結果

問題 No.117 組み合わせの数
ユーザー KoD
提出日時 2021-03-25 20:44:48
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 389 ms / 5,000 ms
コード長 7,105 bytes
コンパイル時間 1,131 ms
コンパイル使用メモリ 79,724 KB
最終ジャッジ日時 2025-01-19 21:43:40
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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ファイルパターン 結果
other AC * 1
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ソースコード

diff # 

#line 1 "test/modint_util.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/117"
#line 2 "utility/int_alias.cpp"
#include <cstdint>
#include <cstddef>

using i32 = std::int32_t;
using u32 = std::uint32_t;
using i64 = std::int64_t;
using u64 = std::uint64_t;
using i128 = __int128_t;
using u128 = __uint128_t;
using isize = std::ptrdiff_t;
using usize = std::size_t;
#line 2 "math/rem_euclid.cpp"

template <class T>
constexpr T rem_euclid(T value, const T& mod) {
    return (value %= mod) >= 0 ? value : mod;
}
#line 4 "math/static_modint.cpp"
#include <type_traits>
#include <ostream>

namespace static_modint_internal {

constexpr u32 totient(u32 x) noexcept {
    u32 ret = x;
    for (u32 i = 2; i * i <= x; ++i) {
        if (x % i == 0) {
            ret /= i; ret *= i - 1;
            while (x % i == 0) x /= i;
        }
    }
    if (x > 1) { ret /= x; ret *= x - 1; }
    return ret;
}

}

template <u32 MOD, std::enable_if_t<((u32) 1 <= MOD and MOD <= ((u32) 1 << 31))>* = nullptr>
class StaticModint {
    using Mint = StaticModint;
    static inline constexpr u32 PHI = static_modint_internal::totient(MOD);
    u32 v;
public:
    static constexpr u32 mod() noexcept { return MOD; }

    template <class T, std::enable_if_t<std::is_signed_v<T> and std::is_integral_v<T>>* = nullptr>
    static constexpr T normalize(const T x) noexcept { return rem_euclid<i64>(x, MOD); }
    template <class T, std::enable_if_t<std::is_unsigned_v<T> and std::is_integral_v<T>>* = nullptr>
    static constexpr T normalize(const T x) noexcept { return x % MOD; }

    constexpr StaticModint() noexcept: v(0) { }
    template <class T>
    explicit constexpr StaticModint(const T x) noexcept: v(normalize(x)) { }
    template <class T>
    static constexpr Mint raw(const T x) noexcept {
        Mint ret;
        ret.v = x;
        return ret;
    }

    constexpr u32 get() const noexcept { return v; }
    constexpr Mint neg() const noexcept { return raw(v == 0 ? 0 : MOD - v); }
    constexpr Mint operator - () const noexcept { return neg(); }
    constexpr Mint inv() const noexcept { return pow(PHI - 1); }
    constexpr Mint operator ~ () const noexcept { return inv(); }
    constexpr Mint pow(u64 exp) const noexcept {
        Mint ret(1), mult(*this);
        for (; exp > 0; exp >>= 1) {
            if (exp & 1) ret *= mult;
            mult *= mult;
        }
        return ret;
    }

    constexpr Mint operator + (const Mint& rhs) const noexcept { return Mint(*this) += rhs; }
    constexpr Mint& operator += (const Mint& rhs) noexcept {
        if ((v += rhs.v) >= MOD) v -= MOD;
        return *this;
    }
    constexpr Mint operator - (const Mint& rhs) const noexcept { return Mint(*this) -= rhs; }
    constexpr Mint& operator -= (const Mint& rhs) noexcept {
        if (v < rhs.v) v += MOD;
        v -= rhs.v;
        return *this;
    }
    constexpr Mint operator * (const Mint& rhs) const noexcept { return Mint(*this) *= rhs; }
    constexpr Mint& operator *= (const Mint& rhs) noexcept {
        v = (u64) v * rhs.v % MOD;
        return *this;
    }
    constexpr Mint operator / (const Mint& rhs) const noexcept { return Mint(*this) /= rhs; }
    constexpr Mint& operator /= (const Mint& rhs) noexcept { 
        return *this *= rhs.inv();
    }
    constexpr bool operator == (const Mint& rhs) const noexcept { return v == rhs.v; }
    constexpr bool operator != (const Mint& rhs) const noexcept { return v != rhs.v; }
    friend std::ostream& operator << (std::ostream& stream, const Mint& rhs) { 
        return stream << rhs.v;
    }
};
#line 3 "utility/rep.cpp"
#include <algorithm>

