結果

問題 No.526 フィボナッチ数列の第N項をMで割った余りを求める
コンテスト
ユーザー minato
提出日時 2020-05-20 05:36:16
言語 C++17
(gcc 13.3.0 + boost 1.89.0)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 4,490 bytes
記録
記録タグの例:
初AC ショートコード 純ショートコード 純主流ショートコード 最速実行時間
コンパイル時間 2,292 ms
コンパイル使用メモリ 195,532 KB
最終ジャッジ日時 2025-01-10 13:16:48
ジャッジサーバーID
（参考情報） 		judge4 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 12
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 #
raw source code 

#include <bits/stdc++.h>
using namespace std;

///////////////////////////////////////////////////////////////////

template<typename T, int sz>
struct Matrix {
   	array<array<T, sz>, sz> A;
	int N;

   	Matrix() : N(sz) {}
   	Matrix(int N) : N(N) {}

	inline const array<T, sz> &operator[](int k) const {return A[k];}
  	inline array<T, sz> &operator[](int k) {return A[k];}

  	static Matrix I(int N) {
    	Matrix<T, sz> mat(N);
    	for(int i = 0; i < N; ++i) mat[i][i] = 1;
    	return mat;
  	}

  	Matrix &operator+=(const Matrix &B) noexcept {
    	for(int i = 0; i < N; ++i) {
      	    for(int j = 0; j < N; ++j) {
        	    (*this)[i][j] += B[i][j];
            }
        }
    	return *this;
  	}

  	Matrix &operator-=(const Matrix &B) noexcept {
    	for(int i = 0; i < N; ++i) {
      		for(int j = 0; j < N; ++j) {
				(*this)[i][j] -= B[i][j];
			}
		}
    	return *this;
  	}

    Matrix &operator*=(const Matrix &B) noexcept {
        Matrix<T, sz> C(N);
        for(int i = 0; i < N; ++i) {
            for(int k = 0; k < N; ++k) {
                for(int j = 0; j < N; ++j) {
                    C[i][j] += (*this)[i][k] * B[k][j];
                }
            }
        }
        for (int i = 0; i < N; ++i) {
            for (int j = 0; j < N; ++j) {
                swap(A[i][j],C.A[i][j]);
            }
        }
        return *this;
    }

    Matrix &operator^=(long long k) noexcept {
        Matrix<T, sz> B = Matrix<T, sz>::I(N);
        while(k) {
            if(k & 1) B *= *this;
            *this *= *this;
            k >>= 1;
        }
        for (int i = 0; i < N; ++i) {
            for (int j = 0; j < N; ++j) {
                swap(A[i][j],B.A[i][j]);
            }
        }
        return *this;
    }

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

/////////////////////////////////////////////////////////////////////////////////////

//ModInt::set(M)
struct ModInt {
    using u64 = uint_fast64_t;

    u64 a;

    ModInt(long long x = 0) : a(x >= 0 ? x % Modulus() : (Modulus() - (-x) % Modulus()) % Modulus()) {}

    static u64 &Modulus() {static u64 Modulus = 0; return Modulus;}
    static void set (u64 M) {Modulus() = M;}

    ModInt operator+(const ModInt rhs) const noexcept {return ModInt(*this) += rhs;}
    ModInt operator-(const ModInt rhs) const noexcept {return ModInt(*this) -= rhs;}
    ModInt operator*(const ModInt rhs) const noexcept {return ModInt(*this) *= rhs;}
    ModInt operator/(const ModInt rhs) const noexcept {return ModInt(*this) /= rhs;}
    ModInt operator^(const long long rhs) const noexcept {return ModInt(*this) ^= rhs;}
    bool operator==(const ModInt &rhs) const noexcept {return a == rhs.a;}
    bool operator!=(const ModInt &rhs) const noexcept {return a != rhs.a;}
    ModInt &operator+=(const ModInt rhs) noexcept {
        a += rhs.a;
        if (a >= Modulus()) {
            a -= Modulus();
        }
        return *this;
    }
    ModInt &operator-=(const ModInt rhs) noexcept {
        if (a < rhs.a) {
            a += Modulus();
        }
        a -= rhs.a;
        return *this;
    }
    ModInt &operator*=(ModInt rhs) noexcept {
        a = a * rhs.a % Modulus();
        return *this;
    }
    ModInt &operator/=(ModInt rhs) noexcept {
        u64 exp = Modulus() - 2;
        while (exp) {
            if (exp&1) *this *= rhs;
            exp >>= 1;
            rhs *= rhs;
        }
        return *this;
    }
    ModInt &operator^=(long long exp) noexcept {
        ModInt rhs = a;
        a = 1;
        while (exp) {
            if (exp&1) *this *= rhs;
            exp >>= 1;
            rhs *= rhs;
        }
        return *this;
    }

    friend ostream &operator<<(ostream& os, const ModInt& rhs) noexcept {return os << rhs.a;}
    friend istream &operator>>(istream& is, ModInt& rhs) noexcept {long long a; is >> a; rhs = a; return is;}
};

using mint = ModInt;

void yuki526() {
    long long N,M; cin >> N >> M;

    ModInt::set(M);
    Matrix<mint,2> mat(2);

    mat[0][0] = mat[0][1] = mat[1][0] = 1;
    mat ^= N-1;

    cout << mat[1][0] << endl;
}

int main() {
    ios::sync_with_stdio(false); cin.tie(nullptr);
    yuki526();
}

/*
  verified on 2020/05/20
*/
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