結果
| 問題 | No.117 組み合わせの数 |
| ユーザー |
 kkishi
|
| 提出日時 | 2021-08-09 03:58:28 |
| 言語 | C++17(clang) (17.0.6 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 95 ms / 5,000 ms |
| コード長 | 11,123 bytes |
| コンパイル時間 | 4,653 ms |
| コンパイル使用メモリ | 164,728 KB |
| 実行使用メモリ | 18,824 KB |
| 最終ジャッジ日時 | 2024-09-20 00:23:12 |
| 合計ジャッジ時間 | 5,422 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
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ソースコード
#include <bits/stdc++.h>
namespace {
using i32 = int32_t;
using i64 = int64_t;
} // namespace
#define BIN_OPS(F) F(+) F(-) F(*) F(/)
#define CMP_OPS(F) F(!=) F(<) F(<=) F(==) F(>) F(>=)
template <i32 Mod = 1000000007>
class ModInt {
public:
ModInt() : n_(0) {}
ModInt(i64 n) : n_(n % Mod) {
if (n_ < 0) {
// In C++, (-n)%m == -(n%m).
n_ += Mod;
}
}
ModInt& operator+=(const ModInt& m) {
n_ += m.n_;
if (n_ >= Mod) {
n_ -= Mod;
}
return *this;
}
ModInt& operator++() { return (*this) += 1; }
ModInt& operator-=(const ModInt& m) {
n_ -= m.n_;
if (n_ < 0) {
n_ += Mod;
}
return *this;
}
ModInt& operator--() { return (*this) -= 1; }
ModInt& operator*=(const ModInt& m) {
n_ = i64(n_) * m.n_ % Mod;
return *this;
}
ModInt& operator/=(const ModInt& m) {
*this *= m.Inv();
return *this;
}
#define DEFINE(op) \
ModInt operator op(const ModInt& m) const { return ModInt(*this) op## = m; }
BIN_OPS(DEFINE)
#undef DEFINE
#define DEFINE(op) \
bool operator op(const ModInt& m) const { return n_ op m.n_; }
CMP_OPS(DEFINE)
#undef DEFINE
ModInt operator-() const { return ModInt(-n_); }
ModInt Pow(i64 n) const {
if (n < 0) {
return Inv().Pow(-n);
}
// a * b ^ n = answer.
ModInt a = 1, b = *this;
while (n != 0) {
if (n & 1) {
a *= b;
}
n /= 2;
b *= b;
}
return a;
}
ModInt Inv() const {
#if DEBUG
assert(n_ != 0);
#endif
if (n_ > kMaxCacheSize) {
// Compute the inverse based on Fermat's little theorem. Note that this
// only works when n_ and Mod are relatively prime. The theorem says that
// n_^(Mod-1) = 1 (mod Mod). So we can compute n_^(Mod-2).
return Pow(Mod - 2);
}
for (i64 i = inv_.size(); i <= n_; ++i) {
inv_.push_back(i <= 1 ? i : (Mod / i * -inv_[Mod % i]));
}
return inv_[n_];
}
i64 value() const { return n_; }
static ModInt Fact(i64 n) {
#if DEBUG
assert(0 <= n && n <= kMaxCacheSize);
#endif
for (i64 i = fact_.size(); i <= n; ++i) {
fact_.push_back(i == 0 ? 1 : fact_.back() * i);
}
return fact_[n];
}
static ModInt InvFact(i64 n) {
#if DEBUG
assert(0 <= n && n <= kMaxCacheSize);
#endif
for (i64 i = inv_fact_.size(); i <= n; ++i) {
inv_fact_.push_back(i == 0 ? 1 : inv_fact_.back() / i);
}
return inv_fact_[n];
}
static ModInt Comb(i64 n, i64 k) {
if (!Valid(n, k)) return 0;
return Perm(n, k) * InvFact(k);
}
static ModInt CombSlow(i64 n, i64 k) {
if (!Valid(n, k)) return 0;
return PermSlow(n, k) * InvFact(k);
}
static ModInt Perm(i64 n, i64 k) {
if (!Valid(n, k)) return 0;
#if DEBUG
assert(n <= kMaxCacheSize &&
