test/verify/yosupo-point-set-range-composite.test.cpp

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• Last update: 2024-05-01 23:44:47+09:00
• Problem: https://judge.yosupo.jp/problem/point_set_range_composite

Depends on

• math/combinatorics/montgomery-mod-int.hpp
• Reversible-Splay-Tree(反転可能Splay木) (structure/bbst/reversible-splay-tree.hpp)
• template/template.hpp

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/point_set_range_composite

#include "../../template/template.hpp"

#include "../../structure/bbst/reversible-splay-tree.hpp"

#include "../../math/combinatorics/montgomery-mod-int.hpp"

using mint = modint998244353;

int main() {
  int N, Q;
  cin >> N >> Q;
  using pi = pair< mint, mint >;
  auto f = [](const pi &a, const pi &b) -> pi {
    return {a.first * b.first, a.second * b.first + b.second};
  };
  ReversibleSplayTree< pi > seg(f, pi(1, 0));
  vector< pi > V(N);
  for(int i = 0; i < N; i++) {
    cin >> V[i].first >> V[i].second;
  }
  auto root = seg.build(V);
  for(int i = 0; i < Q; i++) {
    int t;
    cin >> t;
    if(t == 0) {
      int p;
      mint a, b;
      cin >> p >> a >> b;
      seg.set_element(root, p, pi(a, b));
    } else {
      int l, r;
      mint x;
      cin >> l >> r >> x;
      auto ret = seg.query(root, l, r);
      cout << ret.first * x + ret.second << "\n";
    }
  }
}

#line 1 "test/verify/yosupo-point-set-range-composite.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/point_set_range_composite

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

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 != v.size() ? " " : "");
  }
  return os;
}

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

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/yosupo-point-set-range-composite.test.cpp"

#line 1 "structure/bbst/reversible-splay-tree.hpp"
/**
 * @brief Reversible-Splay-Tree(反転可能Splay木)
 */
template <typename Monoid = int, typename OperatorMonoid = void>
struct ReversibleSplayTree {
 public:
  using F = function<Monoid(Monoid, Monoid)>;
  using S = function<Monoid(Monoid)>;

  struct Node {
    Node *l, *r, *p;
    Monoid key, sum;
    bool rev;
    size_t sz;

    bool is_root() const { return !p || (p->l != this && p->r != this); }

    Node(const Monoid &key)
        : key(key),
          sum(key),
          sz(1),
          rev(false),
          l(nullptr),
          r(nullptr),
          p(nullptr) {}
  };

  ReversibleSplayTree(const F &f, const Monoid &M1)
      : ReversibleSplayTree(f, [](const Monoid &a) { return a; }, M1) {}

  ReversibleSplayTree(const F &f, const S &s, const Monoid &M1)
      : f(f), s(s), M1(M1) {}

  inline size_t count(const Node *t) { return t ? t->sz : 0; }

  inline const Monoid &sum(const Node *t) { return t ? t->sum : M1; }

  Node *alloc(const Monoid &v = Monoid()) { return new Node(v); }

  void splay(Node *t) {
    push(t);
    while (!t->is_root()) {
      auto *q = t->p;
      if (q->is_root()) {
        push(q), push(t);
        if (q->l == t)
          rotr(t);
        else
          rotl(t);
      } else {
        auto *r = q->p;
        push(r), push(q), push(t);
        if (r->l == q) {
          if (q->l == t)
            rotr(q), rotr(t);
          else
            rotl(t), rotr(t);
        } else {
          if (q->r == t)
            rotl(q), rotl(t);
          else
            rotr(t), rotl(t);
        }
      }
    }
  }

  Node *push_front(Node *t, const Monoid &v = Monoid()) {
    if (!t) {
      t = alloc(v);
      return t;
    } else {
      splay(t);
      Node *cur = get_left(t), *z = alloc(v);
      splay(cur);
      z->p = cur;
      cur->l = z;
      splay(z);
      return z;
    }
  }

  Node *push_back(Node *t, const Monoid &v = Monoid()) {
    if (!t) {
      t = alloc(v);
      return t;
    } else {
      splay(t);
      Node *cur = get_right(t), *z = alloc(v);
      splay(cur);
      z->p = cur;
      cur->r = z;
      splay(z);
      return z;
    }
  }

  Node *erase(Node *t) {
    splay(t);
    Node *x = t->l, *y = t->r;
    delete t;
    if (!x) {
      t = y;
      if (t) t->p = nullptr;
    } else if (!y) {
      t = x;
      t->p = nullptr;
    } else {
      x->p = nullptr;
      t = get_right(x);
      splay(t);
      t->r = y;
      y->p = t;
    }
    return t;
  }

