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 |
|
| 提出日時 | 2018-07-27 23:02:25 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 24 ms / 2,000 ms |
| コード長 | 11,120 bytes |
| コンパイル時間 | 2,280 ms |
| コンパイル使用メモリ | 218,012 KB |
| 最終ジャッジ日時 | 2025-01-06 12:03:17 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 20 |
ソースコード
#pragma GCC optimize ("O3")#include "bits/stdc++.h"using namespace std;using ll = long long int;#define debugos cout#define debug(v) {printf("L%d %s > ",__LINE__,#v);debugos<<(v)<<endl;}#define debugv(v) {printf("L%d %s > ",__LINE__,#v);for(auto e:(v)){debugos<<e<<" ";}debugos<<endl;}#define debuga(m,w) {printf("L%d %s > ",__LINE__,#m);for(int x=0;x<(w);x++){debugos<<(m)[x]<<" ";}debugos<<endl;}#define debugaa(m,h,w) {printf("L%d %s >\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){debugos<<(m)[y][x]<<" ";}debugos<<endl;}}#define ALL(v) (v).begin(),(v).end()#define repeat(cnt,l) for(remove_reference<remove_const<decltype(l)>::type>::type cnt=0;(cnt)<(l);++(cnt))#define rrepeat(cnt,l) for(auto cnt=(l)-1;0<=(cnt);--(cnt))#define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt))#define diterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);--(cnt))const ll MD = 1000000007ll; const long double PI = 3.1415926535897932384626433832795L;inline void assert_call(bool assertion, function<void()> f) { if (!assertion) { cerr << "assertion fault:" << endl; f(); abort(); } }template<typename T1, typename T2> inline ostream& operator <<(ostream &o, const pair<T1, T2> p) { o << '(' << p.first << ':' << p.second << ')';return o; }template<typename Vec> inline ostream& _ostream_vecprint(ostream& os, const Vec& a) {os << '['; for (const auto& e : a) os << ' ' << e << ' '; os << ']'; return os;}template<typename T> inline ostream& operator<<(ostream& o, const vector<T>& v) { return _ostream_vecprint(o, v); }template<typename T, size_t S> inline ostream& operator<<(ostream& o, const array<T, S>& v) { return _ostream_vecprint(o, v); }template<typename T> inline T& maxset(T& to, const T& val) { return to = max(to, val); }template<typename T> inline T& minset(T& to, const T& val) { return to = min(to, val); }void bye(string s, int code = 0) { cout << s << endl; exit(code); }mt19937_64 randdev(8901016);template<typename T> inline T rand(T l, T h) { return uniform_int_distribution<T>(l, h)(randdev); }template<> inline double rand<double>(double l, double h) { return uniform_real_distribution<double>(l, h)(randdev); }template<> inline float rand<float>(float l, float h) { return uniform_real_distribution<float>(l, h)(randdev); }#if defined(_WIN32) || defined(_WIN64)#define getchar_unlocked _getchar_nolock#define putchar_unlocked _putchar_nolock#elif defined(__GNUC__)#else#define getchar_unlocked getchar#define putchar_unlocked putchar#endifnamespace {#define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E)class MaiScanner {public:template<typename T> void input_integer(T& var) {var = 0; T sign = 1;int cc = getchar_unlocked();for (; cc<'0' || '9'<cc; cc = getchar_unlocked())if (cc == '-') sign = -1;for (; '0' <= cc && cc <= '9'; cc = getchar_unlocked())var = (var << 3) + (var << 1) + cc - '0';var = var * sign;}inline int c() { return getchar_unlocked(); }inline MaiScanner& operator>>(int& var) { input_integer<int>(var); return *this; }inline