結果

問題 No.906 Y字グラフ
ユーザー kimiyuki
提出日時 2019-10-11 21:52:32
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 70 ms / 2,000 ms
コード長 4,034 bytes
コンパイル時間 2,406 ms
コンパイル使用メモリ 194,348 KB
最終ジャッジ日時 2025-01-07 21:37:49
ジャッジサーバーID
（参考情報） 		judge1 / judge4
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ファイルパターン 結果
sample AC * 4
other AC * 28
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

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
using namespace std;
inline constexpr int32_t modpow(uint_fast64_t x, uint64_t k, int32_t MOD) {
    assert (0 <= x and x < MOD);
    uint_fast64_t y = 1;
    for (; k; k >>= 1) {
        if (k & 1) (y *= x) %= MOD;
        (x *= x) %= MOD;
    }
    assert (0 <= y and y < MOD);
    return y;
}
inline int32_t modinv(int32_t value, int32_t MOD) {
    assert (0 <= value and value < MOD);
    assert (value != 0);
    int64_t a = value, b = MOD;
    int64_t x = 0, y = 1;
    for (int64_t u = 1, v = 0; a; ) {
        int64_t q = b / a;
        x -= q * u; std::swap(x, u);
        y -= q * v; std::swap(y, v);
        b -= q * a; std::swap(b, a);
    }
    assert (value * x + MOD * y == b and b == 1);
    if (x < 0) x += MOD;
    assert (0 <= x and x < MOD);
    return x;
}
template <int32_t MOD>
struct mint {
    int32_t value;
    mint() : value() {}
    mint(int64_t value_) : value(value_ < 0 ? value_ % MOD + MOD : value_ >= MOD ? value_ % MOD : value_) {}
    mint(int32_t value_, std::nullptr_t) : value(value_) {}
    explicit operator bool() const { return value; }
    inline constexpr mint<MOD> operator + (mint<MOD> other) const { return mint<MOD>(*this) += other; }
    inline constexpr mint<MOD> operator - (mint<MOD> other) const { return mint<MOD>(*this) -= other; }
    inline constexpr mint<MOD> operator * (mint<MOD> other) const { return mint<MOD>(*this) *= other; }
    inline constexpr mint<MOD> & operator += (mint<MOD> other) { this->value += other.value; if (this->value >= MOD) this->value -= MOD; return *this; 
        }
    inline constexpr mint<MOD> & operator -= (mint<MOD> other) { this->value -= other.value; if (this->value <    0) this->value += MOD; return *this; 
        }
    inline constexpr mint<MOD> & operator *= (mint<MOD> other) { this->value = (uint_fast64_t)this->value * other.value % MOD; return *this; }
    inline constexpr mint<MOD> operator - () const { return mint<MOD>(this->value ? MOD - this->value : 0, nullptr); }
    inline constexpr mint<MOD> pow(uint64_t k) const { return mint<MOD>(modpow(value, k, MOD), nullptr); }
    inline mint<MOD> inv() const { return mint<MOD>(modinv(value, MOD), nullptr); }
    inline constexpr mint<MOD> operator /  (mint<MOD> other) const { return *this *  other.inv(); }
    inline constexpr mint<MOD> operator /= (mint<MOD> other)       { return *this *= other.inv(); }
    inline constexpr bool operator == (mint<MOD> other) const { return value == other.value; }
    inline constexpr bool operator != (mint<MOD> other) const { return value != other.value; }
};
template <int32_t MOD> mint<MOD> operator * (int64_t value, mint<MOD> n) { return mint<MOD>(value) * n; }
template <int32_t MOD> std::istream & operator >> (std::istream & in, mint<MOD> & n) { int64_t value; in >> value; n = value; return in; }
template <int32_t MOD> std::ostream & operator << (std::ostream & out, mint<MOD> n) { return out << n.value; }
/**
 * @note O(r)
 */
template <int32_t MOD>
mint<MOD> simple_choose(int64_t n, int32_t r) {
    assert (0 <= r and r <= n);
    mint<MOD> num = 1;
    mint<MOD> den = 1;
    REP (i, r) {
        num *= n - i;
        den *= i + 1;
    }
    return num / den;
}
constexpr int MOD = 1e9 + 7;
mint<MOD> solve(int64_t n) {
    int64_t k = n - 4;
    mint<MOD> unsorted = simple_choose<MOD>(k + 2, 2);
    mint<MOD> all_same = (k % 3 == 0 ? 1 : 0);
    mint<MOD> two_same = mint<MOD>(k / 2 + 1) - all_same;  // sorted
    mint<MOD> distinct = (unsorted - all_same - 3 * two_same) / 6;
    return all_same + two_same + distinct;
}
int main() {
    int64_t n; cin >> n;
    cout << solve(n) << endl;
    return 0;
}
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