#859805 (C++23) No.2273 一点乗除区間積

提出ソース

結果

問題	No.2273 一点乗除区間積
ユーザー	👑 emthrm
提出日時	2023-04-14 23:56:20
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	289 ms / 5,000 ms
コード長	10,818 bytes
コンパイル時間	3,214 ms
コンパイル使用メモリ	263,840 KB
実行使用メモリ	13,456 KB
最終ジャッジ日時	2024-10-10 14:56:08
合計ジャッジ時間	5,812 ms
ジャッジサーバーID （参考情報）	judge4 / judge3

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 6,816 KB
testcase_01	AC	1 ms 6,816 KB
testcase_02	AC	2 ms 6,816 KB
testcase_03	AC	2 ms 6,816 KB
testcase_04	AC	2 ms 6,816 KB
testcase_05	AC	2 ms 6,820 KB
testcase_06	AC	2 ms 6,820 KB
testcase_07	AC	1 ms 6,816 KB
testcase_08	AC	2 ms 6,816 KB
testcase_09	AC	2 ms 6,820 KB
testcase_10	AC	2 ms 6,816 KB
testcase_11	AC	2 ms 6,820 KB
testcase_12	AC	2 ms 6,820 KB
testcase_13	AC	2 ms 6,820 KB
testcase_14	AC	2 ms 6,816 KB
testcase_15	AC	2 ms 6,816 KB
testcase_16	AC	8 ms 6,820 KB
testcase_17	AC	6 ms 6,816 KB
testcase_18	AC	81 ms 6,820 KB
testcase_19	AC	87 ms 7,296 KB
testcase_20	AC	216 ms 11,968 KB
testcase_21	AC	289 ms 13,456 KB
testcase_22	AC	200 ms 11,920 KB
testcase_23	AC	192 ms 11,972 KB
testcase_24	AC	216 ms 11,976 KB

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ソースコード

raw source code

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
// constexpr int MOD = 1000000007;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U>
inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;

template <int ID>
struct MInt {
  unsigned int v;

  MInt() : v(0) {}
  MInt(const long long x) : v(x >= 0 ? x % mod() : x % mod() + mod()) {}

  static int get_mod() { return mod(); }
  static void set_mod(const int divisor) { mod() = divisor; }

  static void init(const int x) {
    inv<true>(x);
    fact(x);
    fact_inv(x);
  }

  template <bool MEMOIZES = false>
  static MInt inv(const int n) {
    // assert(0 <= n && n < mod() && std::gcd(x, mod()) == 1);
    static std::vector<MInt> inverse{0, 1};
    const int prev = inverse.size();
    if (n < prev) return inverse[n];
    if constexpr (MEMOIZES) {
      // "n!" and "M" must be disjoint.
      inverse.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        inverse[i] = -inverse[mod() % i] * (mod() / i);
      }
      return inverse[n];
    }
    int u = 1, v = 0;
    for (unsigned int a = n, b = mod(); b;) {
      const unsigned int q = a / b;
      std::swap(a -= q * b, b);
      std::swap(u -= q * v, v);
    }
    return u;
  }

  static MInt fact(const int n) {
    static std::vector<MInt> factorial{1};
    const int prev = factorial.size();
    if (n >= prev) {
      factorial.resize(n + 1);
      for (int i = prev; i <= n; ++i) {
        factorial[i] = factorial[i - 1] * i;
      }
    }
    return factorial[n];
  }

  static MInt fact_inv(const int n) {
    static std::vector<MInt> f_inv{1};
    const int prev = f_inv.size();
    if (n >= prev) {
      f_inv.resize(n + 1);
      f_inv[n] = inv(fact(n).v);
      for (int i = n; i > prev; --i) {
        f_inv[i - 1] = f_inv[i] * i;
      }
    }
    return f_inv[n];
  }

  static MInt nCk(const int n, const int k) {
    if (n < 0 || n < k || k < 0) return 0;
    return fact(n) * (n - k < k ? fact_inv(k) * fact_inv(n - k) :
                                  fact_inv(n - k) * fact_inv(k));
  }
  static MInt nPk(const int n, const int k) {
    return n < 0 || n < k || k < 0 ? 0 : fact(n) * fact_inv(n - k);
  }
  static MInt nHk(const int n, const int k) {
    return n < 0 || k < 0 ? 0 : (k == 0 ? 1 : nCk(n + k - 1, k));
  }

  static MInt large_nCk(long long n, const int k) {
    if (n < 0 || n < k || k < 0) return 0;
    inv<true>(k);
    MInt res = 1;
    for (int i = 1; i <= k; ++i) {
      res *= inv(i) * n--;
    }
    return res;
  }

