結果
問題 | No.891 隣接3項間の漸化式 |
ユーザー |
![]() |
提出日時 | 2019-09-20 22:26:55 |
言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 2 ms / 2,000 ms |
コード長 | 22,950 bytes |
コンパイル時間 | 1,823 ms |
コンパイル使用メモリ | 137,380 KB |
実行使用メモリ | 5,376 KB |
最終ジャッジ日時 | 2024-09-14 18:18:30 |
合計ジャッジ時間 | 2,986 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge6 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 39 |
ソースコード
#ifdef stderr_path#define LOCAL#define _GLIBCXX_DEBUG#endif#pragma GCC optimize("Ofast")#include <algorithm>#include <bitset>#include <cassert>#include <chrono>#include <complex>#include <cstring>#include <deque>#include <functional>#include <iomanip>#include <iostream>#include <map>#include <queue>#include <random>#include <set>#include <stack>#include <unordered_map>#include <unordered_set>// #define NDEBUG#define debug_stream std::cerr#define iostream_untie true#define __precision__ 10#define rep(i, n) for(int i = 0; i < int(n); ++i)#define all(v) std::begin(v), std::end(v)#define rall(v) std::rbegin(v), std::rend(v)#define __odd(n) ((n)&1)#define __even(n) (__odd(n) ^ 1)#define __popcount(n) __builtin_popcountll(n)#define __clz32(n) __builtin_clz(int32_t(n))#define __clz64(n) __builtin_clzll(int64_t(n))#define __ctz32(n) __builtin_ctz(int32_t(n))#define __ctz64(n) __builtin_ctzll(int64_t(n))using i64 = int_fast64_t;using pii = std::pair<int, int>;using pll = std::pair<int_fast64_t, int_fast64_t>;template <class T>using heap = std::priority_queue<T>;template <class T>using minheap = std::priority_queue<T, std::vector<T>, std::greater<T>>;template <class T>constexpr T inf = std::numeric_limits<T>::max() / T(2) - T(1123456);namespace execution{std::chrono::system_clock::time_point start_time, end_time;void print_elapsed_time(){end_time = std::chrono::system_clock::now();std::cerr << "\n----- Exec time : ";std::cerr << std::chrono::duration_cast<std::chrono::milliseconds>(end_time - start_time).count();std::cerr << " ms -----\n\n";}struct setupper{setupper(){if(iostream_untie){std::ios::sync_with_stdio(false);std::cin.tie(nullptr);}std::cout << std::fixed << std::setprecision(__precision__);#ifdef stderr_pathif(freopen(stderr_path, "a", stderr)){std::cerr << std::fixed << std::setprecision(__precision__);}elsefclose(stderr);#endif#ifdef stdout_pathif(not freopen(stdout_path, "w", stdout)){freopen("CON", "w", stdout);std::cerr << "Failed to open the stdout file\n\n";}std::cout << "";#endif#ifdef stdin_pathif(not freopen(stdin_path, "r", stdin)){freopen("CON", "r", stdin);std::cerr << "Failed to open the stdin file\n\n";}#endif#ifdef LOCALatexit(print_elapsed_time);start_time = std::chrono::system_clock::now();#endif}} __setupper;} // namespace executionclass myclock_t{std::chrono::system_clock::time_point built_pt, last_pt;int built_ln, last_ln;std::string built_func, last_func;bool is_built;public:explicit myclock_t() : is_built(false){}void build(int crt_ln, const std::string &crt_func){is_built = true;last_pt = built_pt = std::chrono::system_clock::now();last_ln = built_ln = crt_ln, last_func = built_func = crt_func;}void set(int crt_ln, const std::string &crt_func){if(is_built){last_pt = std::chrono::system_clock::now();last_ln = crt_ln, last_func = crt_func;}else{debug_stream << "[ " << crt_ln << " : " << crt_func << " ] "<< "myclock_t::set failed (yet to be built!)\n";}}void get(int crt_ln, const std::string &crt_func){if(is_built){std::chrono::system_clock::time_point crt_pt(std::chrono::system_clock::now());int64_t diff =std::chrono::duration_cast<std::chrono::milliseconds>(crt_pt -last_pt).count();debug_stream << diff << " ms elapsed from"<< " [ " << last_ln << " : " << last_func << " ]";if(last_ln == built_ln) debug_stream << " (when built)";debug_stream << " to"<< " [ " << crt_ln << " : " << crt_func << " ]"<< "\n";last_pt = built_pt, last_ln = built_ln, last_func = built_func;}else{debug_stream << "[ " << crt_ln << " : " << crt_func << " ] "<< "myclock_t::get failed (yet to be built!)