refactor: upload

config.yml

@@ -740,6 +740,9 @@ notebook:
     - ball_box_iil: 球与盒(球相同,盒相同,至少装一个球)
       code_ext: hpp
       test_ext: cpp
+    - factl_helper: 大数阶乘与阶乘逆辅助类
+      code_ext: hpp
+      test_ext: cpp
     nt:
     - euler_phi_u32: Euler 函数(32 位)
       code_ext: hpp

src/code/comb/binom.hpp

@@ -6,25 +6,25 @@
 
 namespace tifa_libs::math {
 
-template <class mint, template <class> class fact = fact_helper>
-struct binom : fact<mint> {
-  static CEXP auto mod() NE { return fact<mint>::mod(); }
-  CEXPE binom(u32 max_m = fact<mint>::DEFUALT_MAX) NE { this->reset(max_m + 1); }
+template <class mint, class fact = fact_helper<mint>>
+requires std::same_as<mint, TPN fact::val_t>
+struct binom {
+  CEXPE binom(u32 max_m = fact::DEFUALT_MAX) NE { fact::ensure(max_m + 1); }
 
   // $\binom{m}{n}$
-  CEXP mint mCn(uint_c auto m, uint_c auto n) CNE { return m < n ? 0 : mPn(m, n) * this->get_ifact(n); }
+  CEXP mint mCn(uint_c auto m, uint_c auto n) CNE { return m < n ? 0 : mPn(m, n) * fact::get_ifact(n); }
   // $\binom{m}{n}$
   template <sint_c T>
   CEXP mint mCn(T m, T n) CNE { return m < n || n < 0 ? 0 : mCn(to_uint_t<T>(m), to_uint_t<T>(n)); }
   //! mint::mod() must be prime
   template <int_c T>
   CEXP mint lucas(T m, T n) CNE {
     assert(mint::mod() > 1);
-    auto f = [this](auto &&f, auto m, auto n) NE -> mint { return n == 0 ? 1 : this->mCn(m % mod(), n % mod()) * f(f, m / mod(), n / mod()); };
+    auto f = [this](auto &&f, auto m, auto n) NE -> mint { return n == 0 ? 1 : this->mCn(m % fact::mod(), n % fact::mod()) * f(f, m / fact::mod(), n / fact::mod()); };
     return m < n || n < 0 ? 0 : f(f, to_uint_t<T>(m), to_uint_t<T>(n));
   }
   // $\binom{m}{n} \cdot n!$
-  CEXP mint mPn(uint_c auto m, uint_c auto n) CNE { return m < n ? 0 : this->get_fact(m) * this->get_ifact(m - n); }
+  CEXP mint mPn(uint_c auto m, uint_c auto n) CNE { return m < n ? 0 : fact::get_fact(m) * fact::get_ifact(m - n); }
   // $\binom{m}{n} \cdot n!$
   template <sint_c T>
   CEXP mint mPn(T m, T n) CNE { return m < n || n < 0 ? 0 : mPn(to_uint_t<T>(m), to_uint_t<T>(n)); }

src/code/comb/fact_helper.hpp

@@ -1,37 +1,46 @@
 #ifndef TIFALIBS_COMB_FACT_HELPER
 #define TIFALIBS_COMB_FACT_HELPER
 
-#include "gen_fact.hpp"
-#include "gen_ifact.hpp"
+#include "../util/traits.hpp"
 
