test/verify/yosupo-range-affine-range-sum.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
• Lazy-Segment-Tree(遅延伝搬セグメント木) (structure/segment-tree/lazy-segment-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 "../../structure/segment-tree/lazy-segment-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};
  };
  auto seg = get_lazy_segment_tree(N, f, g, h, pi(0, 0), qi(1, 0));
  for(int i = 0; i < N; i++) {
    mint a;
    cin >> a;
    seg.set(i, pi(a, 1));
  }
  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;
      seg.apply(l, r, qi(b, c));
    } else {
      int l, r;
      cin >> l >> r;
      cout << seg.prod(l, r).first << "\n";
    }
  }
}

#line 1 "test/verify/yosupo-range-affine-range-sum.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.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.test.cpp"

#line 1 "structure/segment-tree/lazy-segment-tree.hpp"
/**
 * @brief Lazy-Segment-Tree(遅延伝搬セグメント木)
 * 
 */
template< typename T, typename E, typename F, typename G, typename H >
struct LazySegmentTree {
private:
  int n{}, sz{}, height{};
  vector< T > data;
  vector< E > lazy;
  const F f;
  const G g;
  const H h;
  const T ti;
  const E ei;

  inline void update(int k) {
    data[k] = f(data[2 * k + 0], data[2 * k + 1]);
  }

  inline void all_apply(int k, const E &x) {
    data[k] = g(data[k], x);
    if(k < sz) lazy[k] = h(lazy[k], x);
  }

  inline void propagate(int k) {
    if(lazy[k] != ei) {
      all_apply(2 * k + 0, lazy[k]);
      all_apply(2 * k + 1, lazy[k]);
      lazy[k] = ei;
    }
  }

public:
  LazySegmentTree() = default;

  explicit LazySegmentTree(int n, const F f, const G g, const H h,
                           const T &ti, const E &ei)
      : n(n), f(f), g(g), h(h), ti(ti), ei(ei) {
    sz = 1;
    height = 0;
    while(sz < n) sz <<= 1, height++;
    data.assign(2 * sz, ti);
    lazy.assign(2 * sz, ei);
  }

  explicit LazySegmentTree(const vector< T > &v, const F f, const G g, const H h,
                           const T &ti, const E &ei)
      : LazySegmentTree(v.size(), f, g, h, ti, ei) {
    build(v);
  }

  void build(const vector< T > &v) {
    assert(n == (int) v.size());
    for(int k = 0; k < n; k++) data[k + sz] = v[k];
    for(int k = sz - 1; k > 0; k--) update(k);
  }

  void set(int k, const T &x) {
    k += sz;
    for(int i = height; i > 0; i--) propagate(k >> i);
    data[k] = x;
    for(int i = 1; i <= height; i++) update(k >> i);
  }

  T get(int k) {
    k += sz;
    for(int i = height; i > 0; i--) propagate(k >> i);
    return data[k];
  }

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

  T prod(int l, int r) {
    if(l >= r) return ti;
    l += sz;
    r += sz;
    for(int i = height; i > 0; i--) {
      if(((l >> i) << i) != l) propagate(l >> i);
      if(((r >> i) << i) != r) propagate((r - 1) >> i);
    }
    T L = ti, R = ti;
    for(; l < r; l >>= 1, r >>= 1) {
      if(l & 1) L = f(L, data[l++]);
      if(r & 1) R = f(data[--r], R);
    }
    return f(L, R);
  }

  T all_prod() const {
    return data[1];
  }

  void apply(int k, const E &x) {
    k += sz;
    for(int i = height; i > 0; i--) propagate(k >> i);
    data[k] = g(data[k], x);
    for(int i = 1; i <= height; i++) update(k >> i);
  }

  void apply(int l, int r, const E &x) {
    if(l >= r) return;
    l += sz;
    r += sz;
    for(int i = height; i > 0; i--) {
      if(((l >> i) << i) != l) propagate(l >> i);
      if(((r >> i) << i) != r) propagate((r - 1) >> i);
    }
    {
      int l2 = l, r2 = r;
      for(; l < r; l >>= 1, r >>= 1) {
        if(l & 1) all_apply(l++, x);
        if(r & 1) all_apply(--r, x);
      }
      l = l2, r = r2;
    }
    for(int i = 1; i <= height; i++) {
      if(((l >> i) << i) != l) update(l >> i);
      if(((r >> i) << i) != r) update((r - 1) >> i);
    }
  }

  template< typename C >
  int find_first(int l, const C &check) {
    if(l >= n) return n;
    l += sz;
    for(int i = height; i > 0; i--) propagate(l >> i);
    T sum = ti;
    do {
      while((l & 1) == 0) l >>= 1;
      if(check(f(sum, data[l]))) {
        while(l < sz) {
          propagate(l);
          l <<= 1;
          auto nxt = f(sum, data[l]);
          if(not check(nxt)) {
            sum = nxt;
            l++;
          }
        }
        return l + 1 - sz;
      }
      sum = f(sum, data[l++]);
    } while((l & -l) != l);
    return n;
  }

  template< typename C >
  int find_last(int r, const C &check) {
    if(r <= 0) return -1;
    r += sz;
    for(int i = height; i > 0; i--) propagate((r - 1) >> i);
    T sum = ti;
    do {
      r--;
      while(r > 1 and (r & 1)) r >>= 1;
      if(check(f(data[r], sum))) {
        while(r < sz) {
          propagate(r);
          r = (r << 1) + 1;
          auto nxt = f(data[r], sum);
          if(not check(nxt)) {
            sum = nxt;
            r--;
          }
        }
        return r - sz;
      }
      sum = f(data[r], sum);
    } while((r & -r) != r);
    return -1;
  }
};

template< typename T, typename E, typename F, typename G, typename H >
LazySegmentTree< T, E, F, G, H > get_lazy_segment_tree
    (int N, const F &f, const G &g, const H &h, const T &ti, const E &ei) {
  return LazySegmentTree{N, f, g, h, ti, ei};
}

template< typename T, typename E, typename F, typename G, typename H >
LazySegmentTree< T, E, F, G, H > get_lazy_segment_tree
    (const vector< T > &v, const F &f, const G &g, const H &h, const T &ti, const E &ei) {
  return LazySegmentTree{v, f, g, h, ti, ei};
}
#line 8 "test/verify/yosupo-range-affine-range-sum.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};
  };
  auto seg = get_lazy_segment_tree(N, f, g, h, pi(0, 0), qi(1, 0));
  for(int i = 0; i < N; i++) {
    mint a;
    cin >> a;
    seg.set(i, pi(a, 1));
  }
  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;
      seg.apply(l, r, qi(b, c));
    } else {
      int l, r;
      cin >> l >> r;
      cout << seg.prod(l, r).first << "\n";
    }
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	7 ms	4 MB
g++	max_random_00	AC	764 ms	20 MB
g++	max_random_01	AC	761 ms	20 MB
g++	max_random_02	AC	756 ms	20 MB
g++	random_00	AC	604 ms	20 MB
g++	random_01	AC	641 ms	20 MB
g++	random_02	AC	385 ms	5 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	6 ms	4 MB
g++	small_08	AC	6 ms	4 MB
g++	small_09	AC	7 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	766 ms	20 MB
clang++	max_random_01	AC	748 ms	20 MB
clang++	max_random_02	AC	746 ms	20 MB
clang++	random_00	AC	585 ms	20 MB
clang++	random_01	AC	622 ms	20 MB
clang++	random_02	AC	378 ms	5 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
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	6 ms	4 MB
clang++	small_random_00	AC	7 ms	4 MB
clang++	small_random_01	AC	6 ms	4 MB

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