"n is too large. If k is small, consider using PermSlow.");
#endif
return Fact(n) * InvFact(n - k);
}
static ModInt PermSlow(i64 n, i64 k) {
if (!Valid(n, k)) return 0;
ModInt p = 1;
for (i64 i = 0; i < k; ++i) {
p *= (n - i);
}
return p;
}
private:
static bool Valid(i64 n, i64 k) { return 0 <= n && 0 <= k && k <= n; }
i32 n_;
inline static std::vector<ModInt> fact_;
inline static std::vector<ModInt> inv_fact_;
inline static std::vector<ModInt> inv_;
static const i64 kMaxCacheSize = 10000000;
};
#define DEFINE(op) \
template <i32 Mod, typename T> \
ModInt<Mod> operator op(const T& t, const ModInt<Mod>& m) { \
return ModInt<Mod>(t) op m; \
}
BIN_OPS(DEFINE)
CMP_OPS(DEFINE)
#undef DEFINE
template <i32 Mod>
std::ostream& operator<<(std::ostream& out, const ModInt<Mod>& m) {
out << m.value();
return out;
}
#include <boost/hana/functional/fix.hpp>
template <typename T, typename = void>
struct is_dereferenceable : std::false_type {};
template <typename T>
struct is_dereferenceable<T, std::void_t<decltype(*std::declval<T>())>>
: std::true_type {};
template <typename T, typename = void>
struct is_iterable : std::false_type {};
template <typename T>
struct is_iterable<T, std::void_t<decltype(std::begin(std::declval<T>())),
decltype(std::end(std::declval<T>()))>>
: std::true_type {};
template <typename T, typename = void>
struct is_applicable : std::false_type {};
template <typename T>
struct is_applicable<T, std::void_t<decltype(std::tuple_size<T>::value)>>
: std::true_type {};
template <typename T, typename... Ts>
void debug(const T& value, const Ts&... args);
template <typename T>
void debug(const T& v) {
if constexpr (is_dereferenceable<T>::value) {
std::cerr << "{";
if (v) {
debug(*v);
} else {
std::cerr << "nil";
}
std::cerr << "}";
} else if constexpr (is_iterable<T>::value &&
!std::is_same<T, std::string>::value) {
std::cerr << "{";
for (auto it = std::begin(v); it != std::end(v); ++it) {
if (it != std::begin(v)) std::cerr << ", ";
debug(*it);
}
std::cerr << "}";
} else if constexpr (is_applicable<T>::value) {
std::cerr << "{";
std::apply([](const auto&... args) { debug(args...); }, v);
std::cerr << "}";
} else {
std::cerr << v;
}
}
template <typename T, typename... Ts>
void debug(const T& value, const Ts&... args) {
debug(value);
std::cerr << ", ";
debug(args...);
}
#if DEBUG
#define dbg(...) \
do { \
cerr << #__VA_ARGS__ << ": "; \
debug(__VA_ARGS__); \
cerr << " (L" << __LINE__ << ")\n"; \
} while (0)
#else
#define dbg(...)
#endif
void read_from_cin() {}
template <typename T, typename... Ts>
void read_from_cin(T& value, Ts&... args) {
std::cin >> value;
read_from_cin(args...);
}
#define rd(type, ...) \
type __VA_ARGS__; \
read_from_cin(__VA_ARGS__);
#define ints(...) rd(int, __VA_ARGS__);
#define strings(...) rd(string, __VA_ARGS__);
// Strings used for yes/no questions. Defined as variables so that it can be
// adjusted for each contest site.