  Node *get_left(Node *t) const {
    while (t->l) t = t->l;
    return t;
  }

  Node *get_right(Node *t) const {
    while (t->r) t = t->r;
    return t;
  }

  pair<Node *, Node *> split(Node *t, int k) {
    if (!t) return {nullptr, nullptr};
    push(t);
    if (k <= count(t->l)) {
      auto x = split(t->l, k);
      t->l = x.second;
      t->p = nullptr;
      if (x.second) x.second->p = t;
      return {x.first, update(t)};
    } else {
      auto x = split(t->r, k - count(t->l) - 1);
      t->r = x.first;
      t->p = nullptr;
      if (x.first) x.first->p = t;
      return {update(t), x.second};
    }
  }

  template <typename... Args>
  Node *merge(Node *l, Args... rest) {
    Node *r = merge(rest...);
    if (!l && !r) return nullptr;
    if (!l) return splay(r), r;
    if (!r) return splay(l), l;
    splay(l), splay(r);
    l = get_right(l);
    splay(l);
    l->r = r;
    r->p = l;
    update(l);
    return l;
  }

  void insert(Node *&t, int k, const Monoid &v) {
    splay(t);
    auto x = split(t, k);
    t = merge(merge(x.first, alloc(v)), x.second);
  }

  Monoid erase(Node *&t, int k) {
    splay(t);
    auto x = split(t, k);
    auto y = split(x.second, 1);
    auto v = y.first->c;
    delete y.first;
    t = merge(x.first, y.second);
    return v;
  }

  Monoid query(Node *&t, int a, int b) {
    splay(t);
    auto x = split(t, a);
    auto y = split(x.second, b - a);
    auto ret = sum(y.first);
    t = merge(x.first, y.first, y.second);
    return ret;
  }

  Node *build(const vector<Monoid> &v) { return build(0, (int)v.size(), v); }

  void toggle(Node *t) {
    swap(t->l, t->r);
    t->sum = s(t->sum);
    t->rev ^= true;
  }

  Node *update(Node *t) {
    t->sz = 1;
    t->sum = t->key;
    if (t->l) t->sz += t->l->sz, t->sum = f(t->l->sum, t->sum);
    if (t->r) t->sz += t->r->sz, t->sum = f(t->sum, t->r->sum);
    return t;
  }

  tuple<Node *, Node *, Node *> split3(Node *t, int a, int b) {
    splay(t);
    auto x = split(t, a);
    auto y = split(x.second, b - a);
    return make_tuple(x.first, y.first, y.second);
  }

  void push(Node *t) {
    if (t->rev) {
      if (t->l) toggle(t->l);
      if (t->r) toggle(t->r);
      t->rev = false;
    }
  }

  void set_element(Node *&t, int k, const Monoid &x) {
    splay(t);
    sub_set_element(t, k, x);
  }

 private:
  const Monoid M1;
  const F f;
  const S s;

  Node *build(int l, int r, const vector<Monoid> &v) {
    if (l + 1 >= r) return alloc(v[l]);
    return merge(build(l, (l + r) >> 1, v), build((l + r) >> 1, r, v));
  }

  Node *sub_set_element(Node *&t, int k, const Monoid &x) {
    push(t);
    if (k < count(t->l)) {
      return sub_set_element(t->l, k, x);
    } else if (k == count(t->l)) {
      t->key = x;
      splay(t);
      return t;
    } else {
      return sub_set_element(t->r, k - count(t->l) - 1, x);
    }
  }

  void rotr(Node *t) {
    auto *x = t->p, *y = x->p;
    if ((x->l = t->r)) t->r->p = x;
    t->r = x, x->p = t;
    update(x), update(t);
    if ((t->p = y)) {
      if (y->l == x) y->l = t;
      if (y->r == x) y->r = t;
      update(y);
    }
  }

  void rotl(Node *t) {
    auto *x = t->p, *y = x->p;
    if ((x->r = t->l)) t->l->p = x;
    t->l = x, x->p = t;
    update(x), update(t);
    if ((t->p = y)) {
      if (y->l == x) y->l = t;
      if (y->r == x) y->r = t;
      update(y);
    }
  }

  Node *merge(Node *l) { return l; }
};
#line 6 "test/verify/yosupo-point-set-range-composite.test.cpp"