 namespace tifa_libs::math {
 
-template <class mint>
+template <mint_c mint>
 struct fact_helper {
+  using val_t = mint;
   static CEXP u32 DEFUALT_MAX = 10'000'001;
-  static CEXP u64 mod() NE { return mint::mod(); }
-  static inline vec<mint> fact, ifact;
-
-  CEXP void reset(u32 n = DEFUALT_MAX) NE {
-    if (n = std::min((u32)mod(), n); n < fact.size()) {
-      fact.resize(n), ifact.resize(n);
-      return;
-    }
-    fact = gen_fact<mint>(n), ifact = gen_ifact<mint>(n);
+  static CEXP u64 mod() NE { return val_t::mod(); }
+  static inline vec<val_t> fact, ifact;
+
+  fact_helper() = delete;
+
+  // ensure fact.size() >= sz
+  static CEXP void ensure(u32 sz = DEFUALT_MAX) NE {
+    if (sz = std::max(2_u32, std::min((u32)mod(), sz)); sz <= fact.size()) return;
+    u32 pre = (u32)fact.size();
+    fact.resize(sz), ifact.resize(sz);
+    if (pre < 2) pre = 2, fact[0] = fact[1] = ifact[0] = ifact[1] = 1;
+    flt_ (u32, i, pre, sz) fact[i] = fact[i - 1] * i;
+    ifact.back() = fact.back().inv();
+    for (u32 i = sz - 1; i > pre; --i) ifact[i - 1] = ifact[i] * i;
   }
 
-  CEXP mint get_fact(u64 n) CNE {
+  static CEXP val_t get_fact(u64 n) NE {
     if (n >= mod()) [[unlikely]]
       return 0;
+    if (fact.empty()) [[unlikely]]
+      ensure();
     if (n < fact.size()) [[likely]]
       return fact[n];
-    mint _ = fact.back() * n;
+    val_t _ = fact.back() * n;
     flt_ (u64, i, fact.size(), n) _ *= i;
     return _;
   }
-  CEXP mint get_ifact(u64 n) CNE {
+  static CEXP val_t get_ifact(u64 n) NE {
     if (n >= mod()) [[unlikely]]
       return 0;
+    if (fact.empty()) [[unlikely]]
+      ensure();
     if (n < ifact.size()) [[likely]]
       return ifact[n];
     return get_fact(n).inv();

src/code/comb/factl_helper.hpp

@@ -0,0 +1,82 @@
+#ifndef TIFALIBS_COMB_FACTL_HELPER
+#define TIFALIBS_COMB_FACTL_HELPER
+
+#include "../poly/ctsh_fps.hpp"
+#include "fact_helper.hpp"
+
+namespace tifa_libs::math {
+
+template <class poly_t>
+struct factl_helper {
+  using val_t = TPN poly_t::val_t;
+  using base_t = fact_helper<TPN poly_t::val_t>;
+  static CEXP u32 threshold = 2'000'001;
+
+  factl_helper() = delete;
+
+  static CEXP val_t get_fact(u64 n) NE {
+    if (n >= base_t::mod()) [[unlikely]]
+      return 0;
+    if (base_t::fact.empty()) [[unlikely]]
+      base_t::ensure(threshold);
+    if (n < threshold) return base_t::fact[n];
+    return fact_(n);
+  }
+  static CEXP val_t get_ifact(u64 n) NE {
+    if (n >= base_t::mod()) [[unlikely]]
+      return 0;
+    if (base_t::fact.empty()) [[unlikely]]
+      base_t::ensure(threshold);
+    if (n < threshold) return base_t::ifact[n];
+    return fact_(n).inv();
+  }
+
+ private:
+  static CEXP u32 LBSZ = 9;
+  static CEXP u32 SZ = 1 << LBSZ;
+  static inline u64 B = base_t::mod() >> LBSZ;
+  // f[i] = (i*B + 1) * ... * (i*B + B)
+  static inline poly_t f{1};
+  static val_t fact_(u64 n) NE {
+    static bool inited = false;
+    if (!inited) {
+      inited = true;
+      f.reserve(SZ);
+      flt_ (u32, i, 0, LBSZ) {
+        poly_t g = ctsh_fps(f, val_t(1 << i), base_t::ifact, 3_u32 << i);
+        const auto get = [&](u32 j) { return j < (1_u32 << i) ? f[j] : g[j - (1 << i)]; };
+        f.resize(2_u32 << i);
+        flt_ (u32, j, 0, 2_u32 << i) f[j] = get(2 * j) * get(2 * j + 1) * ((2 * j + 1) << i);
+      }
+      if (B > SZ) {
+        vec<val_t> g = ctsh_fps(f, val_t(SZ), base_t::ifact, u32(B - SZ));
+        std::ranges::move(g, std::back_inserter(f));
+      } else f.resize(B);
+      flt_ (u32, i, 0, (u32)B) f[i] *= val_t(i + 1) * SZ;
+      f.insert(f.begin(), 1);
+      flt_ (u32, i, 0, (u32)B) f[i + 1] *= f[i];
+    }
+    val_t res;
+    u64 q = n / SZ;
+    u32 r = n % SZ;
+    if (2 * r <= SZ) {
+      res = f[q];
+      flt_ (u32, i, 0, r) res *= n - i;
+    } else if (q != B) {
+      res = f[q + 1];
+      val_t den = 1;
+      flt_ (u32, i, 1, SZ - r + 1) den *= n + i;
+      res /= den;
+    } else {
+      res = base_t::mod() - 1;
+      val_t den = 1;
+      for (u64 i = base_t::mod() - 1; i > n; --i) den *= i;
+      res /= den;
+    }
+    return res;
+  }
+};
+
+}  // namespace tifa_libs::math
+
+#endif

