#531852 (C++14) No.1073 無限すごろく

• 問題: No.1073 無限すごろく
• ユーザー: rokahikou1
• 提出日時: 2020-08-16 22:01:41
• 言語: C++14 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 2 ms / 2,000 ms
• コード長: 5,699 bytes
• コンパイル時間: 1,236 ms
• コンパイル使用メモリ: 101,624 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-04-19 18:33:35
• 合計ジャッジ時間: 2,558 ms
• ジャッジサーバーID （参考情報）: judge5 / judge2

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; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	1 ms; 5,376 KB
testcase_04	AC	2 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	2 ms; 5,376 KB
testcase_09	AC	2 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	2 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	2 ms; 5,376 KB
testcase_17	AC	2 ms; 5,376 KB
testcase_18	AC	2 ms; 5,376 KB
testcase_19	AC	2 ms; 5,376 KB
testcase_20	AC	2 ms; 5,376 KB
testcase_21	AC	2 ms; 5,376 KB
testcase_22	AC	2 ms; 5,376 KB
testcase_23	AC	2 ms; 5,376 KB
testcase_24	AC	2 ms; 5,376 KB
testcase_25	AC	2 ms; 5,376 KB
testcase_26	AC	2 ms; 5,376 KB
testcase_27	AC	2 ms; 5,376 KB
testcase_28	AC	2 ms; 5,376 KB
testcase_29	AC	2 ms; 5,376 KB
testcase_30	AC	2 ms; 5,376 KB
testcase_31	AC	2 ms; 5,376 KB
testcase_32	AC	1 ms; 5,376 KB

ソースコード

#include <algorithm>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>
using namespace std;
#define rep(i, n) for(int(i) = 0; (i) < (n); (i)++)
#define FOR(i, m, n) for(int(i) = (m); (i) < (n); (i)++)
#define All(v) (v).begin(), (v).end()
#define pb push_back
#define MP(a, b) make_pair((a), (b))
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
const int INF = 1 << 30;
const ll LINF = 1LL << 60;
const int MOD = 1e9 + 7;

#include <cassert>
// 参考:https://ei1333.github.io/luzhiled/snippets/math/matrix.html
// (掛け算と累乗)https://yukicoder.me/submissions/523126
// 他は知らん
template <class T> struct Matrix {
    vector<vector<T>> A;
    Matrix() {}
    Matrix(size_t n, size_t m) : A(n, vector<T>(m, 0)) {}
    Matrix(size_t n) : A(n, vector<T>(n, 0)) {}

    size_t height() const { return A.size(); }

    size_t width() const { return A[0].size(); }

    inline vector<T> &operator[](int k) { return A.at(k); }
    inline const vector<T> &operator[](int k) const { return A.at(k); }

    static Matrix I(size_t n) {
        Matrix mat(n);
        for(int i = 0; i < n; i++)
            mat[i][i] = 1;
        return mat;
    }

    Matrix &operator+=(const Matrix &B) {
        size_t h = height(), w = width();
        assert(h == B.height() && w == B.width);
        for(int i = 0; i < h; i++) {
            for(int j = 0; j < w; j++) {
                (*this)[i][j] += B[i][j];
            }
        }
        return *this;
    }

    Matrix &operator-=(const Matrix &B) {
        size_t h = height(), w = width();
        assert(h == B.height() && w == B.width);
        for(int i = 0; i < h; i++) {
            for(int j = 0; j < w; j++) {
                (*this)[i][j] -= B[i][j];
            }
        }
        return *this;
    }

    Matrix &operator*=(const Matrix &B) {
        size_t h = height(), w = B.width(), p = width();
        assert(p == B.height());
        vector<vector<T>> C(h, vector<T>(w, 0));
        for(int i = 0; i < h; i++) {
            for(int j = 0; j < w; j++) {
                for(int k = 0; k < p; k++) {
                    C[i][j] += (*this)[i][k] * B[k][j];
                }
            }
        }
        A.swap(C);
        return *this;
    }

    Matrix &operator^=(ll k) {
        Matrix B = Matrix::I(height());
        while(k > 0) {
            if(k & 1)
                B *= *this;
            *this *= *this;
            k >>= 1LL;
        }
        A.swap(B.A);
        return *this;
    }

    Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }
    Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }
    Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }
    Matrix operator^(const ll k) const { return (Matrix(*this) ^= k); }

    friend ostream &operator<<(ostream &os, const Matrix &p) {
        size_t h = p.height(), w = p.width();
        for(int i = 0; i < h; i++) {
            os << "[";
            for(int j = 0; j < w; j++) {
                os << p[i][j] << (j + 1 == w ? "]\n" : ",");
            }
        }
        return os;
    }
};

template <uint_fast64_t MOD> class ModInt {
    using u64 = uint_fast64_t;

  public:
    u64 val;

    ModInt(const u64 x = 0) : val((x + MOD) % MOD) {}
    constexpr u64 &value() { return val; }
    constexpr ModInt operator-() { return val ? MOD - val : 0; }
    constexpr ModInt operator+(const ModInt &rhs) const {
        return ModInt(*this) += rhs;
    }
    constexpr ModInt operator-(const ModInt &rhs) const {
        return ModInt(*this) -= rhs;
    }
    constexpr ModInt operator*(const ModInt &rhs) const {
        return ModInt(*this) *= rhs;
    }
    constexpr ModInt operator/(const ModInt &rhs) const {
        return ModInt(*this) /= rhs;
    }
    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 = val * rhs.val % MOD;
        return *this;
    }

    constexpr ModInt &operator/=(const ModInt &rhs) {
        *this *= rhs.inv();
        return *this;
    }

    constexpr bool operator==(const ModInt &rhs) { return this->a == rhs.a; }
    constexpr bool operator!=(const ModInt &rhs) { return this->a != rhs.a; }
    friend constexpr ostream &operator<<(ostream &os, const ModInt<MOD> &x) {
        return os << x.val;
    }
    friend constexpr istream &operator>>(istream &is, ModInt<MOD> &x) {
        return is >> x.val;
    }

    constexpr ModInt inv() const { return ModInt(*this).pow(MOD - 2); }

    constexpr ModInt pow(ll e) const {
        u64 x = 1, p = val;
        while(e > 0) {
            if(e % 2 == 0) {
                p = (p * p) % MOD;
                e /= 2;
            } else {
                x = (x * p) % MOD;
                e--;
            }
        }
        return ModInt(x);
    }
};

using mint = ModInt<MOD>;

int main() {
    ll N;
    cin >> N;
    Matrix<mint> mat(6, 6), base(6, 1);
    for(int i = 0; i < 6; i++) {
        for(int j = 0; j < 6; j++) {
            if(i == 5) {
                mat[i][j] = mint(6).inv();
            } else if(j == i + 1) {
                mat[i][j] = 1;
            }
        }
    }
    base[5][0] = 1;
    auto res = ((mat ^ N) * base);
    cout << res[5][0] << endl;
    return 0;
}