modulo/mod-log.hpp

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Last update: 2024-08-10 13:03:16+09:00
Include: #include "modulo/mod-log.hpp"

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#pragma once

#include "../hashmap/hashmap.hpp"
#include "../internal/internal-math.hpp"

// a^x = b (mod p) である最小の非負整数 x を返す
int64_t mod_log(int64_t a, int64_t b, int64_t p) {
  if ((a %= p) < 0) a += p;
  if ((b %= p) < 0) b += p;
  int64_t f, g, r = 1 % p;
  for (f = 0; (g = gcd(a, p)) > 1; ++f) {
    if (b % g) return (r == b) ? f : -1;
    b /= g;
    p /= g;
    (r *= (a / g)) %= p;
  }
  if (p == 1) return f;
  int64_t ir = internal::inv(r, p);
  (b *= ir) %= p;
  int64_t k = 0, ak = 1;
  HashMap<int64_t, int64_t> baby;
  for (; k * k < p; ++k) {
    if(baby.find(ak) == baby.end()) baby[ak] = k;
    (ak *= a) %= p;
  }
  int64_t iak = internal::inv(ak, p);
  for (int64_t i = 0; i < k; ++i) {
    if (baby.find(b) != baby.end()) return f + i * k + baby[b];
    (b *= iak) %= p;
  }
  return -1;
}

#line 2 "modulo/mod-log.hpp"

#line 2 "hashmap/hashmap.hpp"

#line 2 "hashmap/hashmap-base.hpp"

#include <cstdint>
using namespace std;

namespace HashMapImpl {
using u32 = uint32_t;
using u64 = uint64_t;

template <typename Key, typename Data>
struct HashMapBase;

template <typename Key, typename Data>
struct itrB
    : iterator<bidirectional_iterator_tag, Data, ptrdiff_t, Data*, Data&> {
  using base =
      iterator<bidirectional_iterator_tag, Data, ptrdiff_t, Data*, Data&>;
  using ptr = typename base::pointer;
  using ref = typename base::reference;

  u32 i;
  HashMapBase<Key, Data>* p;

  explicit constexpr itrB() : i(0), p(nullptr) {}
  explicit constexpr itrB(u32 _i, HashMapBase<Key, Data>* _p) : i(_i), p(_p) {}
  explicit constexpr itrB(u32 _i, const HashMapBase<Key, Data>* _p)
      : i(_i), p(const_cast<HashMapBase<Key, Data>*>(_p)) {}
  friend void swap(itrB& l, itrB& r) { swap(l.i, r.i), swap(l.p, r.p); }
  friend bool operator==(const itrB& l, const itrB& r) { return l.i == r.i; }
  friend bool operator!=(const itrB& l, const itrB& r) { return l.i != r.i; }
  const ref operator*() const {
    return const_cast<const HashMapBase<Key, Data>*>(p)->data[i];
  }
  ref operator*() { return p->data[i]; }
  ptr operator->() const { return &(p->data[i]); }

  itrB& operator++() {
    assert(i != p->cap && "itr::operator++()");
    do {
      i++;
      if (i == p->cap) break;
      if (p->occupied_flag[i] && !p->deleted_flag[i]) break;
    } while (true);
    return (*this);
  }
  itrB operator++(int) {
    itrB it(*this);
    ++(*this);
    return it;
  }
  itrB& operator--() {
    do {
      i--;
      if (p->occupied_flag[i] && !p->deleted_flag[i]) break;
      assert(i != 0 && "itr::operator--()");
    } while (true);
    return (*this);
  }
  itrB operator--(int) {
    itrB it(*this);
    --(*this);
    return it;
  }
};

template <typename Key, typename Data>
struct HashMapBase {
  using u32 = uint32_t;
  using u64 = uint64_t;
  using iterator = itrB<Key, Data>;
  using itr = iterator;

 protected:
  template <typename K>
  inline u64 randomized(const K& key) const {
    return u64(key) ^ r;
  }