MaiScanner& operator>>(long long& var) { input_integer<long long>(var); return *this; }inline MaiScanner& operator>>(string& var) {int cc = getchar_unlocked();for (; !isvisiblechar(cc); cc = getchar_unlocked());for (; isvisiblechar(cc); cc = getchar_unlocked())var.push_back(cc);return *this;}template<typename IT> void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; }};class MaiPrinter {public:template<typename T>void output_integer(T var) {if (var == 0) { putchar_unlocked('0'); return; }if (var < 0)putchar_unlocked('-'),var = -var;char stack[32]; int stack_p = 0;while (var)stack[stack_p++] = '0' + (var % 10),var /= 10;while (stack_p)putchar_unlocked(stack[--stack_p]);}inline MaiPrinter& operator<<(char c) { putchar_unlocked(c); return *this; }inline MaiPrinter& operator<<(int var) { output_integer<int>(var); return *this; }inline MaiPrinter& operator<<(long long var) { output_integer<long long>(var); return *this; }inline MaiPrinter& operator<<(char* str_p) { while (*str_p) putchar_unlocked(*(str_p++)); return *this; }inline MaiPrinter& operator<<(const string& str) {const char* p = str.c_str();const char* l = p + str.size();while (p < l) putchar_unlocked(*p++);return *this;}template<typename IT> void join(IT begin, IT end, char sep = ' ') { for (bool b = 0; begin != end; ++begin, b = 1) b ? *this << sep << *begin: *this << *begin; }};}MaiScanner scanner;MaiPrinter printer;template<typename T>// typedef double T;class Matrix {public:size_t height_, width_;valarray<T> data_;Matrix(size_t height, size_t width) :height_(height), width_(width), data_(height*width) {}Matrix(size_t height, size_t width, const valarray<T>& data) :height_(height), width_(width), data_(data) {}inline T& operator()(size_t y, size_t x) { return data_[y*width_ + x]; }inline T operator() (size_t y, size_t x) const { return data_[y*width_ + x]; }inline T& at(size_t y, size_t x) { return data_[y*width_ + x]; }inline T at(size_t y, size_t x) const { return data_[y*width_ + x]; }inline void resize(size_t h, size_t w) { height_ = h; width_ = w; data_.resize(h*w); }inline void resize(size_t h, size_t w, T val) { height_ = h; width_ = w; data_.resize(h*w, val); }inline void fill(T val) { data_ = val; }Matrix<T>& setDiag(T val) { for (size_t i = 0, en = min(width_, height_); i < en; ++i)at(i, i) = val; return *this; }void print(ostream& os) {os << "- - -" << endl; // << setprecision(3)for (size_t y = 0; y < height_; ++y) {for (size_t x = 0; x < width_; ++x) {os << setw(7) << at(y, x) << ' ';}os << endl;}}valarray<valarray<T>> to_valarray() const {valarray<valarray<T>> work(height_);for (size_t i = 0; i < height_; ++i) {auto &v = work[i]; v.resize(height_);for (size_t j = 0; j < width_; ++j)v[j] = at(i, j);} return work;}// mathematicsMatrix<T> pow(long long);double det() const; T tr();Matrix<T>& transpose_self(); Matrix<T> transpose() const;struct LU {size_t size;vector<int> pivot;vector<T> elem;};};// IOtemplate<typename T> inline ostream& operator << (ostream& os, Matrix<T> mat) { mat.print(os); return os; }// 掛け算template<typename T> Matrix<T> multiply(const Matrix<T>& mat1, const Matrix<T>& mat2) {assert(mat1.width_ == mat2.height_);Matrix<T> result(mat1.height_, mat2.width_);for (size_t i = 0; i < mat1.height_; i++) {for (size_t j = 0; j < mat2.width_; j++) {for (size_t k = 0; k < mat1.width_; k++) {result(i, j) += mat1(i, k) * mat2(k, j);}}}return result;}template<typename T> valarray<T> multiply(const Matrix<T>& mat1, const valarray<T>& vec2) {assert(mat1.width_ == vec2.size());valarray<T> result(mat1.height_);for (size_t i = 0, j; i < mat1.height_; i++) {for (j = 0; j < mat1.width_; j++) {result[i] += mat1(i, j) * vec2[j];}}return result;}template<typename T> inline Matrix<T>& operator*=(Matrix<T>& mat1, Matrix<T>& mat2) { mat1 = multiply(mat1, mat2); return mat1; }template<typename T> inline Matrix<T> operator*(Matrix<T>& mat1, Matrix<T>& mat2) { return multiply(mat1, mat2); }// スカラーtemplate<typename T> inline Matrix<T>& operator+=(Matrix<T>& mat, T val) { mat.data_ += val; return mat; }template<typename T> inline Matrix<T>& operator*=(Matrix<T>& mat, T val) { mat.data_ *= val; return mat; }template<typename T> inline Matrix<T>& operator/=(Matrix<T>& mat, T val) { mat.data_ /= val; return mat; }template<typename T> inline Matrix<T>& operator^=(Matrix<T>& mat, T val) { mat.data_ ^= val; return mat; }// 行列template<typename T> inline Matrix<T>& operator+=(Matrix<T>& mat1, Matrix<T>& mat2) { mat1.data_ += mat2.data_; return mat1; }template<typename T> inline Matrix<T> operator+(Matrix<T>& mat1, Matrix<T>& mat2) { return Matrix<T>(mat1.height_, mat1.width_, mat1.data_ + mat2.data_); }template<typename T> Matrix<T> Matrix<T>::pow(long long p) {assert(height_ == width_);Matrix<T> a = *this;Matrix<T> b(height_, height_); b.setDiag(1);while (0 < p) {if (p % 2) {b *= a;}a *= a; p /= 2;}return b;}class llmod {private:ll val_;inline ll cut(ll v) const { return ((v%MOD) + MOD) % MOD; }public:static const ll MOD = MD; // <=llmod() : val_(0) {}llmod(ll num) :val_(cut(num)) {}llmod(const llmod& lm) : val_(lm.val_) {}inline operator ll() const { return val_; }inline ll operator *() const { return val_; }inline llmod& operator=(const llmod& lm) { val_ = lm.val_; return *this; }inline llmod& operator=(ll v) { val_ = cut(v); return *this; }inline llmod& operator+=(ll v) { val_ = cut(val_ + v); return *this; }inline llmod& operator+=(const llmod& l) { val_ = cut(val_ + l.val_); return *this; }inline llmod& operator-=(ll v) { val_ = cut(val_ - v); return *this; }inline llmod& operator-=(const llmod& l) { val_ = cut(val_ - l.val_); return *this; }inline llmod& operator*=(ll v) { val_ = cut(val_ * v); return *this; }inline llmod& operator*=(const llmod& l) { val_ = cut(val_ * l.val_); return *this; }inline llmod& operator++() { val_ = (val_ + 1) % MOD; return *this; }inline llmod operator++(int) { llmod t = *this; val_ = (val_ + 1) % MOD; return t; }};inline ostream& operator<<(ostream& os, const llmod& l) { os << *l; return os; }inline llmod operator+(llmod t, const llmod& r) { return t += r; }inline llmod operator-(llmod t, const llmod& r) { return t -= r; }inline llmod operator*(llmod t, const llmod& r) { return t *= r; }// MEMO : 逆元...powm(n,MD-2)llmod pow(llmod x, ll p) {llmod y = 1;while (0 < p) {if (p % 2)y *= x;x *= x;p /= 2;}return y;}inline llmod& operator/=(llmod& l, const llmod& r) { return l *= pow(r, llmod::MOD - 2); }int main() {ll N;cin >> N;if (N < 3) {vector<int> hoge = {0,1,2};cout << hoge[N] << endl;return 0;}Matrix<llmod> mat(4, 4, {1,1,2,0,1,0,0,0,1,0,1,0,1,1,2,1});auto mp = mat.pow(N-2);valarray<llmod> v = {1,1,1,2};auto w = multiply(mp, v);cout << *w[3] << endl;return 0;}