#381594 (C++14) No.890 移調の限られた旋法

提出ソース
結果

問題	No.890 移調の限られた旋法
ユーザー	jell
提出日時	2019-09-20 22:20:16
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	52 ms / 2,000 ms
コード長	19,071 bytes
コンパイル時間	7,346 ms
コンパイル使用メモリ	336,884 KB
実行使用メモリ	37,120 KB
最終ジャッジ日時	2024-09-14 18:08:46
合計ジャッジ時間	8,961 ms
ジャッジサーバーID （参考情報）	judge5 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 5,248 KB
testcase_01	AC	2 ms 5,248 KB
testcase_02	AC	2 ms 5,248 KB
testcase_03	AC	3 ms 5,376 KB
testcase_04	AC	3 ms 5,376 KB
testcase_05	AC	2 ms 5,376 KB
testcase_06	AC	2 ms 5,376 KB
testcase_07	AC	2 ms 5,376 KB
testcase_08	AC	3 ms 5,376 KB
testcase_09	AC	3 ms 5,376 KB
testcase_10	AC	3 ms 5,376 KB
testcase_11	AC	3 ms 5,376 KB
testcase_12	AC	2 ms 5,376 KB
testcase_13	AC	52 ms 37,120 KB
testcase_14	AC	31 ms 33,152 KB
testcase_15	AC	38 ms 32,896 KB
testcase_16	AC	31 ms 27,136 KB
testcase_17	AC	24 ms 24,832 KB
testcase_18	AC	29 ms 27,264 KB
testcase_19	AC	15 ms 18,688 KB
testcase_20	AC	11 ms 17,152 KB
testcase_21	AC	3 ms 5,376 KB
testcase_22	AC	21 ms 23,424 KB
testcase_23	AC	22 ms 24,448 KB
testcase_24	AC	13 ms 18,688 KB
testcase_25	AC	3 ms 5,376 KB
testcase_26	AC	34 ms 31,616 KB
testcase_27	AC	30 ms 29,184 KB
testcase_28	AC	16 ms 20,352 KB
testcase_29	AC	6 ms 9,600 KB
testcase_30	AC	23 ms 24,704 KB
testcase_31	AC	15 ms 18,432 KB
testcase_32	AC	27 ms 25,856 KB
testcase_33	AC	49 ms 33,664 KB
testcase_34	AC	27 ms 24,960 KB
権限があれば一括ダウンロードができます
ソースコード

raw source code
#ifdef stderr_path
#define LOCAL
#define _GLIBCXX_DEBUG
#endif
#pragma GCC optimize("Ofast")
#include <algorithm>
#include <bitset>
#include <cassert>
#include <chrono>
#include <complex>
#include <cstring>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <unordered_map>
#include <unordered_set>

// #define NDEBUG
#define debug_stream std::cerr
#define iostream_untie true
#define __precision__ 10

#define rep(i, n) for(int i = 0; i < int(n); ++i)
#define all(v) std::begin(v), std::end(v)
#define rall(v) std::rbegin(v), std::rend(v)
#define __odd(n) ((n)&1)
#define __even(n) (__odd(n) ^ 1)
#define __popcount(n) __builtin_popcountll(n)
#define __clz32(n) __builtin_clz(int32_t(n))
#define __clz64(n) __builtin_clzll(int64_t(n))
#define __ctz32(n) __builtin_ctz(int32_t(n))
#define __ctz64(n) __builtin_ctzll(int64_t(n))

using i64 = int_fast64_t;
using pii = std::pair<int, int>;
using pll = std::pair<int_fast64_t, int_fast64_t>;
template <class T>
using heap = std::priority_queue<T>;
template <class T>
using minheap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <class T>
constexpr T inf = std::numeric_limits<T>::max() / T(2) - T(1123456);

