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#include "src/math/modular-arithmetic/small-mod-combination.hpp"
SmallModCombination< modint >()
mint combination(isize n, isize r) mint C(isize n, isize r)
$_n\mathrm{C}_r$ を計算する。
$r < 0$ または $n < r$ のときは $0$ が返る。
#pragma once #include "src/cpp-template/header/int-alias.hpp" #include "src/cpp-template/header/size-alias.hpp" #include "src/math/modular-arithmetic/modular-combinatorics.hpp" namespace luz { template < typename modint > class SmallModCombination { static constexpr u32 mod = modint::get_mod(); Combinatorics< modint > mc; public: SmallModCombination(): mc(mod - 1) {} modint combination(isize n, isize r) { if (r < 0 or n < r) return 0; modint result(1); while (n) { result *= mc.combination(n % mod, r % mod); n /= mod; r /= mod; } return result; } modint C(isize n, isize r) { return combination(n, r); } }; } // namespace luz
#line 2 "src/math/modular-arithmetic/small-mod-combination.hpp" #line 2 "src/cpp-template/header/int-alias.hpp" #include <cstdint> namespace luz { using i32 = std::int32_t; using i64 = std::int64_t; using i128 = __int128_t; using u32 = std::uint32_t; using u64 = std::uint64_t; using u128 = __uint128_t; } // namespace luz #line 2 "src/cpp-template/header/size-alias.hpp" #include <cstddef> namespace luz { using isize = std::ptrdiff_t; using usize = std::size_t; } // namespace luz #line 2 "src/math/modular-arithmetic/modular-combinatorics.hpp" #line 2 "src/cpp-template/header/rep.hpp" #line 4 "src/cpp-template/header/rep.hpp" #include <algorithm> namespace luz { struct rep { struct itr { usize i; constexpr itr(const usize i) noexcept: i(i) {} void operator++() noexcept { ++i; } constexpr usize operator*() const noexcept { return i; } constexpr bool operator!=(const itr x) const noexcept { return i != x.i; } }; const itr f, l; constexpr rep(const usize f, const usize l) noexcept : f(std::min(f, l)), l(l) {} constexpr auto begin() const noexcept { return f; } constexpr auto end() const noexcept { return l; } }; struct rrep { struct itr { usize i; constexpr itr(const usize i) noexcept: i(i) {} void operator++() noexcept { --i; } constexpr usize operator*() const noexcept { return i; } constexpr bool operator!=(const itr x) const noexcept { return i != x.i; } }; const itr f, l; constexpr rrep(const usize f, const usize l) noexcept : f(l - 1), l(std::min(f, l) - 1) {} constexpr auto begin() const noexcept { return f; } constexpr auto end() const noexcept { return l; } }; } // namespace luz #line 5 "src/math/modular-arithmetic/modular-combinatorics.hpp" #include <vector> namespace luz { template < typename mint > class Combinatorics { static usize bound; static std::vector< mint > fact, finv, inv; static void expand(usize n) { n += 1; if (fact.size() >= n) return; if (bound == 0) bound = 1; fact.resize(n, mint(1)); finv.resize(n, mint(1)); inv.resize(n, mint(1)); for (usize i: rep(bound, n)) { fact[i] = fact[i - 1] * i; } finv.back() = mint(1) / fact.back(); for (usize i: rrep(bound, n)) { finv[i - 1] = finv[i] * i; } for (usize i: rep(bound, n)) { inv[i] = finv[i] * fact[i - 1]; } bound = n; } public: explicit Combinatorics(usize n = 0) { expand(n); } static mint factorial(usize n) { expand(n); return fact[n]; } static mint factorial_inverse(usize n) { expand(n); return finv[n]; } static mint inverse(usize n) { expand(n); return inv[n]; } static mint permutation(isize n, isize r) { if (r < 0 or n < r) return 0; expand(n); return fact[n] * finv[n - r]; } static mint combination(isize n, isize r) { if (r < 0 or n < r) return 0; expand(n); return fact[n] * finv[r] * finv[n - r]; } static mint combination_with_repetitions(isize n, isize r) { if (n < 0 or r < 0) return 0; return (r ? combination(n + r - 1, r) : 1); } static mint P(isize n, isize r) { return permutation(n, r); } static mint C(isize n, isize r) { return combination(n, r); } static mint H(isize n, isize r) { return combination_with_repetitions(n, r); } }; template < typename mint > usize Combinatorics< mint >::bound = 0; template < typename mint > std::vector< mint > Combinatorics< mint >::fact = std::vector< mint >(); template < typename mint > std::vector< mint > Combinatorics< mint >::finv = std::vector< mint >(); template < typename mint > std::vector< mint > Combinatorics< mint >::inv = std::vector< mint >(); } // namespace luz #line 6 "src/math/modular-arithmetic/small-mod-combination.hpp" namespace luz { template < typename modint > class SmallModCombination { static constexpr u32 mod = modint::get_mod(); Combinatorics< modint > mc; public: SmallModCombination(): mc(mod - 1) {} modint combination(isize n, isize r) { if (r < 0 or n < r) return 0; modint result(1); while (n) { result *= mc.combination(n % mod, r % mod); n /= mod; r /= mod; } return result; } modint C(isize n, isize r) { return combination(n, r); } }; } // namespace luz