  template <typename K,
            enable_if_t<is_same<K, Key>::value, nullptr_t> = nullptr,
            enable_if_t<is_integral<K>::value, nullptr_t> = nullptr>
  inline u32 inner_hash(const K& key) const {
    return (randomized(key) * 11995408973635179863ULL) >> shift;
  }
  template <
      typename K, enable_if_t<is_same<K, Key>::value, nullptr_t> = nullptr,
      enable_if_t<is_integral<decltype(K::first)>::value, nullptr_t> = nullptr,
      enable_if_t<is_integral<decltype(K::second)>::value, nullptr_t> = nullptr>
  inline u32 inner_hash(const K& key) const {
    u64 a = randomized(key.first), b = randomized(key.second);
    a *= 11995408973635179863ULL;
    b *= 10150724397891781847ULL;
    return (a + b) >> shift;
  }
  template <typename K,
            enable_if_t<is_same<K, Key>::value, nullptr_t> = nullptr,
            enable_if_t<is_integral<typename K::value_type>::value, nullptr_t> =
                nullptr>
  inline u32 inner_hash(const K& key) const {
    static constexpr u64 mod = (1LL << 61) - 1;
    static constexpr u64 base = 950699498548472943ULL;
    u64 res = 0;
    for (auto& elem : key) {
      __uint128_t x = __uint128_t(res) * base + (randomized(elem) & mod);
      res = (x & mod) + (x >> 61);
    }
    __uint128_t x = __uint128_t(res) * base;
    res = (x & mod) + (x >> 61);
    if (res >= mod) res -= mod;
    return res >> (shift - 3);
  }

  template <typename D = Data,
            enable_if_t<is_same<D, Key>::value, nullptr_t> = nullptr>
  inline u32 hash(const D& dat) const {
    return inner_hash(dat);
  }
  template <
      typename D = Data,
      enable_if_t<is_same<decltype(D::first), Key>::value, nullptr_t> = nullptr>
  inline u32 hash(const D& dat) const {
    return inner_hash(dat.first);
  }

  template <typename D = Data,
            enable_if_t<is_same<D, Key>::value, nullptr_t> = nullptr>
  inline Key data_to_key(const D& dat) const {
    return dat;
  }
  template <
      typename D = Data,
      enable_if_t<is_same<decltype(D::first), Key>::value, nullptr_t> = nullptr>
  inline Key data_to_key(const D& dat) const {
    return dat.first;
  }

  void reallocate(u32 ncap) {
    vector<Data> ndata(ncap);
    vector<bool> nf(ncap);
    shift = 64 - __lg(ncap);
    for (u32 i = 0; i < cap; i++) {
      if (occupied_flag[i] && !deleted_flag[i]) {
        u32 h = hash(data[i]);
        while (nf[h]) h = (h + 1) & (ncap - 1);
        ndata[h] = move(data[i]);
        nf[h] = true;
      }
    }
    data.swap(ndata);
    occupied_flag.swap(nf);
    cap = ncap;
    occupied = s;
    deleted_flag.resize(cap);
    fill(std::begin(deleted_flag), std::end(deleted_flag), false);
  }

  inline bool extend_rate(u32 x) const { return x * 2 >= cap; }

  inline bool shrink_rate(u32 x) const {
    return HASHMAP_DEFAULT_SIZE < cap && x * 10 <= cap;
  }

  inline void extend() { reallocate(cap << 1); }

  inline void shrink() { reallocate(cap >> 1); }

 public:
  u32 cap, s, occupied;
  vector<Data> data;
  vector<bool> occupied_flag, deleted_flag;
  u32 shift;
  static u64 r;
  static constexpr uint32_t HASHMAP_DEFAULT_SIZE = 4;

  explicit HashMapBase()
      : cap(HASHMAP_DEFAULT_SIZE),
        s(0),
        occupied(0),
        data(cap),
        occupied_flag(cap),
        deleted_flag(cap),
        shift(64 - __lg(cap)) {}

  itr begin() const {
    u32 h = 0;
    while (h != cap) {
      if (occupied_flag[h] && !deleted_flag[h]) break;
      h++;
    }
    return itr(h, this);
  }
  itr end() const { return itr(this->cap, this); }

  friend itr begin(const HashMapBase& h) { return h.begin(); }
  friend itr end(const HashMapBase& h) { return h.end(); }

  itr find(const Key& key) const {
    u32 h = inner_hash(key);
    while (true) {
      if (occupied_flag[h] == false) return this->end();
      if (data_to_key(data[h]) == key) {
        if (deleted_flag[h] == true) return this->end();
        return itr(h, this);
      }
      h = (h + 1) & (cap - 1);
    }
  }

  bool contain(const Key& key) const { return find(key) != this->end(); }

  itr insert(const Data& d) {
    u32 h = hash(d);
    while (true) {
      if (occupied_flag[h] == false) {
        if (extend_rate(occupied + 1)) {
          extend();
          h = hash(d);
          continue;
        }
        data[h] = d;
        occupied_flag[h] = true;
        ++occupied, ++s;
        return itr(h, this);
      }
      if (data_to_key(data[h]) == data_to_key(d)) {
        if (deleted_flag[h] == true) {
          data[h] = d;
          deleted_flag[h] = false;
          ++s;
        }
        return itr(h, this);
      }
      h = (h + 1) & (cap - 1);
    }
  }

