結果

問題 No.718 行列のできるフィボナッチ数列道場 (1)
ユーザー ningenMeningenMe
提出日時 2020-04-28 08:57:55
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 6,344 bytes
コンパイル時間 1,628 ms
コンパイル使用メモリ 169,512 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-11-24 01:55:26
合計ジャッジ時間 2,639 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 1 ms
5,248 KB
testcase_02 AC 1 ms
5,248 KB
testcase_03 AC 2 ms
5,248 KB
testcase_04 AC 2 ms
5,248 KB
testcase_05 AC 2 ms
5,248 KB
testcase_06 AC 2 ms
5,248 KB
testcase_07 AC 2 ms
5,248 KB
testcase_08 AC 2 ms
5,248 KB
testcase_09 AC 2 ms
5,248 KB
testcase_10 AC 2 ms
5,248 KB
testcase_11 AC 2 ms
5,248 KB
testcase_12 AC 2 ms
5,248 KB
testcase_13 AC 2 ms
5,248 KB
testcase_14 AC 2 ms
5,248 KB
testcase_15 AC 2 ms
5,248 KB
testcase_16 AC 2 ms
5,248 KB
testcase_17 AC 2 ms
5,248 KB
testcase_18 AC 2 ms
5,248 KB
testcase_19 AC 2 ms
5,248 KB
testcase_20 AC 2 ms
5,248 KB
testcase_21 AC 2 ms
5,248 KB
testcase_22 AC 2 ms
5,248 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

diff # 

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

#define ALL(obj) (obj).begin(),(obj).end()
#define SPEED cin.tie(0);ios::sync_with_stdio(false);

template<class T> using PQ = priority_queue<T>;
template<class T> using PQR = priority_queue<T,vector<T>,greater<T>>;

constexpr long long MOD = (long long)1e9 + 7;
constexpr long long MOD2 = 998244353;
constexpr long long HIGHINF = (long long)1e18;
constexpr long long LOWINF = (long long)1e15;
constexpr long double PI = 3.1415926535897932384626433L;

template <class T> vector<T> multivector(size_t N,T init){return vector<T>(N,init);}
template <class... T> auto multivector(size_t N,T... t){return vector<decltype(multivector(t...))>(N,multivector(t...));}
template <class T> void corner(bool flg, T hoge) {if (flg) {cout << hoge << endl; exit(0);}}
template <class T, class U>ostream &operator<<(ostream &o, const map<T, U>&obj) {o << "{"; for (auto &x : obj) o << " {" << x.first << " : " << x.second << "}" << ","; o << " }"; return o;}
template <class T>ostream &operator<<(ostream &o, const set<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
template <class T>ostream &operator<<(ostream &o, const multiset<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
template <class T>ostream &operator<<(ostream &o, const vector<T>&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o;}
template <class T, class U>ostream &operator<<(ostream &o, const pair<T, U>&obj) {o << "{" << obj.first << ", " << obj.second << "}"; return o;}
void print(void) {cout << endl;}
template <class Head> void print(Head&& head) {cout << head;print();}
template <class Head, class... Tail> void print(Head&& head, Tail&&... tail) {cout << head << " ";print(forward<Tail>(tail)...);}
template <class T> void chmax(T& a, const T b){a=max(a,b);}
template <class T> void chmin(T& a, const T b){a=min(a,b);}
void YN(bool flg) {cout << (flg ? "YES" : "NO") << endl;}
void Yn(bool flg) {cout << (flg ? "Yes" : "No") << endl;}
void yn(bool flg) {cout << (flg ? "yes" : "no") << endl;}


