refactor: fact_helper

config.yml

@@ -644,6 +644,15 @@ notebook:
       code_ext: hpp
       test_ext: cpp
     comb:
+    - gen_fact: 阶乘模序列
+      code_ext: hpp
+      test_ext: cpp
+    - gen_ifact: 阶乘逆模序列
+      code_ext: hpp
+      test_ext: cpp
+    - fact_helper: 阶乘与阶乘逆辅助类
+      code_ext: hpp
+      test_ext: cpp
     - binom: 二项式系数
       code_ext: hpp
       test_ext: cpp
@@ -674,12 +683,6 @@ notebook:
     - gen_partition: 划分数序列
       code_ext: hpp
       test_ext: cpp
-    - gen_fact: 阶乘模序列
-      code_ext: hpp
-      test_ext: cpp
-    - gen_ifact: 阶乘逆模序列
-      code_ext: hpp
-      test_ext: cpp
     - gen_inv: 逆元序列
       code_ext: hpp
       test_ext: cpp

src/code/comb/binom.hpp

@@ -2,20 +2,17 @@
 #define TIFALIBS_COMB_BINOM
 
 #include "../util/traits.hpp"
-#include "gen_fact.hpp"
-#include "gen_ifact.hpp"
+#include "fact_helper.hpp"
 
 namespace tifa_libs::math {
 
-template <class mint>
-struct binom {
-  vec<mint> fact, ifact;
-
-  static CEXP u64 mod() NE { return mint::mod(); }
-  CEXPE binom(u32 max_m = 0) NE : fact(gen_fact<mint>(std::min((u32)mod(), max_m + 1))), ifact(gen_ifact<mint>(std::min((u32)mod(), max_m + 1))) {}
+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 : fact<mint>(std::min((u32)mod(), 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) * ifact[(usz)n]; }
+  CEXP mint mCn(uint_c auto m, uint_c auto n) CNE { return m < n ? 0 : mPn(m, n) * this->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)); }
@@ -27,7 +24,7 @@ struct binom {
     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 : fact[(usz)m] * ifact[(usz)(m - 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); }
   // $\binom{m}{n} \cdot n!$
   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

@@ -0,0 +1,42 @@
+#ifndef TIFALIBS_COMB_FACT_HELPER
+#define TIFALIBS_COMB_FACT_HELPER
+
+#include "gen_fact.hpp"
+#include "gen_ifact.hpp"
+
+namespace tifa_libs::math {
+
+template <class mint>
+struct fact_helper {
+  static CEXP u32 DEFUALT_MAX = 10'000'001;
+  static CEXP u64 mod() NE { return mint::mod(); }
+  static inline vec<mint> fact = gen_fact<mint>(DEFUALT_MAX),
+                          ifact = gen_ifact<mint>(DEFUALT_MAX);
+  CEXPE fact_helper(u32 n = 0) NE {
+    if (u32 _ = std::min((u32)mod(), n); _ > fact.size()) [[unlikely]] {
+      fact = gen_fact<mint>(_);
+      ifact = gen_ifact<mint>(_);
+    }
+  }
+
+  CEXP mint get_fact(u64 n) CNE {
+    if (n >= mod()) [[unlikely]]
+      return 0;
+    if (n < fact.size()) [[likely]]
+      return fact[n];
+    mint _ = fact.back() * n;
+    flt_ (u64, i, fact.size(), n) _ *= i;
+    return _;
+  }
+  CEXP mint get_ifact(u64 n) CNE {
+    if (n >= mod()) [[unlikely]]
+      return 0;
+    if (n < ifact.size()) [[likely]]
+      return ifact[n];
+    return get_fact(n).inv();
+  }
+};
+
+}  // namespace tifa_libs::math
+
+#endif

src/code/comb/qbinom.hpp

@@ -6,28 +6,26 @@
 
 namespace tifa_libs::math {
 
-template <class mint>
-struct qbinom {
+template <class mint, template <class> class fact = fact_helper>
+struct qbinom : binom<mint, fact> {
   vec<mint> qfact, iqfact;
-  binom<mint> b;
 
   static CEXP u64 mod() NE { return mint::mod(); }
-  CEXPE qbinom(u32 max_m, u32 q) NE : qfact(2) {
+  CEXPE qbinom(u32 q, u32 max_m = fact<mint>::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);
-    b = binom<mint>(u32((max_m + qfact.size() - 2) / (qfact.size() - 1)));
   }
 
   // $\binom{m}{n}_q$
   CEXP mint qmCn(uint_c auto m, uint_c auto n) CNE {
     if (m < n) return 0;
     if (m < qfact.size()) return qfact[(usz)m] * iqfact[(usz)n] * iqfact[(usz)(m - n)];
-    return b.mCn(m / qfact.size(), n / qfact.size()) * qmCn(m % qfact.size(), n % qfact.size());
+    return this->mCn(m / qfact.size(), n / qfact.size()) * qmCn(m % qfact.size(), n % qfact.size());
   }
   // $\binom{m}{n}_q$
   template <sint_c T>

src/doc_md/comb/fact_helper.md

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

src/test_cpverifier/library-checker-enumerative_combinatorics/q_binomial_coefficient_prime_mod.test.cpp

@@ -19,7 +19,7 @@ int main() {
     }
     return 0;
   }
-  tifa_libs::math::qbinom<mint> mCn(std::min(MOD - 1, 10'000'000_u32), q);
+  tifa_libs::math::qbinom<mint> mCn(q);
   while (t--) {
     i64 n, k;
     tifa_libs::fin >> n >> k;