test/verify/yosupo-range-affine-range-sum-2.test.cpp

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• Last update: 2026-08-10 15:44:16+00:00
• Problem: https://judge.yosupo.jp/problem/range_affine_range_sum

Depends on

• Montgomery Mod Int (math/combinatorics/montgomery-mod-int.hpp)
• other/vector-pool.hpp
• Lazy Red Black Tree (遅延伝搬赤黒木) (structure/bbst/lazy-red-black-tree.hpp)

Code

// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/range_affine_range_sum
// clang-format on

#include <iostream>
#include <utility>
#include <vector>

#include "../../math/combinatorics/montgomery-mod-int.hpp"
#include "../../other/vector-pool.hpp"
#include "../../structure/bbst/lazy-red-black-tree.hpp"

using namespace std;

using mint = modint998244353;

int main() {
  int N, Q;
  cin >> N >> Q;
  using pi = pair<mint, int>;
  using qi = pair<mint, mint>;
  auto f = [](const pi& a, const pi& b) -> pi {
    return {a.first + b.first, a.second + b.second};
  };
  auto g = [](const pi& a, const qi& b) -> pi {
    return {a.first * b.first + mint(a.second) * b.second, a.second};
  };
  auto h = [](const qi& a, const qi& b) -> qi {
    return {a.first * b.first, a.second * b.first + b.second};
  };
  LazyRedBlackTree<pi, qi, decltype(f), decltype(g), decltype(h)> rbt(
      2 * N, f, g, h, pi(0, 0), pi(1, 0));
  vector<pi> A(N);
  for (int i = 0; i < N; i++) {
    mint a;
    cin >> a;
    A[i] = {a, 1};
  }
  auto root = rbt.build(A);
  for (int i = 0; i < Q; i++) {
    int t;
    cin >> t;
    if (t == 0) {
      int l, r;
      mint b, c;
      cin >> l >> r >> b >> c;
      rbt.set_propagate(root, l, r, qi(b, c));
    } else {
      int l, r;
      cin >> l >> r;
      cout << rbt.query(root, l, r).first << "\n";
    }
  }
}

#line 1 "test/verify/yosupo-range-affine-range-sum-2.test.cpp"
// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/range_affine_range_sum
// clang-format on

#include <iostream>
#include <utility>
#include <vector>

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

#include <cstdint>
#line 5 "math/combinatorics/montgomery-mod-int.hpp"

template <std::uint32_t mod_, bool fast = false>
struct MontgomeryModInt {
 private:
  using mint = MontgomeryModInt;
  using i32 = std::int32_t;
  using i64 = std::int64_t;
  using u32 = std::uint32_t;
  using u64 = std::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 std::ostream& operator<<(std::ostream& os, const mint& p) {
    return os << p.val();
  }

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

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

template <std::uint32_t mod>
using modint = MontgomeryModInt<mod>;
using modint998244353 = modint<998244353>;
using modint1000000007 = modint<1000000007>;
#line 2 "other/vector-pool.hpp"

#line 4 "other/vector-pool.hpp"

template <class T>
struct VectorPool {
  std::vector<T> pool;
  std::vector<T*> stock;
  int ptr;

  VectorPool() = default;

  VectorPool(int sz) : pool(sz), stock(sz) {}

  inline T* alloc() { return stock[--ptr]; }

  inline void free(T* t) { stock[ptr++] = t; }

  void clear() {
    ptr = (int)pool.size();
    for (int i = 0; i < (int)pool.size(); i++) stock[i] = &pool[i];
  }
};
#line 2 "structure/bbst/lazy-red-black-tree.hpp"

#include <cstddef>
#include <iterator>
#include <string>
#include <tuple>
#line 9 "structure/bbst/lazy-red-black-tree.hpp"

#line 11 "structure/bbst/lazy-red-black-tree.hpp"

/**
 * @brief Lazy-Red-Black-Tree(遅延伝搬赤黒木)
 *
 */
template <typename Monoid, typename OperatorMonoid, typename F, typename G,
          typename H>
struct LazyRedBlackTree {
 public:
  enum COLOR { BLACK, RED };

  struct Node {
    Node *l, *r;
    COLOR color;
    int level, cnt;
    Monoid key, sum;
    OperatorMonoid lazy;

    Node() {}

    Node(const Monoid& k, const OperatorMonoid& laz)
        : key(k),
          sum(k),
          l(nullptr),
          r(nullptr),
          color(BLACK),
          level(0),
          cnt(1),
          lazy(laz) {}