  MInt pow(long long exponent) const {
    MInt res = 1, tmp = *this;
    for (; exponent > 0; exponent >>= 1) {
      if (exponent & 1) res *= tmp;
      tmp *= tmp;
    }
    return res;
  }

  MInt& operator+=(const MInt& x) {
    if (std::cmp_greater_equal(v += x.v, mod())) v -= mod();
    return *this;
  }
  MInt& operator-=(const MInt& x) {
    if (std::cmp_greater_equal(v += mod() - x.v, mod())) v -= mod();
    return *this;
  }
  MInt& operator*=(const MInt& x) {
    v = static_cast<unsigned long long>(v) * x.v % mod();
    return *this;
    }
  MInt& operator/=(const MInt& x) { return *this *= inv(x.v); }

  auto operator<=>(const MInt& x) const = default;

  MInt& operator++() {
    if (std::cmp_equal(++v, mod())) v = 0;
    return *this;
  }
  MInt operator++(int) {
    const MInt res = *this;
    ++*this;
    return res;
  }
  MInt& operator--() {
    v = (v == 0 ? mod() - 1 : v - 1);
    return *this;
  }
  MInt operator--(int) {
    const MInt res = *this;
    --*this;
    return res;
  }

  MInt operator+() const { return *this; }
  MInt operator-() const { return MInt(v ? mod() - v : 0); }

  MInt operator+(const MInt& x) const { return MInt(*this) += x; }
  MInt operator-(const MInt& x) const { return MInt(*this) -= x; }
  MInt operator*(const MInt& x) const { return MInt(*this) *= x; }
  MInt operator/(const MInt& x) const { return MInt(*this) /= x; }

  friend std::ostream& operator<<(std::ostream& os, const MInt& x) {
    return os << x.v;
  }
  friend std::istream& operator>>(std::istream& is, MInt& x) {
    long long v;
    is >> v;
    x = MInt(v);
    return is;
  }

 private:
  static int& mod() {
    static int divisor = 0;
    return divisor;
  }
};

template <typename T>
struct SegmentTree {
  using Monoid = typename T::Monoid;

  explicit SegmentTree(const int n)
      : SegmentTree(std::vector<Monoid>(n, T::id())) {}

  explicit SegmentTree(const std::vector<Monoid>& a)
      : n(a.size()), p2(std::bit_ceil(a.size())) {
    dat.assign(p2 << 1, T::id());
    std::copy(a.begin(), a.end(), dat.begin() + p2);
    for (int i = p2 - 1; i > 0; --i) {
      dat[i] = T::merge(dat[i << 1], dat[(i << 1) + 1]);
    }
  }

  void set(int idx, const Monoid val) {
    idx += p2;
    dat[idx] = val;
    while (idx >>= 1) dat[idx] = T::merge(dat[idx << 1], dat[(idx << 1) + 1]);
  }

  Monoid get(int left, int right) const {
    Monoid res_l = T::id(), res_r = T::id();
    for (left += p2, right += p2; left < right; left >>= 1, right >>= 1) {
      if (left & 1) res_l = T::merge(res_l, dat[left++]);
      if (right & 1) res_r = T::merge(dat[--right], res_r);
    }
    return T::merge(res_l, res_r);
  }

  Monoid operator[](const int idx) const { return dat[idx + p2]; }

  template <typename G>
  int find_right(int left, const G g) {
    if (left >= n) [[unlikely]] return n;
    Monoid val = T::id();
    left += p2;
    do {
      while (!(left & 1)) left >>= 1;
      Monoid nxt = T::merge(val, dat[left]);
      if (!g(nxt)) {
        while (left < p2) {
          left <<= 1;
          nxt = T::merge(val, dat[left]);
          if (g(nxt)) {
            val = nxt;
            ++left;
          }
        }
        return left - p2;
      }
      val = nxt;
      ++left;
    } while (!std::has_single_bit(static_cast<unsigned int>(left)));
    return n;
  }

  template <typename G>
  int find_left(int right, const G g) {
    if (right <= 0) [[unlikely]] return -1;
    Monoid val = T::id();
    right += p2;
    do {
      --right;
      while (right > 1 && (right & 1)) right >>= 1;
      Monoid nxt = T::merge(dat[right], val);
      if (!g(nxt)) {
        while (right < p2) {
          right = (right << 1) + 1;
          nxt = T::merge(dat[right], val);
          if (g(nxt)) {
            val = nxt;
            --right;
          }
        }
        return right - p2;
      }
      val = nxt;
    } while (!std::has_single_bit(static_cast<unsigned int>(right)));
    return -1;
  }