#line 2 "math/combinatorics/montgomery-mod-int.hpp"

template <uint32_t mod_, bool fast = false>
struct MontgomeryModInt {
 private:
  using mint = MontgomeryModInt;
  using i32 = int32_t;
  using i64 = int64_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod_;
    for (i32 i = 0; i < 4; i++) ret *= 2 - mod_ * ret;
    return ret;
  }

  static constexpr u32 r = get_r();

  static constexpr u32 n2 = -u64(mod_) % mod_;

  static_assert(r * mod_ == 1, "invalid, r * mod != 1");
  static_assert(mod_ < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod_ & 1) == 1, "invalid, mod % 2 == 0");

  u32 x;

 public:
  MontgomeryModInt() : x{} {}

  MontgomeryModInt(const i64 &a)
      : x(reduce(u64(fast ? a : (a % mod() + mod())) * n2)) {}

  static constexpr u32 reduce(const u64 &b) {
    return u32(b >> 32) + mod() - u32((u64(u32(b) * r) * mod()) >> 32);
  }

  mint &operator+=(const mint &p) {
    if (i32(x += p.x - 2 * mod()) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator-=(const mint &p) {
    if (i32(x -= p.x) < 0) x += 2 * mod();
    return *this;
  }

  mint &operator*=(const mint &p) {
    x = reduce(u64(x) * p.x);
    return *this;
  }

  mint &operator/=(const mint &p) {
    *this *= p.inv();
    return *this;
  }

  mint operator-() const { return mint() - *this; }

  mint operator+(const mint &p) const { return mint(*this) += p; }

  mint operator-(const mint &p) const { return mint(*this) -= p; }

  mint operator*(const mint &p) const { return mint(*this) *= p; }

  mint operator/(const mint &p) const { return mint(*this) /= p; }

  bool operator==(const mint &p) const {
    return (x >= mod() ? x - mod() : x) == (p.x >= mod() ? p.x - mod() : p.x);
  }

  bool operator!=(const mint &p) const {
    return (x >= mod() ? x - mod() : x) != (p.x >= mod() ? p.x - mod() : p.x);
  }

  u32 val() const {
    u32 ret = reduce(x);
    return ret >= mod() ? ret - mod() : ret;
  }

  mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  mint inv() const { return pow(mod() - 2); }

  friend ostream &operator<<(ostream &os, const mint &p) {
    return os << p.val();
  }

  friend istream &operator>>(istream &is, mint &a) {
    i64 t;
    is >> t;
    a = mint(t);
    return is;
  }

  static constexpr u32 mod() { return mod_; }
};

template <uint32_t mod>
using modint = MontgomeryModInt<mod>;
using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;
#line 8 "test/verify/yosupo-point-set-range-composite.test.cpp"

using mint = modint998244353;

int main() {
  int N, Q;
  cin >> N >> Q;
  using pi = pair< mint, mint >;
  auto f = [](const pi &a, const pi &b) -> pi {
    return {a.first * b.first, a.second * b.first + b.second};
  };
  ReversibleSplayTree< pi > seg(f, pi(1, 0));
  vector< pi > V(N);
  for(int i = 0; i < N; i++) {
    cin >> V[i].first >> V[i].second;
  }
  auto root = seg.build(V);
  for(int i = 0; i < Q; i++) {
    int t;
    cin >> t;
    if(t == 0) {
      int p;
      mint a, b;
      cin >> p >> a >> b;
      seg.set_element(root, p, pi(a, b));
    } else {
      int l, r;
      mint x;
      cin >> l >> r >> x;
      auto ret = seg.query(root, l, r);
      cout << ret.first * x + ret.second << "\n";
    }
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	6 ms	4 MB
g++	max_random_00	AC	2062 ms	39 MB
g++	max_random_01	AC	2053 ms	39 MB
g++	max_random_02	AC	1964 ms	39 MB
g++	max_random_03	AC	1989 ms	39 MB
g++	max_random_04	AC	2009 ms	39 MB
g++	random_00	AC	1580 ms	31 MB
g++	random_01	AC	1702 ms	36 MB
g++	random_02	AC	1048 ms	7 MB
g++	random_03	AC	201 ms	34 MB
g++	random_04	AC	404 ms	23 MB
g++	small_00	AC	6 ms	4 MB
g++	small_01	AC	6 ms	4 MB
g++	small_02	AC	6 ms	4 MB
g++	small_03	AC	6 ms	4 MB
g++	small_04	AC	6 ms	4 MB
clang++	example_00	AC	6 ms	4 MB
clang++	max_random_00	AC	1515 ms	39 MB
clang++	max_random_01	AC	1521 ms	39 MB
clang++	max_random_02	AC	1587 ms	39 MB
clang++	max_random_03	AC	1517 ms	39 MB
clang++	max_random_04	AC	1501 ms	39 MB
clang++	random_00	AC	1152 ms	31 MB
clang++	random_01	AC	1237 ms	36 MB
clang++	random_02	AC	757 ms	7 MB
clang++	random_03	AC	173 ms	34 MB
clang++	random_04	AC	315 ms	23 MB
clang++	small_00	AC	7 ms	4 MB
clang++	small_01	AC	6 ms	4 MB
clang++	small_02	AC	6 ms	4 MB
clang++	small_03	AC	6 ms	4 MB
clang++	small_04	AC	6 ms	4 MB

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