    Node(Node* l, Node* r, const Monoid& k, const OperatorMonoid& laz)
        : key(k), color(RED), l(l), r(r), lazy(laz) {}

    bool is_leaf() const { return l == nullptr; }
  };

 private:
  Node* propagate(Node* t) {
    t = clone(t);
    if (t->lazy != OM0) {
      if (t->is_leaf()) {
        t->key = g(t->key, t->lazy);
      } else {
        if (t->l) {
          t->l = clone(t->l);
          t->l->lazy = h(t->l->lazy, t->lazy);
          t->l->sum = g(t->l->sum, t->lazy);
        }
        if (t->r) {
          t->r = clone(t->r);
          t->r->lazy = h(t->r->lazy, t->lazy);
          t->r->sum = g(t->r->sum, t->lazy);
        }
      }
      t->lazy = OM0;
    }
    return update(t);
  }

  inline Node* alloc(Node* l, Node* r) {
    auto t = &(*pool.alloc() = Node(l, r, M1, OM0));
    return update(t);
  }

  virtual Node* clone(Node* t) { return t; }

  Node* rotate(Node* t, bool b) {
    t = propagate(t);
    Node* s;
    if (b) {
      s = propagate(t->l);
      t->l = s->r;
      s->r = t;
    } else {
      s = propagate(t->r);
      t->r = s->l;
      s->l = t;
    }
    update(t);
    return update(s);
  }

  Node* submerge(Node* l, Node* r) {
    if (l->level == r->level) {
      if (l->color != r->color) {
        if (l->color == RED) {
          l = propagate(l);
          l->color = BLACK;
        } else {
          r = propagate(r);
          r->color = BLACK;
        }
      }
      return alloc(l, r);
    } else if (l->level < r->level) {
      r = propagate(r);
      Node* c = (r->l = submerge(l, r->l));
      if (r->color == BLACK && c->color == RED && c->l && c->l->color == RED) {
        r->color = RED;
        c->color = BLACK;
        if (r->r->color == BLACK) return rotate(r, true);
        r->r->color = BLACK;
      }
      return update(r);
    } else {
      l = propagate(l);
      Node* c = (l->r = submerge(l->r, r));
      if (l->color == BLACK && c->color == RED && c->r && c->r->color == RED) {
        l->color = RED;
        c->color = BLACK;
        if (l->l->color == BLACK) return rotate(l, false);
        l->l->color = BLACK;
      }
      return update(l);
    }
  }

  Node* build(int l, int r, const std::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* update(Node* t) {
    t->cnt = count(t->l) + count(t->r) + t->is_leaf();
    t->level = t->is_leaf() ? 0 : t->l->level + (t->l->color == BLACK);
    t->sum = f(f(sum(t->l), t->key), sum(t->r));
    return t;
  }

  void dump(Node* r, typename std::vector<Monoid>::iterator& it,
            OperatorMonoid lazy) {
    if (r->lazy != OM0) lazy = h(lazy, r->lazy);
    if (r->is_leaf()) {
      *it++ = g(r->key, lazy);
      return;
    }
    dump(r->l, it, lazy);
    dump(r->r, it, lazy);
  }

  Node* merge(Node* l) { return l; }

 public:
  VectorPool<Node> pool;
  const F f;
  const G g;
  const H h;
  const OperatorMonoid OM0;
  const Monoid M1;

  LazyRedBlackTree(int sz, const F& f, const G& g, const H& h, const Monoid& M1,
                   const OperatorMonoid& OM0)
      : pool(sz), M1(M1), OM0(OM0), f(f), g(g), h(h) {
    pool.clear();
  }

  inline Node* alloc(const Monoid& key) {
    return &(*pool.alloc() = Node(key, OM0));
  }

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

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

  std::pair<Node*, Node*> split(Node* t, int k) {
    if (!t) return {nullptr, nullptr};
    t = propagate(t);
    if (k == 0) return {nullptr, t};
    if (k >= count(t)) return {t, nullptr};
    Node *l = t->l, *r = t->r;
    pool.free(t);
    if (k < count(l)) {
      auto pp = split(l, k);
      return {pp.first, merge(pp.second, r)};
    }
    if (k > count(l)) {
      auto pp = split(r, k - count(l));
      return {merge(l, pp.first), pp.second};
    }
    return {l, r};
  }

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

  template <typename... Args>
  Node* merge(Node* l, Args... rest) {
    Node* r = merge(rest...);
    if (!l || !r) return l ? l : r;
    Node* c = submerge(l, r);
    c->color = BLACK;
    return c;
  }

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

  std::vector<Monoid> dump(Node* r) {
    std::vector<Monoid> v((std::size_t)count(r));
    auto it = std::begin(v);
    dump(r, it, OM0);
    return v;
  }

  std::string to_string(Node* r) {
    auto s = dump(r);
    std::string ret;
    for (int i = 0; i < s.size(); i++) {
      ret += std::to_string(s[i]);
      ret += ", ";
    }
    return ret;
  }