 private:
  const int n, p2;
  std::vector<Monoid> dat;
};

namespace monoid {

template <typename T>
struct RangeMinimumQuery {
  using Monoid = T;
  static constexpr Monoid id() { return std::numeric_limits<Monoid>::max(); }
  static Monoid merge(const Monoid& a, const Monoid& b) {
    return std::min(a, b);
  }
};

template <typename T>
struct RangeMaximumQuery {
  using Monoid = T;
  static constexpr Monoid id() { return std::numeric_limits<Monoid>::lowest(); }
  static Monoid merge(const Monoid& a, const Monoid& b) {
    return std::max(a, b);
  }
};

template <typename T>
struct RangeSumQuery {
  using Monoid = T;
  static constexpr Monoid id() { return 0; }
  static Monoid merge(const Monoid& a, const Monoid& b) { return a + b; }
};

}  // namespace monoid

template <typename Abelian>
struct FenwickTree {
  explicit FenwickTree(const int n, const Abelian ID = 0)
      : n(n), ID(ID), data(n, ID) {}

  void add(int idx, const Abelian val) {
    for (; idx < n; idx |= idx + 1) {
      data[idx] += val;
    }
  }

  Abelian sum(int idx) const {
    Abelian res = ID;
    for (--idx; idx >= 0; idx = (idx & (idx + 1)) - 1) {
      res += data[idx];
    }
    return res;
  }

  Abelian sum(const int left, const int right) const {
    return left < right ? sum(right) - sum(left) : ID;
  }

  Abelian operator[](const int idx) const { return sum(idx, idx + 1); }

  int lower_bound(Abelian val) const {
    if (val <= ID) [[unlikely]] return 0;
    int res = 0;
    for (int mask = std::bit_ceil(static_cast<unsigned int>(n + 1)) >> 1;
         mask > 0; mask >>= 1) {
      const int idx = res + mask - 1;
      if (idx < n && data[idx] < val) {
        val -= data[idx];
        res += mask;
      }
    }
    return res;
  }

 private:
  const int n;
  const Abelian ID;
  std::vector<Abelian> data;
};

template <typename T>
std::vector<std::pair<T, int>> prime_factorization(T n) {
  std::vector<std::pair<T, int>> res;
  for (T i = 2; i * i <= n; ++i) {
    if (n % i == 0) [[unlikely]] {
      int exponent = 0;
      for (; n % i == 0; n /= i) {
        ++exponent;
      }
      res.emplace_back(i, exponent);
    }
  }
  if (n > 1) res.emplace_back(n, 1);
  return res;
}

int main() {
  using ModInt = MInt<0>;
  struct M {
    using Monoid = ModInt;
    static Monoid id() { return 1; }
    static Monoid merge(const Monoid& a, const Monoid& b) { return a * b; }
  };

  int n, b, q; cin >> n >> b >> q;
  ModInt::set_mod(b);
  if (b == 1) {
    while (q--) cout << 0 << '\n';
    return 0;
  }
  const auto pf_b = prime_factorization(b);
  const int s = pf_b.size();
  vector fac(n, vector(s, 0));
  SegmentTree<M> seg(n), other(n);
  FenwickTree<ll> num_b(n);
  const auto mul = [&](const int i, ll m) {
    if (m == 0) {
      ranges::fill(fac[i], 0);
      seg.set(i, 0);
      num_b.add(i, -num_b[i]);
      other.set(i, 0);
      return;
    }
    if (m == b && num_b[i] > 0) {
      num_b.add(i, -1);
      return;
    }
    int ex = INF;
    REP(x, s) {
      for (; m % pf_b[x].first == 0; m /= pf_b[x].first) {
        ++fac[i][x];
      }
      chmin(ex, fac[i][x] / pf_b[x].second);
    }
    ModInt tmp = 1;
    REP(x, s) tmp *= ModInt(pf_b[x].first).pow(fac[i][x] - pf_b[x].second * ex);
    seg.set(i, seg[i] * m);
    other.set(i, tmp);
    if (ex > 0) {
      REP(x, s) fac[i][x] -= pf_b[x].second * ex;
      num_b.add(i, ex);
    }
  };
  REP(i, n) {
    ll a; cin >> a;
    mul(i, a);
  }
  while (q--) {
    int j, l, r; ll m; cin >> j >> m >> l >> r;
    mul(j, m);
    // REP(i, n) cout << other[i] << " \n"[i + 1 == n];
    cout << (num_b.sum(l, r + 1) == 0 ? seg.get(l, r + 1) * other.get(l, r + 1) : 0) << '\n';
  }
  return 0;
}

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結果

テストケース

ソースコード