL木にkeyを挿入する。挿入されたらtrue、keyがすでに存在したらfalseを返す(何もしない)
    bool insert(int key) {
        Node *z = new Node();
        z->key = key;
        z->left = NIL;
        z->right = NIL;
        z->height = 1;
        z->subtree_size = 1;
        return insert(z);
    }

    // AVL木からkeyを削除する。削除されたらtrue、keyが存在しなかったらfalseを返す（何もしない）
    bool erase(int key) {
        Node *z = contains(root, key);
        if (z != NIL) {
            erase(z);
            return true;
        } else {
            return false;
        }
    }

    // AVL木にkeyが含まれているならtrue、そうでなければfalseを返す
    bool contains(int key) {
        Node *z = contains(root, key);
        return z != NIL;
    }

    // 現在のAVL木の要素数を返す
    int size() {
        return siz;
    }

    // key未満の要素の個数を返す
    int less_count(int key) {
        return less_count(root, key);
    }

    // 0-indexedで昇順idx番目の要素を返す。存在しないなら-1を返す
    int kth_element(int idx) {
        Node *z = kth_element(root, idx + 1);
        if (z != NIL) {
            return z->key;
        } else {
            return -1;
        }
    }

    // key以上の要素のうち最小のものを返す。存在しないなら-1を返す
    int lower_bound(int key) {
        Node *z = lower_bound(root, key);
        if (z == NIL) return -1;
        return z->key;
    }

    // key以下の要素のうち最大のものを返す。存在しないなら-1を返す
    int upper_bound(int key) {
        Node *z = upper_bound(root, key);
        if (z == NIL) return -1;
        return z->key;
    }
};
#line 4 "verify/LibraryChecker/data-structure/balanced-binary-search-tree/OrderedSet.test.cpp"

int main() {
    cin.tie(0)->sync_with_stdio(0);
    AVLTree avl;
    int n, q;
    in(n, q);
    rep(i, n) {
        int a;
        in(a);
        avl.insert(a);
    }

    rep(i, q) {
        int t, x;
        in(t, x);
        if (t == 0) {
            avl.insert(x);
        } else if (t == 1) {
            avl.erase(x);
        } else if (t == 2) {
            out(avl.kth_element(x - 1));
        } else if (t == 3) {
            out(avl.less_count(x + 1));
        } else if (t == 4) {
            out(avl.upper_bound(x));
        } else if (t == 5) {
            out(avl.lower_bound(x));
        }
    }
}