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

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

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

  void set_propagate(Node*& t, int a, int b, const OperatorMonoid& pp) {
    auto x = split(t, a);
    auto y = split(x.second, b - a);
    y.first->lazy = h(y.first->lazy, pp);
    t = merge(x.first, propagate(y.first), y.second);
  }

  void set_element(Node*& t, int k, const Monoid& x) {
    t = propagate(t);
    if (t->is_leaf()) {
      t->key = t->sum = x;
      return;
    }
    if (k < count(t->l))
      set_element(t->l, k, x);
    else
      set_element(t->r, k - count(t->l), x);
    t = update(t);
  }

  void push_front(Node*& t, const Monoid& v) { t = merge(alloc(v), t); }

  void push_back(Node*& t, const Monoid& v) { t = merge(t, alloc(v)); }

  Monoid pop_front(Node*& t) {
    auto ret = split(t, 1);
    t = ret.second;
    return ret.first->key;
  }

  Monoid pop_back(Node*& t) {
    auto ret = split(t, count(t) - 1);
    t = ret.first;
    return ret.second->key;
  }
};
#line 12 "test/verify/yosupo-range-affine-range-sum-2.test.cpp"

using namespace std;

using mint = modint998244353;

int main() {
  int N, Q;
  cin >> N >> Q;
  using pi = pair<mint, int>;
  using qi = pair<mint, mint>;
  auto f = [](const pi& a, const pi& b) -> pi {
    return {a.first + b.first, a.second + b.second};
  };
  auto g = [](const pi& a, const qi& b) -> pi {
    return {a.first * b.first + mint(a.second) * b.second, a.second};
  };
  auto h = [](const qi& a, const qi& b) -> qi {
    return {a.first * b.first, a.second * b.first + b.second};
  };
  LazyRedBlackTree<pi, qi, decltype(f), decltype(g), decltype(h)> rbt(
      2 * N, f, g, h, pi(0, 0), pi(1, 0));
  vector<pi> A(N);
  for (int i = 0; i < N; i++) {
    mint a;
    cin >> a;
    A[i] = {a, 1};
  }
  auto root = rbt.build(A);
  for (int i = 0; i < Q; i++) {
    int t;
    cin >> t;
    if (t == 0) {
      int l, r;
      mint b, c;
      cin >> l >> r >> b >> c;
      rbt.set_propagate(root, l, r, qi(b, c));
    } else {
      int l, r;
      cin >> l >> r;
      cout << rbt.query(root, l, r).first << "\n";
    }
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	2 ms	4 MB
g++	max_random_00	AC	3547 ms	70 MB
g++	max_random_01	AC	3565 ms	70 MB
g++	max_random_02	AC	3499 ms	70 MB
g++	random_00	AC	2410 ms	55 MB
g++	random_01	AC	2844 ms	65 MB
g++	random_02	AC	1580 ms	10 MB
g++	small_00	AC	3 ms	4 MB
g++	small_01	AC	3 ms	4 MB
g++	small_02	AC	3 ms	4 MB
g++	small_03	AC	3 ms	4 MB
g++	small_04	AC	3 ms	4 MB
g++	small_05	AC	3 ms	4 MB
g++	small_06	AC	3 ms	4 MB
g++	small_07	AC	4 ms	4 MB
g++	small_08	AC	4 ms	4 MB
g++	small_09	AC	4 ms	4 MB
g++	small_random_00	AC	7 ms	4 MB
g++	small_random_01	AC	6 ms	4 MB
clang++	example_00	AC	2 ms	4 MB
clang++	max_random_00	AC	3863 ms	70 MB
clang++	max_random_01	AC	3714 ms	70 MB
clang++	max_random_02	AC	4204 ms	70 MB
clang++	random_00	AC	2772 ms	55 MB
clang++	random_01	AC	2897 ms	65 MB
clang++	random_02	AC	1665 ms	10 MB
clang++	small_00	AC	3 ms	4 MB
clang++	small_01	AC	4 ms	4 MB
clang++	small_02	AC	3 ms	4 MB
clang++	small_03	AC	4 ms	4 MB
clang++	small_04	AC	4 ms	4 MB
clang++	small_05	AC	4 ms	4 MB
clang++	small_06	AC	3 ms	4 MB
clang++	small_07	AC	3 ms	4 MB
clang++	small_08	AC	3 ms	4 MB
clang++	small_09	AC	3 ms	4 MB
clang++	small_random_00	AC	5 ms	4 MB
clang++	small_random_01	AC	4 ms	4 MB

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