src/code/comb/gen_ball_box_ii.hpp

@@ -7,8 +7,8 @@
 namespace tifa_libs::math {
 
 // f = \\prod_{i=1}^m 1/(1-x^i), deg(f) = n
-template <class poly>
-CEXP poly gen_ball_box_ii(u32 m, u32 n, spnuu inv) NE {
+template <class poly, class T>
+CEXP poly gen_ball_box_ii(u32 m, u32 n, vec<T> CR inv) NE {
   poly f(n + 1);
   flt_ (u32, i, 1, m + 1)
     flt_ (u32, k, 1, n / i + 1) f[i * k] += inv[k];

src/code/comb/gen_bernoulli.hpp

@@ -8,8 +8,8 @@
 namespace tifa_libs::math {
 
 // bernoulli[i] = B_i, i=0,1,...,n
-template <class poly, std::same_as<TPN poly::val_t> mint>
-CEXP poly gen_bernoulli(u32 n, vec<mint> CR fact, vec<mint> CR ifact) NE {
+template <class poly, class T, std::same_as<TPN poly::val_t> mint>
+CEXP poly gen_bernoulli(u32 n, vec<T> CR fact, vec<T> CR ifact) NE {
   if (!n) return poly{1};
   poly b(n + 1);
   flt_ (u32, i, 0, n + 1) b[i] = ifact[i + 1];

src/code/comb/gen_stirling1_col.hpp

@@ -9,8 +9,8 @@
 namespace tifa_libs::math {
 
 // stirling1[i] = {i \\brack k}, i=0,1,...,n
-template <class poly, bool with_sgn = true>
-CEXP poly gen_stirling1_col(u32 n, u32 k, spnuu fact, spnuu inv, spnuu invfact) NE {
+template <class poly, class T, bool with_sgn = true>
+CEXP poly gen_stirling1_col(u32 n, u32 k, vec<T> CR fact, vec<T> CR inv, vec<T> CR invfact) NE {
   if (n < k) return poly(n + 1);
   poly f(n + 1);
   flt_ (u32, i, 1, n + 1) f[i] = inv[i];

src/code/comb/gen_stirling1_row.hpp

@@ -9,8 +9,8 @@
 namespace tifa_libs::math {
 
 // stirling1[i] = {n \\brace i}, i=0,1,...,n
-template <class poly, bool with_sgn = true>
-CEXP poly gen_stirling1_row(u32 n, spnuu fact, spnuu ifact) NE {
+template <class poly, class T, bool with_sgn = true>
+CEXP poly gen_stirling1_row(u32 n, vec<T> CR fact, vec<T> CR ifact) NE {
   using mint = TPN poly::val_t;
   if (!n) return poly{1};
   poly f{0, 1};

