結果

問題 No.194 フィボナッチ数列の理解(1)
ユーザー tu-satu-sa
提出日時 2018-07-18 04:19:36
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 10 ms / 5,000 ms
コード長 7,533 bytes
コンパイル時間 2,128 ms
コンパイル使用メモリ 179,772 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-11-28 15:20:24
合計ジャッジ時間 3,567 ms
ジャッジサーバーID
（参考情報） 		judge3 / 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 * 37
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 # 

////////////////////////////////////////
///  tu3 pro-con template            ///
////////////////////////////////////////
#include "bits/stdc++.h"
using namespace std;

// -- loop macros -- //
#define REP(i,n) for (int i = 0; i < (n); i++)
#define RREP(i,n) for (int i = (n)-1; i >= 0; i--)
#define FOR(i,s,n) for (int i = (int)(s); i < (n); i++)
#define RFOR(i,s,n) for (int i = (n)-1; i >= (s); i--)
#define FOREACH(i,container) for (auto &&i : container)
#define allof(c) c.begin(), c.end()
#define partof(c,i,n) c.begin() + (i), c.begin() + (i) + (n)

// -- functors -- //
#define PREDICATE(t,a,exp) [&](const t & a) -> bool { return exp; }
#define COMPARISON(t,a,b,exp) [&](const t & a, const t & b) -> bool { return exp; }

#define PRED(a,exp) [&](const auto & a) -> bool { return exp; }
#define COMP(a,b,exp) [&](const auto & a, const auto & b) -> bool { return exp; }
#define CONV1(a,exp) [&](const auto & a) -> auto { return exp; }
#define CONV2(a,b,exp) [&](const auto & a, const auto & b) -> auto { return exp; }
#define CONV3(a,b,c,exp) [&](const auto & a, const auto & b, const auto & c) -> auto { return exp; }

// -- typedefs -- //
#define EPS 1e-9

typedef unsigned int uint;
typedef long long llong;
typedef unsigned long long ullong;

// -- I/O Helper -- //
struct _Reader { _Reader(istream &cin) :cin(cin) {} istream &cin; template <class T> _Reader operator ,(T &rhs) { cin >> rhs; return *this; } };
struct _Writer { _Writer(ostream &cout) :cout(cout) {} ostream &cout; bool f{ false }; template <class T> _Writer operator ,(const T &rhs) { cout << (f ? " " : "") << rhs; f = true; return *this; } };
#define READ(t,...) t __VA_ARGS__; (_Reader{cin}), __VA_ARGS__
#define WRITE(...) (_Writer{cout}), __VA_ARGS__; cout << '\n'
#define DEBUG(...) (_Writer{cerr}), __VA_ARGS__; cerr << '\n'

// -- vevector -- //
template <class T> struct vevector : public vector<vector<T>> { vevector(size_t n = 0, size_t m = 0, const T &initial = T()) : vector<vector<T>>(n, vector<T>(m, initial)) { } };
template <class T> struct vevevector : public vector<vevector<T>> { vevevector(size_t n = 0, size_t m = 0, size_t l = 0, const T &initial = T()) : vector<vevector<T>>(n, vevector<T>(m, l, initial)) { } };
template <class T> struct vevevevector : public vector<vevevector<T>> { vevevevector(size_t n = 0, size_t m = 0, size_t l = 0, size_t k = 0, const T &initial = T()) : vector<vevevector<T>>(n, vevevector<T>(m, l, k, initial)) { } };

namespace std {
	template <class T1, class T2> inline istream & operator >> (istream & in, pair<T1, T2> &p) { in >> p.first >> p.second; return in; }
	template <class T1, class T2> inline ostream & operator << (ostream &out, const pair<T1, T2> &p) { out << p.first << " " << p.second; return out; }
}

template <class T> T read() { T t; cin >> t; return t; }
template <class T> vector<T> read(int n) { vector<T> v; REP(i, n) { v.push_back(read<T>()); } return v; }
template <class T> vevector<T> read(int n, int m) { vevector<T> v; REP(i, n) v.push_back(read<T>(m)); return v; }
template <class T> vector<T> readjag() { return read<T>(read<int>()); }
template <class T> vevector<T> readjag(int n) { vevector<T> v; REP(i, n) v.push_back(readjag<T>()); return v; }

template <class T> struct iter_pair_t { T beg, end; };
template <class T> iter_pair_t<T> iter_pair(T beg, T end) { return iter_pair_t<T>{beg, end}; }
template <class T> ostream & operator << (ostream &out, iter_pair_t<T> v) { if (v.beg != v.end) { out << *v.beg++; while (v.beg != v.end) { out << " " << *v.beg++; } } return out; }
template <class T1> ostream & operator << (ostream &out, const vector<T1> &v) { return out << iter_pair(begin(v), end(v)); }