class rep {
    struct Iter {
        usize itr;
        constexpr Iter(const usize pos) noexcept: itr(pos) { }
        constexpr void operator ++ () noexcept { ++itr; }
        constexpr bool operator != (const Iter& other) const noexcept { return itr != other.itr; }
        constexpr usize operator * () const noexcept { return itr; }
    };
    const Iter first, last;
public:
    explicit constexpr rep(const usize first, const usize last) noexcept: first(first), last(std::max(first, last)) { }
    constexpr Iter begin() const noexcept { return first; }
    constexpr Iter end() const noexcept { return last; }
};
#line 3 "bit/ceil_log2.cpp"

constexpr u64 ceil_log2(const u64 x) {
    u64 e = 0;
    while (((u64) 1 << e) < x) ++e;
    return e;
}
#line 4 "utility/auto_realloc.cpp"
#include <utility>
#include <vector>

template <class F>
class AutoRealloc {
    using R = typename decltype(std::declval<F>().operator()(std::declval<usize>()))::value_type;
    F func;
    std::vector<R> data;
public:
    explicit AutoRealloc(F&& func): func(std::forward<F>(func)), data() { }
    explicit AutoRealloc(F&& func, const usize capacity): func(std::forward<F>(func)) { reserve(capacity); }
    void reserve(const usize size) {
        if (data.size() < size) {
            const usize pow2 = ((usize) 1 << ceil_log2(size));
            data = func(pow2);
        }
    }
    R operator [] (const usize i) {
        reserve(i + 1);
        return data[i];
    }
};
#line 6 "math/modint_util.cpp"
#include <cassert>

template <class M>
struct ModintUtil {
    static inline auto fact = AutoRealloc([](const usize n) {
        std::vector<M> ret(n);
        ret[0] = M(1);
        for (const usize i: rep(1, n)) {
            ret[i] = ret[i - 1] * M(i);
        }
        return ret;
    });
    static inline auto inv = AutoRealloc([](const usize n) {
        std::vector<M> ret(n);
        if (n == 1) return ret;
        ret[1] = M(1);
        for (const usize i: rep(2, n)) {
            ret[i] = -M(M::mod() / i) * ret[M::mod() % i];
        }
        return ret;
    });
    static inline auto inv_fact = AutoRealloc([](const usize n) {
        std::vector<M> ret(n);
        ret[0] = M(1);
        for (const usize i: rep(1, n)) {
            ret[i] = ret[i - 1] * inv[i];
        }
        return ret;
    });
    static M binom(const usize n, const usize k) {
        assert(k <= n);
        return fact[n] * inv_fact[n - k] * inv_fact[k];
    }
    static M factpow(const usize n, const usize k) {
        assert(k <= n);
        return fact[n] * inv_fact[n - k];
    }
    static M homo(const usize n, const usize k) {
        if (n == 0 && k == 0) return M(1);
        return binom(n + k - 1, k);
    }
};
#line 5 "test/modint_util.test.cpp"
#include <iostream>

using Fp = StaticModint<1000000007>;
using FpUtil = ModintUtil<Fp>;

int main() {
    usize T;
    std::cin >> T;
    while (T--) {
        char type, dust;
        usize N, K;
        std::cin >> type >> dust >> N >> dust >> K >> dust;
        if (type == 'C') {
            if (N < K) std::cout << 0 << '\n';
            else std::cout << FpUtil::binom(N, K) << '\n';
        }
        if (type == 'P') {
            if (N < K) std::cout << 0 << '\n';
            else std::cout << FpUtil::factpow(N, K) << '\n';
        }
        if (type == 'H') {
            if (N == 0 && K > 0) std::cout << 0 << '\n';
            else std::cout << FpUtil::homo(N, K) << '\n';
        }
    }
    return 0;
}
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