\n";}}};#ifdef LOCALmyclock_t __myclock;#define build_clock() __myclock.build(__LINE__, __func__)#define set_clock() __myclock.set(__LINE__, __func__)#define get_clock() __myclock.get(__LINE__, __func__)#else#define build_clock() ((void)0)#define set_clock() ((void)0)#define get_clock() ((void)0)#endifnamespace std{template <class RAitr>void rsort(RAitr __first, RAitr __last){sort(__first, __last, greater<>());}template <class T>size_t hash_combine(size_t seed, T const &key){return seed ^ (hash<T>()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2));}template <class T, class U>struct hash<pair<T, U>>{size_t operator()(pair<T, U> const &pr) const{return hash_combine(hash_combine(0, pr.first), pr.second);}};template <class tuple_t, size_t index = tuple_size<tuple_t>::value - 1>struct tuple_hash_calc{static size_t apply(size_t seed, tuple_t const &t){return hash_combine(tuple_hash_calc<tuple_t, index - 1>::apply(seed, t),get<index>(t));}};template <class tuple_t>struct tuple_hash_calc<tuple_t, 0>{static size_t apply(size_t seed, tuple_t const &t){return hash_combine(seed, get<0>(t));}};template <class... T>struct hash<tuple<T...>>{size_t operator()(tuple<T...> const &t) const{return tuple_hash_calc<tuple<T...>>::apply(0, t);}};template <class T, class U>istream &operator>>(std::istream &s, pair<T, U> &p){return s >> p.first >> p.second;}template <class T, class U>ostream &operator<<(std::ostream &s, const pair<T, U> p){return s << p.first << " " << p.second;}template <class T>istream &operator>>(istream &s, vector<T> &v){for(T &e : v){s >> e;}return s;}template <class T>ostream &operator<<(ostream &s, const vector<T> &v){bool is_front = true;for(const T &e : v){if(not is_front){s << ' ';}else{is_front = false;}s << e;}return s;}template <class tuple_t, size_t index>struct tupleos{static ostream &apply(ostream &s, const tuple_t &t){tupleos<tuple_t, index - 1>::apply(s, t);return s << " " << get<index>(t);}};template <class tuple_t>struct tupleos<tuple_t, 0>{static ostream &apply(ostream &s, const tuple_t &t){return s << get<0>(t);}};template <class... T>ostream &operator<<(ostream &s, const tuple<T...> &t){return tupleos<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(s, t);}template <>ostream &operator<<(ostream &s, const tuple<> &t){return s;}string revstr(string str){reverse(str.begin(), str.end());return str;}} // namespace std#ifdef LOCAL#define dump(...) \debug_stream << "[ " << __LINE__ << " : " << __FUNCTION__ << " ]\n", \dump_func(#__VA_ARGS__, __VA_ARGS__)template <class T>void dump_func(const char *ptr, const T &x){debug_stream << '\t';for(char c = *ptr; c != '\0'; c = *++ptr){if(c != ' ') debug_stream << c;}debug_stream << " : " << x << '\n';}template <class T, class... rest_t>void dump_func(const char *ptr, const T &x, rest_t... rest){debug_stream << '\t';for(char c = *ptr; c != ','; c = *++ptr){if(c != ' ') debug_stream << c;}debug_stream << " : " << x << ",\n";dump_func(++ptr, rest...);}#else#define dump(...) ((void)0)#endiftemplate <class P>void read_range(P __first, P __second){for(P i = __first; i != __second; ++i)std::cin >> *i;}template <class P>void write_range(P __first, P __second){for(P i = __first; i != __second;std::cout << (++i == __second ? '\n' : ' ')){std::cout << *i;}}// substitute y for x.template <class T>void subst(T &x, const T &y){x = y;}// substitue y for x iff x > y.template <class T>bool chmin(T &x, const T &y){return x > y ? x = y, true : false;}// substitue y for x iff x < y.template <class T>bool chmax(T &x, const T &y){return x < y ? x = y, true : false;}template <class T>constexpr T minf(const T &x, const T &y){return std::min(x, y);}template <class T>constexpr T maxf(const T &x, const T &y){return std::max(x, y);}// binary search.template <class int_t, class F>int_t bin(int_t ok, int_t ng, const F &f){while(std::abs(ok - ng) > 1){int_t mid = (ok + ng) / 2;(f(mid) ? ok : ng) = mid;}return ok;}template <class T, class A, size_t N>void init(A (&array)[N], const T &val){std::fill((T *)array, (T *)(array + N), val);}void reset(){}template <class A, class... rest_t>void reset(A &array, rest_t... rest){memset(array, 0, sizeof(array));reset(rest...);}// a integer uniformly and randomly chosen from the interval [l, r).template <typename int_t>int_t rand_int(int_t l, int_t