#769987 (C++17) No.1978 Permutation Repetition

提出ソース

結果

問題	No.1978 Permutation Repetition
ユーザー	Forested
提出日時	2022-06-10 23:18:52
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	130 ms / 2,000 ms
コード長	10,778 bytes
コンパイル時間	1,746 ms
コンパイル使用メモリ	145,036 KB
実行使用メモリ	6,948 KB
最終ジャッジ日時	2024-09-21 06:51:28
合計ジャッジ時間	3,510 ms
ジャッジサーバーID （参考情報）	judge2 / judge4

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 6,812 KB
testcase_01	AC	2 ms 6,944 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	AC	2 ms 6,940 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	2 ms 6,944 KB
testcase_06	AC	2 ms 6,944 KB
testcase_07	AC	2 ms 6,940 KB
testcase_08	AC	2 ms 6,944 KB
testcase_09	AC	2 ms 6,944 KB
testcase_10	AC	2 ms 6,944 KB
testcase_11	AC	3 ms 6,944 KB
testcase_12	AC	2 ms 6,944 KB
testcase_13	AC	2 ms 6,948 KB
testcase_14	AC	2 ms 6,944 KB
testcase_15	AC	2 ms 6,944 KB
testcase_16	AC	2 ms 6,944 KB
testcase_17	AC	3 ms 6,940 KB
testcase_18	AC	2 ms 6,944 KB
testcase_19	AC	2 ms 6,940 KB
testcase_20	AC	2 ms 6,944 KB
testcase_21	AC	2 ms 6,944 KB
testcase_22	AC	2 ms 6,944 KB
testcase_23	AC	2 ms 6,944 KB
testcase_24	AC	2 ms 6,944 KB
testcase_25	AC	2 ms 6,940 KB
testcase_26	AC	3 ms 6,944 KB
testcase_27	AC	3 ms 6,940 KB
testcase_28	AC	2 ms 6,944 KB
testcase_29	AC	2 ms 6,940 KB
testcase_30	AC	2 ms 6,940 KB
testcase_31	AC	2 ms 6,940 KB
testcase_32	AC	3 ms 6,940 KB
testcase_33	AC	3 ms 6,944 KB
testcase_34	AC	2 ms 6,944 KB
testcase_35	AC	2 ms 6,940 KB
testcase_36	AC	2 ms 6,944 KB
testcase_37	AC	3 ms 6,940 KB
testcase_38	AC	2 ms 6,944 KB
testcase_39	AC	2 ms 6,944 KB
testcase_40	AC	2 ms 6,940 KB
testcase_41	AC	3 ms 6,940 KB
testcase_42	AC	130 ms 6,944 KB
testcase_43	AC	89 ms 6,944 KB
testcase_44	AC	2 ms 6,940 KB
testcase_45	AC	2 ms 6,940 KB

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ソースコード

raw source code

#ifndef LOCAL
#define FAST_IO
#endif

// ===== template.hpp =====
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32) (n); ++i)
#define REP3(i, m, n) for (i32 i = (i32) (m); i < (i32) (n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER(i, n) for (i32 i = (i32) (n) - 1; i >= 0; --i)
#define ALL(x) begin(x), end(x)

using namespace std;

using u32 = unsigned int;
using u64 = unsigned long long;
using u128 = __uint128_t;
using i32 = signed int;
using i64 = signed long long;
using i128 = __int128_t;
using f64 = double;
using f80 = long double;

template <typename T>
using Vec = vector<T>;

template <typename T>
bool chmin(T &x, const T &y) {
    if (x > y) {
        x = y;
        return true;
    }
    return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
    if (x < y) {
        x = y;
        return true;
    }
    return false;
}

istream &operator>>(istream &is, i128 &x) {
    i64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, i128 x) {
    os << (i64) x;
    return os;
}
istream &operator>>(istream &is, u128 &x) {
    u64 v;
    is >> v;
    x = v;
    return is;
}
ostream &operator<<(ostream &os, u128 x) {
    os << (u64) x;
    return os;
}

template <typename F, typename Comp = less<>>
Vec<i32> sort_index(i32 n, F f, Comp comp = Comp()) {
    Vec<i32> idx(n);
    iota(ALL(idx), 0);
    sort(ALL(idx), [&](i32 i, i32 j) -> bool {
        return comp(f(i), f(j));
    });
    return idx;
}

[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;