  // tips for speed up :
  // if return value is unnecessary, make argument_2 false.
  itr erase(itr it, bool get_next = true) {
    if (it == this->end()) return this->end();
    s--;
    if (!get_next) {
      this->deleted_flag[it.i] = true;
      if (shrink_rate(s)) shrink();
      return this->end();
    }
    itr nxt = it;
    nxt++;
    this->deleted_flag[it.i] = true;
    if (shrink_rate(s)) {
      Data d = data[nxt.i];
      shrink();
      it = find(data_to_key(d));
    }
    return nxt;
  }

  itr erase(const Key& key) { return erase(find(key)); }

  int count(const Key& key) { return find(key) == end() ? 0 : 1; }

  bool empty() const { return s == 0; }

  int size() const { return s; }

  void clear() {
    fill(std::begin(occupied_flag), std::end(occupied_flag), false);
    fill(std::begin(deleted_flag), std::end(deleted_flag), false);
    s = occupied = 0;
  }

  void reserve(int n) {
    if (n <= 0) return;
    n = 1 << min(23, __lg(n) + 2);
    if (cap < u32(n)) reallocate(n);
  }
};

template <typename Key, typename Data>
uint64_t HashMapBase<Key, Data>::r =
    chrono::duration_cast<chrono::nanoseconds>(
        chrono::high_resolution_clock::now().time_since_epoch())
        .count();

}  // namespace HashMapImpl

/**
 * @brief Hash Map(base)　(ハッシュマップ・基底クラス)
 */
#line 4 "hashmap/hashmap.hpp"

template <typename Key, typename Val>
struct HashMap : HashMapImpl::HashMapBase<Key, pair<Key, Val>> {
  using base = typename HashMapImpl::HashMapBase<Key, pair<Key, Val>>;
  using HashMapImpl::HashMapBase<Key, pair<Key, Val>>::HashMapBase;
  using Data = pair<Key, Val>;

  Val& operator[](const Key& k) {
    typename base::u32 h = base::inner_hash(k);
    while (true) {
      if (base::occupied_flag[h] == false) {
        if (base::extend_rate(base::occupied + 1)) {
          base::extend();
          h = base::hash(k);
          continue;
        }
        base::data[h].first = k;
        base::data[h].second = Val();
        base::occupied_flag[h] = true;
        ++base::occupied, ++base::s;
        return base::data[h].second;
      }
      if (base::data[h].first == k) {
        if (base::deleted_flag[h] == true) {
          base::data[h].second = Val();
          base::deleted_flag[h] = false;
          ++base::s;
        }
        return base::data[h].second;
      }
      h = (h + 1) & (base::cap - 1);
    }
  }

  typename base::itr emplace(const Key& key, const Val& val) {
    return base::insert(Data(key, val));
  }
};

/*
 * @brief ハッシュマップ(連想配列)
 * @docs docs/hashmap/hashmap.md
 **/
#line 2 "internal/internal-math.hpp"

#line 2 "internal/internal-type-traits.hpp"

#include <type_traits>
using namespace std;

namespace internal {
template <typename T>
using is_broadly_integral =
    typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> ||
                               is_same_v<T, __uint128_t>,
                           true_type, false_type>::type;

template <typename T>
using is_broadly_signed =
    typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>,
                           true_type, false_type>::type;

template <typename T>
using is_broadly_unsigned =
    typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>,
                           true_type, false_type>::type;

#define ENABLE_VALUE(x) \
  template <typename T> \
  constexpr bool x##_v = x<T>::value;

ENABLE_VALUE(is_broadly_integral);
ENABLE_VALUE(is_broadly_signed);
ENABLE_VALUE(is_broadly_unsigned);
#undef ENABLE_VALUE

