add rbst

Author: KumaCS

binary-search-tree/rbst-array.hpp

@@ -0,0 +1,47 @@
+#pragma once
+#include "binary-search-tree/rbst-base.hpp"
+
+template <typename T>
+struct RBSTArrayNode {
+  typename RBSTBase<RBSTArrayNode>::Ptr l, r;
+  T key;
+  int cnt;
+  RBSTArrayNode(const T& t = T()) : l(), r(), key(t), cnt(1) {}
+};
+
+template <class T>
+struct RBSTArray : RBSTBase<RBSTArrayNode<T>> {
+  using Node = RBSTArrayNode<T>;
+  using base = RBSTBase<Node>;
+  using base::merge;
+  using base::split;
+  using typename base::Ptr;
+
+  RBSTArray() = default;
+  T get(Ptr& t, int k) {
+    auto x = split(t, k);
+    auto y = split(x.second, 1);
+    T v = y.first->key;
+    t = merge(x.first, merge(y.first, y.second));
+    return v;
+  }
+  void set(Ptr& t, int k, T v) {
+    auto x = split(t, k);
+    auto y = split(x.second, 1);
+    y.first->key = v;
+    t = merge(x.first, merge(y.first, y.second));
+  }
+
+ protected:
+  Ptr update(Ptr t) override {
+    t->cnt = 1;
+    if (t->l) t->cnt += t->l->cnt;
+    if (t->r) t->cnt += t->r->cnt;
+    return t;
+  }
+  void push(Ptr t) override {}
+};
+
+/**
+ * @brief 挿入/削除の可能な配列 (乱択二分探索木)
+ */

binary-search-tree/rbst-base.hpp

@@ -0,0 +1,75 @@
+#pragma once
+
+template <class Node>
+struct RBSTBase {
+  using Ptr = Node*;
+  template <typename... Args>
+  inline Ptr my_new(Args... args) {
+    return new Node(args...);
+  }
+  inline void my_del(Ptr t) { delete t; }
+  inline Ptr make_tree() const { return nullptr; }
+
+  int size(Ptr t) const { return count(t); }
+  Ptr merge(Ptr l, Ptr r) {
+    if (!l || !r) return l ? l : r;
+    if (int((rng() * (l->cnt + r->cnt)) >> 32) < l->cnt) {
+      push(l);
+      l->r = merge(l->r, r);
+      return update(l);
+    } else {
+      push(r);
+      r->l = merge(l, r->l);
+      return update(r);
+    }
+  }
+  pair<Ptr, Ptr> split(Ptr t, int k) {
+    if (!t) return {nullptr, nullptr};
+    push(t);
+    if (k <= count(t->l)) {
+      auto s = split(t->l, k);
+      t->l = s.second;
+      return {s.first, update(t)};
+    } else {
+      auto s = split(t->r, k - count(t->l) - 1);
+      t->r = s.first;
+      return {update(t), s.second};
+    }
+  }
+  Ptr build(int l, int r, const vector<decltype(Node::key)>& v) {
+    if (l + 1 == r) return my_new(v[l]);
+    int m = (l + r) >> 1;
+    Ptr pm = my_new(v[m]);
+    if (l < m) pm->l = build(l, m, v);
+    if (m + 1 < r) pm->r = build(m + 1, r, v);
+    return update(pm);
+  }
+  Ptr build(const vector<decltype(Node::key)>& v) {
+    return build(0, (int)v.size(), v);
+  }
+  template <typename... Args>
+  void insert(Ptr& t, int k, const Args&... args) {
+    auto x = split(t, k);
+    t = merge(merge(x.first, my_new(args...)), x.second);
+  }
+  void erase(Ptr& t, int k) {
+    auto x = split(t, k);
+    auto y = split(x.second, 1);
+    my_del(y.first);
+    t = merge(x.first, y.second);
+  }
+
+ protected:
+  static uint64_t rng() {
+    static uint64_t x_ = 123456789ull;
+    return x_ ^= x_ << 7, x_ ^= x_ >> 9, x_ & 0xFFFFFFFFull;
+  }
+  inline int count(const Ptr t) const { return t ? t->cnt : 0; }
+  virtual void push(Ptr) = 0;
+  virtual Ptr update(Ptr) = 0;
+};
+
+/**
+ * @brief Randomized Binary Search Tree (基底クラス)
+ * @docs docs/binary-search-tree/rbst-base.md
+ */

docs/binary-search-tree/rbst-base.md

@@ -0,0 +1,5 @@
+乱択二分探索木
+
+実装は [https://nyaannyaan.github.io/library/rbst/rbst-base.hpp] を参考
+
+split / merge を基にした実装．

util/xorshift.hpp

@@ -0,0 +1,18 @@
+#pragma once
+
+namespace XORShift {
+unsigned int xor32() {
+  static unsigned int x = 123456789u;
+  x ^= x << 13, x ^= x >> 17, x ^= x << 5;
+  return x;
+}
+unsigned long long xor64() {
+  static unsigned long long x = 123456789ull;
+  x ^= x << 13, x ^= x >> 7, x ^= x << 17;
+  return x;
+}
+};  // namespace XORShift
+
+/**
+ * @brief XOR shift
+ */

verify/binary-search-tree/UNIT_rbst_array.test.cpp

@@ -0,0 +1,41 @@
+#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
+
+#include "template/template.hpp"
+#include "binary-search-tree/rbst-array.hpp"
+#include "util/xorshift.hpp"
+
+void test() {
+  vector<int> a;
+  RBSTArray<int> ar;
+  auto t = ar.make_tree();
+
+  rep(loop, 0, 10000) {
+    int type = XORShift::xor32() % 3;
+    if (a.empty()) type = 0;
+    if (type == 0) {
+      int x = XORShift::xor32() % (a.size() + 1);
+      int v = XORShift::xor32();
+      a.insert(a.begin() + x, v);
+      ar.insert(t, x, v);
+    } else if (type == 1) {
+      int x = XORShift::xor32() % a.size();
+      int v = XORShift::xor32();
+      a[x] = v;
+      ar.set(t, x, v);
+    } else {
+      int x = XORShift::xor32() % a.size();
+      a.erase(a.begin() + x);
+      ar.erase(t, x);
+    }
+    assert(a.size() == ar.size(t));
+    rep(i, 0, a.size()) assert(a[i] == ar.get(t, i));
+  }
+}
+
+int main() {
+  test();
+
+  int a, b;
+  in(a, b);
+  out(a + b);
+}