#ifdef FAST_IO
__attribute__((constructor)) void fast_io() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(10);
}
#endif
// ===== template.hpp =====

#ifdef DEBUGF
#include  "cpl/template/debug.hpp"
#else
#define DBG(x) (void) 0
#endif

// ===== mod_int.hpp =====

#include <cassert>
#include <iostream>
#include <type_traits>

// ===== utils.hpp =====

constexpr bool is_prime(unsigned n) {
    if (n == 0 || n == 1) {
        return false;
    }
    for (unsigned i = 2; i * i <= n; ++i) {
        if (n % i == 0) {
            return false;
        }
    }
    return true;
}

constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
    unsigned ret = 1, self = x;
    while (y != 0) {
        if (y & 1) {
            ret = static_cast<unsigned>(static_cast<unsigned long long>(ret) * self % mod);
        }
        self = static_cast<unsigned>(static_cast<unsigned long long>(self) * self % mod);
        y /= 2;
    }
    return ret;
}

template <unsigned mod>
constexpr unsigned primitive_root() {
    static_assert(is_prime(mod), "`mod` must be a prime number.");
    if (mod == 2) {
        return 1;
    }

    unsigned primes[32] = {};
    int it = 0;
    {
        unsigned m = mod - 1;
        for (unsigned i = 2; i * i <= m; ++i) {
            if (m % i == 0) {
                primes[it++] = i;
                while (m % i == 0) {
                    m /= i;
                }
            }
        }
        if (m != 1) {
            primes[it++] = m;
        }
    }
    for (unsigned i = 2; i < mod; ++i) {
        bool ok = true;
        for (int j = 0; j < it; ++j) {
            if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
                ok = false;
                break;
            }
        }
        if (ok)
            return i;
    }
    return 0;
}

// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
    x %= y;
    if (x < 0) {
        x += y;
    }
    return x;
}

// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return x / y;
    } else {
        return -((-x + y - 1) / y);
    }
}

// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
    if (y < 0) {
        x *= -1;
        y *= -1;
    }
    if (x >= 0) {
        return (x + y - 1) / y;
    } else {
        return -(-x / y);
    }
}
// ===== utils.hpp =====

template <unsigned mod>
class ModInt {
    static_assert(mod != 0, "`mod` must not be equal to 0.");
    static_assert(
        mod < (1u << 31),
        "`mod` must be less than (1u << 31) = 2147483648.");

    unsigned val;

public:
    constexpr ModInt() : val(0) {}
    template <typename T>
    constexpr ModInt(T x) : val(static_cast<unsigned>(safe_mod(x, static_cast<T>(mod)))) {}

    static constexpr ModInt raw(unsigned x) {
        ModInt<mod> ret;
        ret.val = x;
        return ret;
    }

    constexpr unsigned get_val() const {
        return val;
    }

    constexpr ModInt operator+() const {
        return *this;
    }
    constexpr ModInt operator-() const {
        return ModInt<mod>(0u) - *this;
    }

    constexpr ModInt &operator+=(const ModInt &rhs) {
        val += rhs.val;
        if (val >= mod)
            val -= mod;
        return *this;
    }
    constexpr ModInt &operator-=(const ModInt &rhs) {
        if (val < rhs.val)
            val += mod;
        val -= rhs.val;
        return *this;
    }
    constexpr ModInt &operator*=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.val % mod;
        return *this;
    }
    constexpr ModInt &operator/=(const ModInt &rhs) {
        val = (unsigned long long)val * rhs.inv().val % mod;
        return *this;
    }

    friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) += rhs;
    }
    friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) -= rhs;
    }
    friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) *= rhs;
    }
    friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
        return ModInt<mod>(lhs) /= rhs;
    }

    constexpr ModInt pow(unsigned long long x) const {
        ModInt<mod> ret = ModInt<mod>::raw(1);
        ModInt<mod> self = *this;
        while (x != 0) {
            if (x & 1)
                ret *= self;
            self *= self;
            x >>= 1;
        }
        return ret;
    }
    constexpr ModInt inv() const {
        static_assert(is_prime(mod), "`mod` must be a prime number.");
        assert(val != 0);
        return this->pow(mod - 2);
    }

    friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
        is >> x.val;
        x.val %= mod;
        return is;
    }

    friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
        os << x.val;
        return os;
    }

    friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val == rhs.val;
    }
    
    friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
        return lhs.val != rhs.val;
    }
};