// -- etc -- //
template <class T> T infinity_value();
#define DEFINE_INFINITY_VALUE(T, val) template <> constexpr T infinity_value<T>() { return (val); }
DEFINE_INFINITY_VALUE(int, 1 << 28);
DEFINE_INFINITY_VALUE(uint, 1u << 28);
DEFINE_INFINITY_VALUE(llong, 1ll << 60);
DEFINE_INFINITY_VALUE(ullong, 1ull << 60);
DEFINE_INFINITY_VALUE(double, HUGE_VAL);
DEFINE_INFINITY_VALUE(float, HUGE_VAL);
#define INF(T) infinity_value<T>()

inline int sign_of(double x) { return (abs(x) < EPS ? 0 : x > 0 ? 1 : -1); }
template <class TInt> bool in_range(TInt val, TInt min, TInt max) { return val >= min && val < max; }
template <> bool in_range<double>(double val, double min, double max) { return val - min > -EPS && val - max < EPS; }
template <> bool in_range<float>(float val, float min, float max) { return val - min > -EPS && val - max < EPS; }
template <class TInt> bool in_range2d(TInt x, TInt y, TInt w, TInt h) { return x >= 0 && x < w && y >= 0 && y < h; }
vector<int> iotavn(int start, int count) { vector<int> r(count); iota(allof(r), start);	return r; }

//// start up ////
void solve();
int main()
{
	//// for local debugging
	//freopen("input.txt", "r", stdin);
	//freopen("output.txt", "w", stdout);

	//auto classic_table = ctype<char>::classic_table();
	//vector<ctype<char>::mask> ctable(classic_table, classic_table + ctype<char>::table_size);
	//ctable[':'] |= ctype_base::space; // as delimitor
	//ctable['/'] |= ctype_base::space; // as delimitor
	//cin.imbue(locale(cin.getloc(), new ctype<char>(ctable.data())));

	cin.tie(nullptr);
	ios_base::sync_with_stdio(false);
	cout << fixed;
	cout << setprecision(std::numeric_limits<double>::max_digits10);
	solve();

	return 0;
}

// 初項A の n-bonacci 数列の第k項
// first = F[k]
// second = ΣF[k]
template <llong mod>
pair<llong, llong> nbonacci(vector<llong> A, llong k)
{
	int N = static_cast<int>(A.size());

	if (k < N)
	{
		return pair<llong, llong>(A[k] % mod, accumulate(partof(A, 0, k + 1), 0ll, CONV2(a, b, (a + b) % mod)));
	}

	// O(N^3 * log(k)) N=1e10, k=1e20 で約 6e7
	if (N <= 100)
	{
		struct Matrix
		{
			typedef llong T;
			vevector<T> value;
			static Matrix Identity(size_t n) { Matrix e(n, n); REP(i, n) e[i][i] = 1; return e; }

			Matrix(size_t n, size_t m) : value(n, m) { }
			vector<T> &operator [](int i) { return value[i]; }
			const vector<T> &operator [](int i) const { return value[i]; }

			Matrix operator * (const Matrix &m) const
			{
				size_t H = value.size(), X = value[0].size(), W = m[0].size();
				assert(X == m.value.size());
				Matrix mtx(H, W);
				REP(i, H) REP(j, W) REP(k, X) { mtx[i][j] = (mtx[i][j] + value[i][k] * m[k][j]) % mod; }
				return mtx;
			}

			Matrix power(llong y) const
			{
				size_t X = value.size(); assert(X == value[0].size());
				Matrix r = Identity(X);
				Matrix x = *this;
				for (; y > 0; y >>= 1)
				{
					if (y & 1) { r = r * x; }
					x = x * x;
				}
				return r;
			}
		};

		Matrix m(N + 1, N + 1);
		// 1 1 1 ... 1 1
		// 0 1 1 ... 1 1
		// 0 1 0 ... 0 0
		// 0 0 1 ... 0 0
		//       ...
		// 0 0 0 ... 1 0
		REP(i, N + 1) { m[0][i] = 1; }
		REP(i, N) { m[1][i + 1] = 1; }
		REP(i, N - 1) { m[i + 2][i + 1] = 1; }
		m = m.power(k - N + 1);

		Matrix v(N + 1, 1);
		v[0][0] = accumulate(allof(A), 0ll, CONV2(a, b, (a + b) % mod));
		REP(i, N) { v[N - i][0] = A[i]; }
		auto c = m * v;
		return pair<llong, llong>(c[1][0], c[0][0]);
	}

	// O(k)
	{
		llong f = accumulate(allof(A), 0ll, CONV2(a, b, (a + b) % mod));
		llong s = f;

		FOR(i, N, k)
		{
			llong x = A[i % N];
			A[i % N] = f;
			s = (s + f) % mod;
			f = (f + f - x + mod) % mod;
		}
		return pair<llong, llong>(f, (s + f) % mod);
	}
}

////////////////////
/// template end ///
////////////////////

void solve()
{
	READ(llong, N, K);
	vector<llong> A = read<llong>(N);
	auto ans = nbonacci<1000000007LL>(A, K - 1);
	WRITE(ans);
}
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