const char *yes_str = "Yes", *no_str = "No";
template <typename T>
void write_to_cout(const T& value) {
if constexpr (std::is_same<T, bool>::value) {
std::cout << (value ? yes_str : no_str);
} else if constexpr (is_iterable<T>::value &&
!std::is_same<T, std::string>::value) {
for (auto it = std::begin(value); it != std::end(value); ++it) {
if (it != std::begin(value)) std::cout << " ";
std::cout << *it;
}
} else {
std::cout << value;
}
}
template <typename T, typename... Ts>
void write_to_cout(const T& value, const Ts&... args) {
write_to_cout(value);
std::cout << ' ';
write_to_cout(args...);
}
#define wt(...) \
do { \
write_to_cout(__VA_ARGS__); \
cout << '\n'; \
} while (0)
#define all(x) (x).begin(), (x).end()
#define eb(...) emplace_back(__VA_ARGS__)
#define pb(...) push_back(__VA_ARGS__)
#define dispatch(_1, _2, _3, name, ...) name
#define as_i64(x) \
( \
[] { \
static_assert( \
std::is_integral< \
typename std::remove_reference<decltype(x)>::type>::value, \
"rep macro supports std integral types only"); \
}, \
static_cast<int64_t>(x))
#define rep3(i, a, b) for (int64_t i = as_i64(a); i < as_i64(b); ++i)
#define rep2(i, n) rep3(i, 0, n)
#define rep1(n) rep2(_loop_variable_, n)
#define rep(...) dispatch(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep3(i, a, b) for (int64_t i = as_i64(b) - 1; i >= as_i64(a); --i)
#define rrep2(i, n) rrep3(i, 0, n)
#define rrep1(n) rrep2(_loop_variable_, n)
#define rrep(...) dispatch(__VA_ARGS__, rrep3, rrep2, rrep1)(__VA_ARGS__)
#define each3(k, v, c) for (auto&& [k, v] : c)
#define each2(e, c) for (auto&& e : c)
#define each(...) dispatch(__VA_ARGS__, each3, each2)(__VA_ARGS__)
template <typename T>
std::istream& operator>>(std::istream& is, std::vector<T>& v) {
for (T& vi : v) is >> vi;
return is;
}
template <typename T, typename U>
std::istream& operator>>(std::istream& is, std::pair<T, U>& p) {
is >> p.first >> p.second;
return is;
}
template <typename T, typename U>
bool chmax(T& a, U b) {
if (a < b) {
a = b;
return true;
}
return false;
}
template <typename T, typename U>
bool chmin(T& a, U b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <typename T, typename U>
auto max(T a, U b) {
return a > b ? a : b;
}
template <typename T, typename U>
auto min(T a, U b) {
return a < b ? a : b;
}
template <typename T>
int64_t sz(const T& v) {
return std::size(v);
}
template <typename T>
int64_t popcount(T i) {
return std::bitset<std::numeric_limits<T>::digits>(i).count();
}
template <typename T>
bool hasbit(T s, int i) {
return std::bitset<std::numeric_limits<T>::digits>(s)[i];
}
template <typename T, typename U>
auto div_floor(T n, U d) {
if (d < 0) {
n = -n;
d = -d;
}
if (n < 0) {
return -((-n + d - 1) / d);
}
return n / d;
};
template <typename T, typename U>
auto div_ceil(T n, U d) {
if (d < 0) {
n = -n;
d = -d;
}
if (n < 0) {
return -(-n / d);
}
return (n + d - 1) / d;
}
template <typename T>
bool even(T x) {
return x % 2 == 0;
}
std::array<std::pair<int64_t, int64_t>, 4> adjacent(int64_t i, int64_t j) {
return {{{i + 1, j}, {i, j + 1}, {i - 1, j}, {i, j - 1}}};
}
bool inside(int64_t i, int64_t j, int64_t I, int64_t J) {
return 0 <= i && i < I && 0 <= j && j < J;
}
constexpr int64_t int_pow(int64_t b, int64_t e) {
int64_t x = 1;
for (int64_t i = 0; i < e; ++i) {
x *= b;
}
return x;
}
// big = 2305843009213693951 = 2^61-1 ~= 2.3*10^18
const int64_t big = std::numeric_limits<int64_t>::max() / 4;
using i64 = int64_t;
using i32 = int32_t;
template <typename T>
using low_priority_queue =
std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <typename T>
using V = std::vector<T>;
template <typename T>
using VV = V<V<T>>;
void Main();
int main() {
std::ios_base::sync_with_stdio(false);
std::cin.tie(NULL);
std::cout << std::fixed << std::setprecision(20);
Main();
return 0;
}
const auto& Fix = boost::hana::fix;
using namespace std;
#define int i64
using mint = ModInt<>;
void Main() {
ints(t);
rep(t) {
char kind, _;
int n, k;
cin >> kind >> _ >> n >> _ >> k >> _;
if (kind == 'C') wt(mint::Comb(n, k));
if (kind == 'P') wt(mint::Perm(n, k));
if (kind == 'H') {
if (n == 0 && k == 0) {
// TODO: Add this case to pclib.
wt(1);
} else {
wt(mint::Comb(n + k - 1, k));
}
}
}
}