test/verify/yosupo-range-affine-range-sum-3.test.cpp

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• Last update: 2024-04-24 02:34:04+09:00
• Problem: https://judge.yosupo.jp/problem/range_affine_range_sum

Depends on

• math/combinatorics/montgomery-mod-int.hpp
• other/vector-pool.hpp
• Lazy-Weight-Balanced-Tree(遅延伝搬重み平衡木) (structure/bbst/lazy-weight-balanced-tree.hpp)
• template/template.hpp

Code

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

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

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

#include "../../other/vector-pool.hpp"

#include "../../structure/bbst/lazy-weight-balanced-tree.hpp"

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};
  };
  LazyWeightBalancedTree< 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-3.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/range_affine_range_sum

#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-range-affine-range-sum-3.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 6 "test/verify/yosupo-range-affine-range-sum-3.test.cpp"

#line 1 "other/vector-pool.hpp"
template< class T >
struct VectorPool {
  vector< T > pool;
  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 < pool.size(); i++) stock[i] = &pool[i];
  }
};
#line 8 "test/verify/yosupo-range-affine-range-sum-3.test.cpp"

#line 1 "structure/bbst/lazy-weight-balanced-tree.hpp"
/**
 * @brief Lazy-Weight-Balanced-Tree(遅延伝搬重み平衡木)
 */
template< typename Monoid, typename OperatorMonoid, typename F, typename G, typename H >
struct LazyWeightBalancedTree {
public:
  struct Node {
    Node *l, *r;
    int cnt;
    Monoid key, sum;
    OperatorMonoid lazy;

    Node() {}

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

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

    bool is_leaf() { return !l || !r; }
  };

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);
  }

  Node *update(Node *t) {
    t->cnt = count(t->l) + count(t->r) + t->is_leaf();
    t->sum = f(f(sum(t->l), t->key), sum(t->r));
    return t;
  }

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

  Node *submerge(Node *l, Node *r) {
    if(count(l) > count(r) * 4) {
      l = propagate(l);
      auto nl = propagate(l->l);
      auto nr = submerge(l->r, r);
      if(count(nl) * 4 >= count(nr)) {
        l->r = nr;
        return update(l);
      }
      l->r = nr->l;
      nr->l = l;
      update(l);
      return update(nr);
    }
    if(count(l) * 4 < count(r)) {
      r = propagate(r);
      auto nl = submerge(l, r->l);
      auto nr = propagate(r->r);
      if(count(nl) <= count(nr) * 4) {
        r->l = nl;
        return update(r);
      }
      r->l = nl->r;
      nl->r = r;
      update(r);
      return update(nl);
    }
    return alloc(l, r);
  }

  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));
  }

  void dump(Node *r, typename 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);
  }

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

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


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

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

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

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

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

  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};
  }

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

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

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

  string to_string(Node *r) {
    auto s = dump(r);
    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->c;
    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 10 "test/verify/yosupo-range-affine-range-sum-3.test.cpp"

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};
  };
  LazyWeightBalancedTree< 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	6 ms	4 MB
g++	max_random_00	AC	1953 ms	62 MB
g++	max_random_01	AC	1980 ms	62 MB
g++	max_random_02	AC	1991 ms	62 MB
g++	random_00	AC	1406 ms	49 MB
g++	random_01	AC	1458 ms	58 MB
g++	random_02	AC	788 ms	10 MB
g++	small_00	AC	7 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
g++	small_05	AC	6 ms	4 MB
g++	small_06	AC	6 ms	4 MB
g++	small_07	AC	7 ms	4 MB
g++	small_08	AC	6 ms	4 MB
g++	small_09	AC	6 ms	4 MB
g++	small_random_00	AC	7 ms	4 MB
g++	small_random_01	AC	7 ms	4 MB
clang++	example_00	AC	6 ms	4 MB
clang++	max_random_00	AC	2011 ms	62 MB
clang++	max_random_01	AC	2061 ms	62 MB
clang++	max_random_02	AC	2034 ms	62 MB
clang++	random_00	AC	1530 ms	49 MB
clang++	random_01	AC	1597 ms	58 MB
clang++	random_02	AC	850 ms	10 MB
clang++	small_00	AC	7 ms	4 MB
clang++	small_01	AC	6 ms	4 MB
clang++	small_02	AC	7 ms	4 MB
clang++	small_03	AC	6 ms	4 MB
clang++	small_04	AC	6 ms	4 MB
clang++	small_05	AC	6 ms	4 MB
clang++	small_06	AC	6 ms	4 MB
clang++	small_07	AC	6 ms	4 MB
clang++	small_08	AC	6 ms	4 MB
clang++	small_09	AC	7 ms	4 MB
clang++	small_random_00	AC	8 ms	4 MB
clang++	small_random_01	AC	7 ms	4 MB

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