namespace execution
{
    std::chrono::system_clock::time_point start_time, end_time;
    void print_elapsed_time()
    {
        end_time = std::chrono::system_clock::now();
        std::cerr << "\n----- Exec time : ";
        std::cerr << std::chrono::duration_cast<std::chrono::milliseconds>(
                         end_time - start_time)
                         .count();
        std::cerr << " ms -----\n\n";
    }
    struct setupper
    {
        setupper()
        {
            if(iostream_untie)
            {
                std::ios::sync_with_stdio(false);
                std::cin.tie(nullptr);
            }
            std::cout << std::fixed << std::setprecision(__precision__);
#ifdef stderr_path
            if(freopen(stderr_path, "a", stderr))
            {
                std::cerr << std::fixed << std::setprecision(__precision__);
            }
            else
                fclose(stderr);
#endif
#ifdef stdout_path
            if(not freopen(stdout_path, "w", stdout))
            {
                freopen("CON", "w", stdout);
                std::cerr << "Failed to open the stdout file\n\n";
            }
            std::cout << "";
#endif
#ifdef stdin_path
            if(not freopen(stdin_path, "r", stdin))
            {
                freopen("CON", "r", stdin);
                std::cerr << "Failed to open the stdin file\n\n";
            }
#endif
#ifdef LOCAL
            atexit(print_elapsed_time);
            start_time = std::chrono::system_clock::now();
#endif
        }
    } __setupper;
} // namespace execution

class myclock_t
{
    std::chrono::system_clock::time_point built_pt, last_pt;
    int built_ln, last_ln;
    std::string built_func, last_func;
    bool is_built;

  public:
    explicit myclock_t() : is_built(false)
    {}
    void build(int crt_ln, const std::string &crt_func)
    {
        is_built = true;
        last_pt = built_pt = std::chrono::system_clock::now();
        last_ln = built_ln = crt_ln, last_func = built_func = crt_func;
    }
    void set(int crt_ln, const std::string &crt_func)
    {
        if(is_built)
        {
            last_pt = std::chrono::system_clock::now();
            last_ln = crt_ln, last_func = crt_func;
        }
        else
        {
            debug_stream << "[ " << crt_ln << " : " << crt_func << " ] "
                         << "myclock_t::set failed (yet to be built!)\n";
        }
    }
    void get(int crt_ln, const std::string &crt_func)
    {
        if(is_built)
        {
            std::chrono::system_clock::time_point crt_pt(
                std::chrono::system_clock::now());
            int64_t diff =
                std::chrono::duration_cast<std::chrono::milliseconds>(crt_pt -
                                                                      last_pt)
                    .count();
            debug_stream << diff << " ms elapsed from"
                         << " [ " << last_ln << " : " << last_func << " ]";
            if(last_ln == built_ln) debug_stream << " (when built)";
            debug_stream << " to"
                         << " [ " << crt_ln << " : " << crt_func << " ]"
                         << "\n";
            last_pt = built_pt, last_ln = built_ln, last_func = built_func;
        }
        else
        {
            debug_stream << "[ " << crt_ln << " : " << crt_func << " ] "
                         << "myclock_t::get failed (yet to be built!)\n";
        }
    }
};
#ifdef LOCAL
myclock_t __myclock;
#define build_clock() __myclock.build(__LINE__, __func__)
#define set_clock() __myclock.set(__LINE__, __func__)
#define get_clock() __myclock.get(__LINE__, __func__)
#else
#define build_clock() ((void)0)
#define set_clock() ((void)0)
#define get_clock() ((void)0)
#endif

namespace std
{
    template <class RAitr>
    void rsort(RAitr __first, RAitr __last)
    {
        sort(__first, __last, greater<>());
    }
    template <class T>
    size_t hash_combine(size_t seed, T const &key)
    {
        return seed ^ (hash<T>()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2));
    }
    template <class T, class U>
    struct hash<pair<T, U>>
    {
        size_t operator()(pair<T, U> const &pr) const
        {
            return hash_combine(hash_combine(0, pr.first), pr.second);
        }
    };
    template <class tuple_t, size_t index = tuple_size<tuple_t>::value - 1>
    struct tuple_hash_calc
    {
        static size_t apply(size_t seed, tuple_t const &t)
        {
            return hash_combine(
                tuple_hash_calc<tuple_t, index - 1>::apply(seed, t),
                get<index>(t));
        }
    };
    template <class tuple_t>
    struct tuple_hash_calc<tuple_t, 0>
    {
        static size_t apply(size_t seed, tuple_t const &t)
        {
            return hash_combine(seed, get<0>(t));
        }
    };
    template <class... T>
    struct hash<tuple<T...>>
    {
        size_t operator()(tuple<T...> const &t) const
        {
            return tuple_hash_calc<tuple<T...>>::apply(0, t);
        }
    };
    template <class T, class U>
    istream &operator>>(std::istream &s, pair<T, U> &p)
    {
        return s >> p.first >> p.second;
    }
    template <class T, class U>
    ostream &operator<<(std::ostream &s, const pair<T, U> p)
    {
        return s << p.first << " " << p.second;
    }
    template <class T>
    istream &operator>>(istream &s, vector<T> &v)
    {
        for(T &e : v)
        {
            s >> e;
        }
        return s;
    }
    template <class T>
    ostream &operator<<(ostream &s, const vector<T> &v)
    {
        bool is_front = true;
        for(const T &e : v)
        {
            if(not is_front)
            {
                s << ' ';
            }
            else
            {
                is_front = false;
            }
            s << e;
        }
        return s;
    }
    template <class tuple_t, size_t index>
    struct tupleos
    {
        static ostream &apply(ostream &s, const tuple_t &t)
        {
            tupleos<tuple_t, index - 1>::apply(s, t);
            return s << " " << get<index>(t);
        }
    };
    template <class tuple_t>
    struct tupleos<tuple_t, 0>
    {
        static ostream &apply(ostream &s, const tuple_t &t)
        {
            return s << get<0>(t);
        }
    };
    template <class... T>
    ostream &operator<<(ostream &s, const tuple<T...> &t)
    {
        return tupleos<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(
            s, t);
    }
    template <>
    ostream &operator<<(ostream &s, const tuple<> &t)
    {
        return s;
    }
    string revstr(string str)
    {
        reverse(str.begin(), str.end());
        return str;
    }
} // namespace std