src/code/comb/gen_stirling2_col.hpp

@@ -8,8 +8,8 @@
 namespace tifa_libs::math {
 
 // stirling2[i] = {i \\brack k}, i=0,1,...,n
-template <class poly>
-CEXP poly gen_stirling2_col(u32 n, u32 k, spnuu fact, spnuu ifact) NE {
+template <class poly, class T>
+CEXP poly gen_stirling2_col(u32 n, u32 k, vec<T> CR fact, vec<T> CR ifact) NE {
   using mint = TPN poly::val_t;
   if (k > n) return poly(n + 1);
   auto g = [&](auto&& g, poly& f, u32 n) NE -> void {

src/code/comb/qbinom.hpp

@@ -6,20 +6,18 @@
 
 namespace tifa_libs::math {
 
-template <class mint, template <class> class fact = fact_helper>
+template <class mint, class fact = fact_helper<mint>>
 struct qbinom : binom<mint, fact> {
   vec<mint> qfact, iqfact;
 
-  static CEXP u64 mod() NE { return mint::mod(); }
-  CEXPE qbinom(u32 q, u32 max_m = fact<mint>::DEFUALT_MAX) NE : binom<mint, fact>(max_m), qfact(2) {
+  CEXPE qbinom(u32 q, u32 max_m = fact::DEFUALT_MAX) NE : binom<mint, fact>(max_m), qfact(2) {
     assert(q), qfact[0] = qfact[1] = 1;
     mint x = 1;
     flt_ (u32, i, 2, max_m + 1)
       if ((x = x * q + 1).val()) qfact.push_back(x);
       else break;
     flt_ (u32, i, 3, (u32)qfact.size()) qfact[i] *= qfact[i - 1];
     iqfact = gen_invseq(qfact);
-    this->reset(max_m / ((u32)qfact.size() - 1) + 2);
   }
 
   // $\binom{m}{n}_q$

src/code/poly/comp_fpssps.hpp

@@ -9,8 +9,8 @@
 namespace tifa_libs::math {
 
 // @return $f(g(x_0, \dots, x_{n-1}))$
-template <class poly, u32 N = 21>
-auto comp_fpssps(u32 n, poly f, vec<TPN poly::val_t> g, spnuu fact, spnuu ifact) NE {
+template <class poly, class T, u32 N = 21>
+auto comp_fpssps(u32 n, poly f, vec<TPN poly::val_t> g, vec<T> CR fact, vec<T> CR ifact) NE {
   using mint = TPN poly::val_t;
   static conv_subset<mint, N> ss;
   if (assert(n <= N); !f.size()) return vec<mint>(1 << n);

src/code/poly/compinv_fps.hpp

@@ -10,8 +10,8 @@
 namespace tifa_libs::math {
 
 // @return g s.t. $g(f(x)) \equiv x \pmod{\deg(f)+1}$
-template <template <class... Ts> class ccore, class mint, class... args>
-CEXP auto compinv_fps(poly<ccore, mint, args...> CR f, spnuu inv, u32 n = 0) NE {
+template <template <class... Ts> class ccore, class mint, class T, class... args>
+CEXP auto compinv_fps(poly<ccore, mint, args...> CR f, vec<T> CR inv, u32 n = 0) NE {
   using poly_t = poly<ccore, mint, args...>;
   if (assert(f.size() > 1 && f[0] == 0 && f[1] != 0); !n) n = (u32)f.size();
   if (n < 2) return poly_t{0, f[1].inv()}.pre(n);

src/code/poly/ctsh_fps.hpp

@@ -6,8 +6,8 @@
 
 namespace tifa_libs::math {
 
-template <template <class... Ts> class ccore, class mint, class... args>
-CEXP poly<ccore, mint, args...> ctsh_fps(poly<ccore, mint, args...> CR f, mint c, spnuu ifact, u32 m = 0) NE {
+template <template <class... Ts> class ccore, class mint, class T, class... args>
+CEXP poly<ccore, mint, args...> ctsh_fps(poly<ccore, mint, args...> CR f, mint c, vec<T> CR ifact, u32 m = 0) NE {
   using poly_t = poly<ccore, mint, args...>;
   const u32 n = (u32)f.size(), k = n - 1;
   if (!m) m = n;