[[maybe_unused]] constexpr unsigned mod998244353 = 998244353;
[[maybe_unused]] constexpr unsigned mod1000000007 = 1000000007;

// ===== mod_int.hpp =====

using Mint = ModInt<mod1000000007>;

// ===== factorial_table.hpp =====

#include <vector>
#include <cassert>

template <typename T>
class FactorialTable {
    std::vector<T> fac;
    std::vector<T> ifac;
    
public:
    FactorialTable() : fac(1, T(1)), ifac(1, T(1)) {}
    
    FactorialTable(int n) : fac(n + 1), ifac(n + 1) {
        assert(n >= 0);
        fac[0] = T(1);
        for (int i = 1; i <= n; ++i) {
            fac[i] = fac[i - 1] * T(i);
        }
        ifac[n] = T(1) / T(fac[n]);
        for (int i = n; i > 0; --i) {
            ifac[i - 1] = ifac[i] * T(i);
        }
    }
    
    void resize(int n) {
        int old = n_max();
        if (n <= old) {
            return;
        }
        fac.resize(n + 1);
        for (int i = old + 1; i <= n; ++i) {
            fac[i] = fac[i - 1] * T(i);
        }
        ifac.resize(n + 1);
        ifac[n] = T(1) / T(fac[n]);
        for (int i = n; i > old; --i) {
            ifac[i - 1] = ifac[i] * T(i);
        }
    }
    
    inline int n_max() const {
        return static_cast<int>(fac.size() - 1);
    }
    
    inline T fact(int n) const {
        assert(n >= 0 && n <= n_max());
        return fac[n];
    }
    
    inline T inv_fact(int n) const {
        assert(n >= 0 && n <= n_max());
        return ifac[n];
    }
    
    inline T choose(int n, int k) const {
        assert(k <= n_max() && n <= n_max());
        if (k > n || k < 0) {
            return T(0);
        }
        return fac[n] * ifac[k] * ifac[n - k];
    }
    
    inline T multi_choose(int n, int k) const {
        assert(n >= 1 && k >= 0 && k + n - 1 <= n_max());
        return choose(k + n - 1, k);
    }
    
    inline T n_terms_sum_k(int n, int k) const {
        assert(n >= 0);
        if (k < 0) {
            return T(0);
        }
        if (n == 0) {
            return k == 0 ? T(1) : T(0);
        }
        return choose(n + k - 1, n - 1);
    }
};
// ===== factorial_table.hpp =====

int main() {
    i32 n, m;
    cin >> n >> m;
    Vec<i32> a(n);
    REP(i, n) {
        cin >> a[i];
        --a[i];
    }
    
    FactorialTable<Mint> table(n);
    
    Vec<i32> cycle_cnt(n + 1, 0);
    {
        Vec<bool> checked(n, false);
        REP(i, n) {
            if (checked[i]) {
                continue;
            }
            i32 cur = i, cnt = 0;
            while (!checked[cur]) {
                checked[cur] = true;
                ++cnt;
                cur = a[cur];
            }
            ++cycle_cnt[cnt];
        }
    }
    
    DBG(cycle_cnt);
    
    Vec<Vec<pair<i32, Mint>>> gens(n + 1);
    REP(i, 1, n + 1) {
        i32 gc = gcd(i, m);
        gens[i / gc].emplace_back(gc, Mint(i / gc).pow(gc - 1) * table.fact(gc - 1));
    }
    DBG(gens);
    
    Mint ans(1);
    REP(i, 1, n + 1) {
        Vec<Mint> dp(cycle_cnt[i] + 1);
        dp[0] = Mint(1);
        for (auto [cnt, wgt] : gens[i]) {
            Vec<Mint> ndp(cycle_cnt[i] + 1);
            REP(j, cycle_cnt[i] + 1) {
                for (i32 k = 0; j + k * cnt <= cycle_cnt[i]; ++k) {
                    ndp[j + k * cnt] += dp[j] * table.choose(cycle_cnt[i] - j, k * cnt) * table.fact(k * cnt) * table.inv_fact(cnt).pow(k) * table.inv_fact(k) * wgt.pow(k);
                }
            }
            dp = ndp;
            DBG(dp);
        }
        DBG(dp);
        ans *= dp[cycle_cnt[i]];
    }
    cout << ans << '\n';
}

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結果

テストケース

ソースコード