#define ENABLE_HAS_TYPE(var)                                   \
  template <class, class = void>                               \
  struct has_##var : false_type {};                            \
  template <class T>                                           \
  struct has_##var<T, void_t<typename T::var>> : true_type {}; \
  template <class T>                                           \
  constexpr auto has_##var##_v = has_##var<T>::value;

#define ENABLE_HAS_VAR(var)                                     \
  template <class, class = void>                                \
  struct has_##var : false_type {};                             \
  template <class T>                                            \
  struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \
  template <class T>                                            \
  constexpr auto has_##var##_v = has_##var<T>::value;

}  // namespace internal
#line 4 "internal/internal-math.hpp"

namespace internal {

#include <cassert>
#include <utility>
#include <vector>
using namespace std;

// a mod p
template <typename T>
T safe_mod(T a, T p) {
  a %= p;
  if constexpr (is_broadly_signed_v<T>) {
    if (a < 0) a += p;
  }
  return a;
}

// 返り値：pair(g, x)
// s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
template <typename T>
pair<T, T> inv_gcd(T a, T p) {
  static_assert(is_broadly_signed_v<T>);
  a = safe_mod(a, p);
  if (a == 0) return {p, 0};
  T b = p, x = 1, y = 0;
  while (a != 0) {
    T q = b / a;
    swap(a, b %= a);
    swap(x, y -= q * x);
  }
  if (y < 0) y += p / b;
  return {b, y};
}

// 返り値 : a^{-1} mod p
// gcd(a, p) != 1 が必要
template <typename T>
T inv(T a, T p) {
  static_assert(is_broadly_signed_v<T>);
  a = safe_mod(a, p);
  T b = p, x = 1, y = 0;
  while (a != 0) {
    T q = b / a;
    swap(a, b %= a);
    swap(x, y -= q * x);
  }
  assert(b == 1);
  return y < 0 ? y + p : y;
}

// T : 底の型
// U : T*T がオーバーフローしない かつ 指数の型
template <typename T, typename U>
T modpow(T a, U n, T p) {
  a = safe_mod(a, p);
  T ret = 1 % p;
  while (n != 0) {
    if (n % 2 == 1) ret = U(ret) * a % p;
    a = U(a) * a % p;
    n /= 2;
  }
  return ret;
}

// 返り値 : pair(rem, mod)
// 解なしのときは {0, 0} を返す
template <typename T>
pair<T, T> crt(const vector<T>& r, const vector<T>& m) {
  static_assert(is_broadly_signed_v<T>);
  assert(r.size() == m.size());
  int n = int(r.size());
  T r0 = 0, m0 = 1;
  for (int i = 0; i < n; i++) {
    assert(1 <= m[i]);
    T r1 = safe_mod(r[i], m[i]), m1 = m[i];
    if (m0 < m1) swap(r0, r1), swap(m0, m1);
    if (m0 % m1 == 0) {
      if (r0 % m1 != r1) return {0, 0};
      continue;
    }
    auto [g, im] = inv_gcd(m0, m1);
    T u1 = m1 / g;
    if ((r1 - r0) % g) return {0, 0};
    T x = (r1 - r0) / g % u1 * im % u1;
    r0 += x * m0;
    m0 *= u1;
    if (r0 < 0) r0 += m0;
  }
  return {r0, m0};
}

}  // namespace internal
#line 5 "modulo/mod-log.hpp"

// a^x = b (mod p) である最小の非負整数 x を返す
int64_t mod_log(int64_t a, int64_t b, int64_t p) {
  if ((a %= p) < 0) a += p;
  if ((b %= p) < 0) b += p;
  int64_t f, g, r = 1 % p;
  for (f = 0; (g = gcd(a, p)) > 1; ++f) {
    if (b % g) return (r == b) ? f : -1;
    b /= g;
    p /= g;
    (r *= (a / g)) %= p;
  }
  if (p == 1) return f;
  int64_t ir = internal::inv(r, p);
  (b *= ir) %= p;
  int64_t k = 0, ak = 1;
  HashMap<int64_t, int64_t> baby;
  for (; k * k < p; ++k) {
    if(baby.find(ak) == baby.end()) baby[ak] = k;
    (ak *= a) %= p;
  }
  int64_t iak = internal::inv(ak, p);
  for (int64_t i = 0; i < k; ++i) {
    if (baby.find(b) != baby.end()) return f + i * k + baby[b];
    (b *= iak) %= p;
  }
  return -1;
}

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