src/code/poly/exp_fpssp.hpp

@@ -6,8 +6,8 @@
 
 namespace tifa_libs::math {
 
-template <template <class... Ts> class ccore, class mint, class... args>
-CEXP auto exp_fpssp(poly<ccore, mint, args...> CR p, spnuu inv, u32 n = 0) NE {
+template <template <class... Ts> class ccore, class mint, class T, class... args>
+CEXP auto exp_fpssp(poly<ccore, mint, args...> CR p, vec<T> CR inv, u32 n = 0) NE {
   if (!p.size()) return p;
   if (assert(p[0] == 0); !n) n = (u32)p.size();
   polysp<mint> ps = poly2sp(p, n);

src/code/poly/ln_fpssp.hpp

@@ -6,8 +6,8 @@
 
 namespace tifa_libs::math {
 
-template <template <class... Ts> class ccore, class mint, class... args>
-CEXP auto ln_fpssp(poly<ccore, mint, args...> CR p, spnuu inv, u32 n = 0) NE {
+template <template <class... Ts> class ccore, class mint, class T, class... args>
+CEXP auto ln_fpssp(poly<ccore, mint, args...> CR p, vec<T> CR inv, u32 n = 0) NE {
   if (assert(!p.empty() && p[0] == 1); !n) n = (u32)p.size();
   auto ps = poly2sp(p, n);
   poly<ccore, mint, args...> g(n);

src/code/poly/pow_fpssp.hpp

@@ -9,8 +9,8 @@
 
 namespace tifa_libs::math {
 
-template <template <class... Ts> class ccore, class mint, class... args>
-CEXP auto pow_fpssp(poly<ccore, mint, args...> CR p, u64 y, spnuu inv, u32 n = 0) NE {
+template <template <class... Ts> class ccore, class mint, class T, class... args>
+CEXP auto pow_fpssp(poly<ccore, mint, args...> CR p, u64 y, vec<T> CR inv, u32 n = 0) NE {
   if (!n) n = (u32)p.size();
   if (!y) return poly<ccore, mint, args...>{1}.pre(n);
   if (p.is_zero()) return p.pre(n);

src/code/poly/tsh_fps.hpp

@@ -7,8 +7,8 @@
 
 namespace tifa_libs::math {
 
-template <template <class... Ts> class ccore, class mint, class... args>
-CEXP auto tsh_fps(poly<ccore, mint, args...> CR f, mint c, spnuu fact, spnuu ifact) NE {
+template <template <class... Ts> class ccore, class mint, class T, class... args>
+CEXP auto tsh_fps(poly<ccore, mint, args...> CR f, mint c, vec<T> CR fact, vec<T> CR ifact) NE {
   const u32 n = (u32)f.size();
   if (n == 1) return f;
   poly<ccore, mint, args...> s = f, p((u32)f.size());

src/doc_md/comb/factl_helper.md

@@ -0,0 +1,4 @@
+---
+title: factl_helper
+documentation_of: //src/code/comb/factl_helper.hpp
+---

src/meta_test/library-checker-enumerative_combinatorics/factorial.factl-helper.cppmeta

@@ -0,0 +1,29 @@
+#define AUTO_GENERATED
+#define PROBLEM "https://judge.yosupo.jp/problem/factorial"
+
+#include "../../code/comb/factl_helper.hpp"
+
+CEXP u32 MOD = 998244353;
+
+#define GENTCs_p3ntts30s
+#define GENTCs_p3ntts63s
+#define GENTCs_p3ntts30d_0
+#define GENTCs_p3ntts63d_0
+#define GENTCs_pmtts
+#define GENTCs_pmttd0
+#define GENTCs_pntt
+
+int main() {
+#define GENTCs_p3ntts30d_1
+#define GENTCs_p3ntts63d_1
+#define GENTCs_pmttd1
+  std::cin.tie(nullptr)->std::ios::sync_with_stdio(false);
+  u32 t;
+  std::cin >> t;
+  while (t--) {
+    u32 n;
+    std::cin >> n;
+    std::cout << tifa_libs::math::factl_helper<poly>::get_fact(n) << '\n';
+  }
+  return 0;
+}