#ifdef LOCAL
#define dump(...)                                                              \
    debug_stream << "[ " << __LINE__ << " : " << __FUNCTION__ << " ]\n",       \
        dump_func(#__VA_ARGS__, __VA_ARGS__)
template <class T>
void dump_func(const char *ptr, const T &x)
{
    debug_stream << '\t';
    for(char c = *ptr; c != '\0'; c = *++ptr)
    {
        if(c != ' ') debug_stream << c;
    }
    debug_stream << " : " << x << '\n';
}
template <class T, class... rest_t>
void dump_func(const char *ptr, const T &x, rest_t... rest)
{
    debug_stream << '\t';
    for(char c = *ptr; c != ','; c = *++ptr)
    {
        if(c != ' ') debug_stream << c;
    }
    debug_stream << " : " << x << ",\n";
    dump_func(++ptr, rest...);
}
#else
#define dump(...) ((void)0)
#endif
template <class P>
void read_range(P __first, P __second)
{
    for(P i = __first; i != __second; ++i)
        std::cin >> *i;
}
template <class P>
void write_range(P __first, P __second)
{
    for(P i = __first; i != __second;
        std::cout << (++i == __second ? '\n' : ' '))
    {
        std::cout << *i;
    }
}

// substitute y for x.
template <class T>
void subst(T &x, const T &y)
{
    x = y;
}
// substitue y for x iff x > y.
template <class T>
bool chmin(T &x, const T &y)
{
    return x > y ? x = y, true : false;
}
// substitue y for x iff x < y.
template <class T>
bool chmax(T &x, const T &y)
{
    return x < y ? x = y, true : false;
}
template <class T>
constexpr T minf(const T &x, const T &y)
{
    return std::min(x, y);
}
template <class T>
constexpr T maxf(const T &x, const T &y)
{
    return std::max(x, y);
}
// binary search.
template <class int_t, class F>
int_t bin(int_t ok, int_t ng, const F &f)
{
    while(std::abs(ok - ng) > 1)
    {
        int_t mid = (ok + ng) / 2;
        (f(mid) ? ok : ng) = mid;
    }
    return ok;
}
template <class T, class A, size_t N>
void init(A (&array)[N], const T &val)
{
    std::fill((T *)array, (T *)(array + N), val);
}
void reset()
{}
template <class A, class... rest_t>
void reset(A &array, rest_t... rest)
{
    memset(array, 0, sizeof(array));
    reset(rest...);
}
// a integer uniformly and randomly chosen from the interval [l, r).
template <typename int_t>
int_t rand_int(int_t l, int_t r)
{
    static std::random_device seed_gen;
    static std::mt19937 engine(seed_gen());
    std::uniform_int_distribution<int_t> unid(l, r - 1);
    return unid(engine);
}
// a real number uniformly and randomly chosen from the interval [l, r).
template <typename real_t>
real_t rand_real(real_t l, real_t r)
{
    static std::random_device seed_gen;
    static std::mt19937 engine(seed_gen());
    std::uniform_real_distribution<real_t> unid(l, r);
    return unid(engine);
}

