test/verify/yosupo-range-affine-point-get.test.cpp

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• Last update: 2024-09-23 18:42:59+09:00
• Problem: https://judge.yosupo.jp/problem/range_affine_point_get

Depends on

• math/combinatorics/montgomery-mod-int.hpp
• structure/class/act.hpp
• structure/class/affine.hpp
• Dual Segment Tree (双対セグメント木) (structure/segment-tree/dual-segment-tree.hpp)
• template/template.hpp

Code

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

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

#include "../../structure/segment-tree/dual-segment-tree.hpp"
#include "../../structure/class/affine.hpp"

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

using mint = modint998244353;

int main() {
  int N, Q;
  cin >> N >> Q;
  vector< int > A(N);
  for(auto& a : A) cin >> a;

  using pi = Affine< mint >;
  auto h = [](const pi& a, const pi& b) -> pi {
    return pi::op(a, b);
  };
  auto id = []() -> pi { return {1, 0}; };
  DualSegmentTree seg(LambdaAct(h, id), N);
  while(Q--) {
    int t;
    cin >> t;
    if(t == 0) {
      int l, r, b, c;
      cin >> l >> r >> b >> c;
      seg.apply(l, r, {b, c});
    } else {
      int i;
      cin >> i;
      cout << seg[i].eval(A[i]).val() << "\n";
    }
  }
}

#line 1 "test/verify/yosupo-range-affine-point-get.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/range_affine_point_get

#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif

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(std::forward<F>(f)) {}

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

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

#line 2 "structure/class/act.hpp"

template <typename F2, typename Composition, typename Id>
struct LambdaAct {
  using F = F2;

  F composition(const F &f, const F &g) const { return _composition(f, g); }

  F id() const { return _id(); }

  LambdaAct(Composition _composition, Id _id)
      : _composition(_composition), _id(_id) {}

 private:
  Composition _composition;
  Id _id;
};

template <typename Composition, typename Id>
LambdaAct(Composition _composition, Id _id)
    -> LambdaAct<decltype(_id()), Composition, Id>;

/*
struct Act {
  using F = ?;
  static constexpr F composition(const F &f, const F &g) {}
  static constexpr F id() const {}
};
*/
#line 2 "structure/segment-tree/dual-segment-tree.hpp"

template <typename Act>
struct DualSegmentTree {
  using F = typename Act::F;

 private:
  int sz, height;
  vector<F> lazy;
  Act m;

  inline void propagate(int k) {
    if (lazy[k] != m.id()) {
      lazy[2 * k + 0] = m.composition(lazy[2 * k + 0], lazy[k]);
      lazy[2 * k + 1] = m.composition(lazy[2 * k + 1], lazy[k]);
      lazy[k] = m.id();
    }
  }

  inline void thrust(int k) {
    for (int i = height; i > 0; i--) propagate(k >> i);
  }

 public:
  DualSegmentTree(Act m, int n) : m(m) {
    sz = 1;
    height = 0;
    while (sz < n) sz <<= 1, height++;
    lazy.assign(2 * sz, m.id());
  }

  F get(int k) {
    thrust(k += sz);
    return lazy[k];
  }

  F operator[](int k) { return get(k); }

  void apply(int a, int b, const F &f) {
    thrust(a += sz);
    thrust(b += sz - 1);
    for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
      if (l & 1) lazy[l] = m.composition(lazy[l], f), ++l;
      if (r & 1) --r, lazy[r] = m.composition(lazy[r], f);
    }
  }
};
#line 1 "structure/class/affine.hpp"
template <typename T>
struct Affine {
  T a, b;  // ax+b
  Affine() : a(1), b(0) {}
  Affine(T a, T b) : a(a), b(b) {}
  T eval(T x) const { return a * x + b; }
  static constexpr Affine op(const Affine& l, const Affine& r) {
    return {l.a * r.a, l.b * r.a + r.b};
  }
  constexpr bool operator==(const Affine& p) const {
    return a == p.a and b == p.b;
  }
  constexpr bool operator!=(const Affine& p) const {
    return a != p.a or b != p.b;
  }
};
#line 7 "test/verify/yosupo-range-affine-point-get.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 9 "test/verify/yosupo-range-affine-point-get.test.cpp"

using mint = modint998244353;

int main() {
  int N, Q;
  cin >> N >> Q;
  vector< int > A(N);
  for(auto& a : A) cin >> a;

  using pi = Affine< mint >;
  auto h = [](const pi& a, const pi& b) -> pi {
    return pi::op(a, b);
  };
  auto id = []() -> pi { return {1, 0}; };
  DualSegmentTree seg(LambdaAct(h, id), N);
  while(Q--) {
    int t;
    cin >> t;
    if(t == 0) {
      int l, r, b, c;
      cin >> l >> r >> b >> c;
      seg.apply(l, r, {b, c});
    } else {
      int i;
      cin >> i;
      cout << seg[i].eval(A[i]).val() << "\n";
    }
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	5 ms	3 MB
g++	max_random_00	AC	324 ms	13 MB
g++	max_random_01	AC	316 ms	13 MB
g++	max_random_02	AC	325 ms	13 MB
g++	random_00	AC	255 ms	13 MB
g++	random_01	AC	266 ms	13 MB
g++	random_02	AC	185 ms	4 MB
g++	small_00	AC	5 ms	3 MB
g++	small_01	AC	5 ms	3 MB
g++	small_02	AC	5 ms	3 MB
g++	small_03	AC	5 ms	3 MB
g++	small_04	AC	5 ms	3 MB
g++	small_05	AC	5 ms	3 MB
g++	small_06	AC	5 ms	3 MB
g++	small_07	AC	5 ms	3 MB
g++	small_08	AC	5 ms	3 MB
g++	small_09	AC	5 ms	3 MB
g++	small_random_00	AC	5 ms	4 MB
g++	small_random_01	AC	5 ms	3 MB
clang++	example_00	AC	5 ms	3 MB
clang++	max_random_00	AC	330 ms	13 MB
clang++	max_random_01	AC	333 ms	13 MB
clang++	max_random_02	AC	330 ms	13 MB
clang++	random_00	AC	262 ms	13 MB
clang++	random_01	AC	275 ms	13 MB
clang++	random_02	AC	193 ms	4 MB
clang++	small_00	AC	5 ms	3 MB
clang++	small_01	AC	5 ms	3 MB
clang++	small_02	AC	5 ms	3 MB
clang++	small_03	AC	5 ms	3 MB
clang++	small_04	AC	5 ms	3 MB
clang++	small_05	AC	5 ms	3 MB
clang++	small_06	AC	5 ms	3 MB
clang++	small_07	AC	5 ms	3 MB
clang++	small_08	AC	5 ms	3 MB
clang++	small_09	AC	5 ms	3 MB
clang++	small_random_00	AC	5 ms	3 MB
clang++	small_random_01	AC	5 ms	3 MB

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