template<long long mod> class ModInt {
public:
	long long x;
	ModInt():x(0) {
		// do nothing
	}
	ModInt(long long y) : x(y>=0?(y%mod): (mod - (-y)%mod)%mod) {
		// do nothing
	}
	ModInt &operator+=(const ModInt &p) {
		if((x += p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator+=(const long long y) {
        ModInt p(y);
		if((x += p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator+=(const int y) {
        ModInt p(y);
		if((x += p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator-=(const ModInt &p) {
		if((x += mod - p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator-=(const long long y) {
        ModInt p(y);
		if((x += mod - p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator-=(const int y) {
        ModInt p(y);
		if((x += mod - p.x) >= mod) x -= mod;
		return *this;
	}
	ModInt &operator*=(const ModInt &p) {
		x = (x * p.x % mod);
		return *this;
	}
	ModInt &operator*=(const long long y) {
        ModInt p(y);
		x = (x * p.x % mod);
		return *this;
	}
	ModInt &operator*=(const int y) {
        ModInt p(y);
		x = (x * p.x % mod);
		return *this;
	}
	ModInt &operator/=(const ModInt &p) {
		*this *= p.inv();
		return *this;
	}
	ModInt &operator/=(const long long y) {
        ModInt p(y);
		*this *= p.inv();
		return *this;
	}
	ModInt &operator/=(const int y) {
        ModInt p(y);
		*this *= p.inv();
		return *this;
	}
	ModInt operator=(const int y) {
        ModInt p(y);
        *this = p;
        return *this;
    }
    ModInt operator=(const long long y) {
        ModInt p(y);
		*this = p;
        return *this;
    }
	ModInt operator-() const { return ModInt(-x); }
	ModInt operator++() { 
        x++;
        if(x>=mod) x-=mod;
        return *this; 
    }
	ModInt operator--() { 
        x--;
        if(x<0) x+=mod;
        return *this; 
    }
	ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
	ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
	ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
	ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
	bool operator==(const ModInt &p) const { return x == p.x; }
	bool operator!=(const ModInt &p) const { return x != p.x; }
	ModInt inv() const {
		int a = x, b = mod, u = 1, v = 0, t;
		while(b > 0) {
			t = a / b;
			swap(a -= t * b, b);
			swap(u -= t * v, v);
		}
		return ModInt(u);
	}
	ModInt pow(long long n) const {
		ModInt ret(1), mul(x);
		while(n > 0) {
			if(n & 1) ret *= mul;
			mul *= mul;
			n >>= 1;
		}
		return ret;
	}
	friend ostream &operator<<(ostream &os, const ModInt &p) {
		return os << p.x;
	}
	friend istream &operator>>(istream &is, ModInt &a) {
		long long t;
		is >> t;
		a = ModInt<mod>(t);
		return (is);
	}
};
using modint = ModInt<MOD>;

//Matrix_Repeated_Multiplication_Mod O((N^3)(logK))
template <class T,int N> class Matrix {
public:
    inline static constexpr array<array<T,N>,N> pow(array<array<T,N>,N> matrix, long long K){
        array<array<T,N>,N> res,tmp;
        for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) res[i][j] = (i == j);
        for (; K > 0; K /= 2) {
            if (K & 1) {
                for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) tmp[i][j] = 0;
                for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) for (int k = 0; k < N; ++k) tmp[i][j] += matrix[i][k] * res[k][j];
                res = tmp;
            }
            for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) tmp[i][j] = 0;
            for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) for (int k = 0; k < N; ++k) tmp[i][j] += matrix[i][k] * matrix[k][j];
            matrix = tmp;
        }
        return res;
    }
};

//verify  https://atcoder.jp/contests/dp/tasks/dp_r

int main() {
    array<array<modint,4>,4> a;
    a[0] = {1,2,2,-1};
    a[1] = {0,2,2,-1};
    a[2] = {0,1,0,0};
    a[3] = {0,0,1,0};
    long long N; cin >> N;
    corner(N==1,1);
    corner(N==2,2);
    auto s = Matrix<modint,4>::pow(a,N-2);
    cout << s[0][0]*2+s[0][1]+s[0][2] << endl;
    return 0;
}
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