/* The main code follows. */

namespace math
{
    template <int_fast32_t mod>
    struct modint
    {
        int x;

        constexpr modint() : x(0)
        {}
        constexpr modint(int_fast64_t y)
            : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod)
        {}

        constexpr modint &operator+=(const modint &p)
        {
            if((x += p.x) >= mod) x -= mod;
            return *this;
        }

        constexpr modint &operator++()
        {
            return ++x, *this;
        }

        constexpr modint operator++(int)
        {
            modint t = *this;
            return ++x, t;
        }

        constexpr modint &operator-=(const modint &p)
        {
            if((x += mod - p.x) >= mod) x -= mod;
            return *this;
        }

        constexpr modint &operator--()
        {
            return --x, *this;
        }

        constexpr modint operator--(int)
        {
            modint t = *this;
            return --x, t;
        }

        constexpr modint &operator*=(const modint &p)
        {
            return x = (int_fast64_t)x * p.x % mod, *this;
        }

        constexpr modint &operator/=(const modint &p)
        {
            return *this *= inverse(p);
        }

        // constexpr modint &operator%=(int m) { return x %= m, *this; }

        constexpr modint operator-() const
        {
            return modint(-x);
        }

        constexpr modint operator+(const modint &p) const
        {
            return modint(*this) += p;
        }

        constexpr modint operator-(const modint &p) const
        {
            return modint(*this) -= p;
        }

        constexpr modint operator*(const modint &p) const
        {
            return modint(*this) *= p;
        }

        constexpr modint operator/(const modint &p) const
        {
            return modint(*this) /= p;
        }

        // constexpr modint operator%(int m) const { return modint(*this) %= m;
        // }

        constexpr bool operator==(const modint &p) const
        {
            return x == p.x;
        }

        constexpr bool operator!=(const modint &p) const
        {
            return x != p.x;
        }

        constexpr bool operator!() const
        {
            return !x;
        }

        // constexpr bool operator>(const modint &p) const { return x > p.x; }

        // constexpr bool operator<(const modint &p) const { return x <  p.x; }

        // constexpr bool operator>=(const modint &p) const { return x >= p.x; }

        // constexpr bool operator<=(const modint &p) const { return x <= p.x; }

        constexpr friend modint inverse(const modint &p)
        {
            int a = p.x, b = mod, u = 1, v = 0;
            while(b > 0)
            {
                int t = a / b;
                a -= t * b;
                a ^= b ^= a ^= b;
                u -= t * v;
                u ^= v ^= u ^= v;
            }
            return modint(u);
        }

        constexpr friend modint pow(modint p, int_fast64_t e)
        {
            if(e < 0) e = (e % (mod - 1) + mod - 1) % (mod - 1);
            modint ret = 1;
            while(e)
            {
                if(e & 1) ret *= p;
                p *= p;
                e >>= 1;
            }
            return ret;
        }

        friend std::ostream &operator<<(std::ostream &s, const modint &p)
        {
            return s << p.x;
        }

        friend std::istream &operator>>(std::istream &s, modint &p)
        {
            int_fast64_t x;
            p = modint((s >> x, x));
            return s;
        }
    };
} // namespace math

// require modint
namespace math
{
    constexpr int mod = 1000000007;

    constexpr int N = 2.2e5, N_max = 2.2e6;

    struct impl
    {
        int_fast64_t _fact[N + 1], _invfact[N + 1], _inv[N + 1];

        constexpr impl() : _fact(), _invfact(), _inv()
        {
            _fact[0] = 1;
            for(int i = 1; i <= N; ++i)
                _fact[i] = _fact[i - 1] * i % mod;
            _inv[1] = 1;
            for(int i = 2; i <= N && i < mod; ++i)
                _inv[i] = mod - _inv[mod % i] * (mod / i) % mod;
            _invfact[0] = 1;
            for(int i = 1; i <= N && i < mod; ++i)
                _invfact[i] = _invfact[i - 1] * _inv[i] % mod;
        }
    };
    constexpr impl _impl;

    int_fast64_t _dyn_fact[N_max + 1];
    int_fast64_t _dyn_inv[N_max + 1];
    int_fast64_t _dyn_invfact[N_max + 1];

    int_fast64_t dyn_fact(int x)
    {
        assert(x <= N_max);
        if(x < 0) return 0;
        static int _size = 1;
        for(int &i = _size; i <= x; ++i)
        {
            if(i <= N)
                _dyn_fact[i] = _impl._fact[i];
            else
                _dyn_fact[i] = _dyn_fact[i - 1] * i % mod;
        }
        return _dyn_fact[x];
    }

    int_fast64_t dyn_invfact(int x)
    {
        assert(x <= N_max && x < mod);
        if(x < 0) return 0;
        static int _size = 1;
        for(int &i = _size; i <= x; ++i)
        {
            if(i <= N)
            {
                _dyn_inv[i] = _impl._inv[i];
                _dyn_invfact[i] = _impl._invfact[i];
            }
            else
            {
                _dyn_inv[i] = mod - _dyn_inv[mod % i] * (mod / i) % mod;
                _dyn_invfact[i] = _dyn_invfact[i - 1] * _dyn_inv[i] % mod;
            }
        }
        return _dyn_invfact[x];
    }

    modint<mod> fact(int x)
    {
        return x > N ? dyn_fact(x) : x < 0 ? 0 : _impl._fact[x];
    }

    modint<mod> invfact(int x)
    {
        return x > N ? dyn_invfact(x) : x < 0 ? 0 : _impl._invfact[x];
    }

    modint<mod> binom(int x, int y)
    {
        return fact(x) * invfact(y) * invfact(x - y);
    }

    modint<mod> perm(int x, int y)
    {
        return binom(x, y) * fact(y);
    }
} // namespace math

namespace math
{
    template <class int_t>
    constexpr int_t gcd(int_t x, int_t y)
    {
        x = x > 0 ? x : -x, y = y > 0 ? y : -y;
        while(y)
            y ^= x ^= y ^= x %= y;
        return x;
    }
    template <class int_t>
    constexpr int_t lcm(int_t x, int_t y)
    {
        return x ? x / gcd(x, y) * y : 0;
    }
    // a tuple (g, x, y) s.t. g = gcd(a, b) && ax + by = g.
    template <class int_t>
    constexpr std::tuple<int_t, int_t, int_t> ext_gcd(int_t a, int_t b)
    {
        int_t sgn_a = a >= 0 ? 1 : (a = -a, 0),
              sgn_b = b >= 0 ? 1 : (b = -b, 0);
        int_t p = 1, q = 0, r = 0, s = 1;
        while(b)
        {
            int_t t = a / b;
            r ^= p ^= r ^= p -= t * r;
            s ^= q ^= s ^= q -= t * s;
            b ^= a ^= b ^= a %= b;
        }
        return std::tuple<int_t, int_t, int_t>(a, sgn_a ? p : -p,
                                               sgn_b ? q : -q);
    }
    // a pair (x, y) s.t. "x mod y" is true iff "k mod m" && "l mod n" if exist, otherwise (-1, -1).
    template <class int_t>
    constexpr std::pair<int_t, int_t> mod_comp(int_t k, int_t m, int_t l,
                                               int_t n)
    {
        assert(m > 0 and n > 0);
        int_t g, x, y;
        std::tie(g, x, y) = ext_gcd(m, n);
        k += ((k %= m) < 0) * m, l += ((l %= n) < 0) * n;
        int_t s = k / g, t = l / g, r = k % g;
        if(r != l % g) return std::pair<int_t, int_t>(-1, -1);
        int_t lcm = m / g * n;
        return std::pair<int_t, int_t>(
            (m * x % lcm * t % lcm + n * y % lcm * s % lcm + r + lcm * 2) % lcm,
            lcm);
    }
} // namespace math

using namespace std;
using namespace math;

signed main()
{
    void __solve();
    void __precalc();

    unsigned int t = 1;
    // cin >> t;
    __precalc();

#ifdef LOCAL
    t=3;
#endif

    while(t--)
    {
        __solve();
    }
}

void __precalc()
{}

void __solve()
{
    using mint=modint<mod>;
    int n,k; cin>>n>>k;
    int g=gcd(n,k);
    static mint f[1<<20];
    for(int i=1; i<=g; i++)
    {
        if(g%i) f[i]=0;
        else
        {
            f[i]=binom(n/i,k/i);
        }
    }
    static bool isp[1<<20];
    init(isp,true);
    for(int i=2; i<=g; i++)
    {
        if(isp[i])
        {
            for(int k=1; k*i<=g; k++)
            {
                f[k]-=f[i*k];
                isp[k*i]=false;
            }
        }
    }
    std::cout << binom(n,k)-f[1] << "\n";
}
yukicoder

結果

テストケース

ソースコード