r){static std::random_device seed_gen;static std::mt19937 engine(seed_gen());std::uniform_int_distribution<int_t> unid(l, r - 1);return unid(engine);}// a real number uniformly and randomly chosen from the interval [l, r).template <typename real_t>real_t rand_real(real_t l, real_t r){static std::random_device seed_gen;static std::mt19937 engine(seed_gen());std::uniform_real_distribution<real_t> unid(l, r);return unid(engine);}/* The main code follows. */namespace math{template <int_fast32_t mod>struct modint{int x;constexpr modint() : x(0){}constexpr modint(int_fast64_t y): x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod){}constexpr modint &operator+=(const modint &p){if((x += p.x) >= mod) x -= mod;return *this;}constexpr modint &operator++(){return ++x, *this;}constexpr modint operator++(int){modint t = *this;return ++x, t;}constexpr modint &operator-=(const modint &p){if((x += mod - p.x) >= mod) x -= mod;return *this;}constexpr modint &operator--(){return --x, *this;}constexpr modint operator--(int){modint t = *this;return --x, t;}constexpr modint &operator*=(const modint &p){return x = (int_fast64_t)x * p.x % mod, *this;}constexpr modint &operator/=(const modint &p){return *this *= inverse(p);}// constexpr modint &operator%=(int m) { return x %= m, *this; }constexpr modint operator-() const{return modint(-x);}constexpr modint operator+(const modint &p) const{return modint(*this) += p;}constexpr modint operator-(const modint &p) const{return modint(*this) -= p;}constexpr modint operator*(const modint &p) const{return modint(*this) *= p;}constexpr modint operator/(const modint &p) const{return modint(*this) /= p;}// constexpr modint operator%(int m) const { return modint(*this) %= m;// }constexpr bool operator==(const modint &p) const{return x == p.x;}constexpr bool operator!=(const modint &p) const{return x != p.x;}constexpr bool operator!() const{return !x;}// constexpr bool operator>(const modint &p) const { return x > p.x; }// constexpr bool operator<(const modint &p) const { return x < p.x; }// constexpr bool operator>=(const modint &p) const { return x >= p.x; }// constexpr bool operator<=(const modint &p) const { return x <= p.x; }constexpr friend modint inverse(const modint &p){int a = p.x, b = mod, u = 1, v = 0;while(b > 0){int t = a / b;a -= t * b;a ^= b ^= a ^= b;u -= t * v;u ^= v ^= u ^= v;}return modint(u);}constexpr friend modint pow(modint p, int_fast64_t e){if(e < 0) e = (e % (mod - 1) + mod - 1) % (mod - 1);modint ret = 1;while(e){if(e & 1) ret *= p;p *= p;e >>= 1;}return ret;}friend std::ostream &operator<<(std::ostream &s, const modint &p){return s << p.x;}friend std::istream &operator>>(std::istream &s, modint &p){int_fast64_t x;p = modint((s >> x, x));return s;}};} // namespace mathtemplate <class K>// K must be a field.struct matrix{std::vector<std::vector<K>> mat;matrix(){}matrix(size_t n){assign(n, n);}matrix(size_t h, size_t w){assign(h, w);}matrix(const matrix &x) : mat(x.mat){}matrix(const std::vector<std::vector<K>> _mat) : mat(_mat){}void resize(size_t h, size_t w, const K v = K(0)){mat.resize(h, std::vector<K>(w, v));}void assign(size_t h, size_t w, const K v = K()){mat.assign(h, std::vector<K>(w, v));}size_t height() const{return mat.size();}size_t width() const{return mat.empty() ? 0 : mat[0].size();}bool is_square() const{return height() == width();}std::vector<K> &operator[](const size_t i){return mat[i];}static matrix identity(size_t n){matrix ret(n, n);for(size_t i = 0; i < n; ++i)ret[i][i] = K(1);return ret;}matrix operator-() const{size_t h = height(), w = width();matrix res(*this);for(size_t i = 0; i < h; ++i){for(size_t j = 0; j < w; ++j){res[i][j] = -mat[i][j];}}return res;}matrix operator&(const matrix &x) const{return matrix(*this) &= x;}matrix operator|(const matrix &x) const{return matrix(*this) |= x;}matrix operator^(const matrix &x) const{return matrix(*this) ^= x;}matrix operator+(const matrix &x) const{return matrix(*this) += x;}matrix operator-(const matrix &x) const{return matrix(*this) -= x;}matrix operator*(const matrix &x) const{return matrix(*this) *= x;}matrix &operator&=(const matrix &x){size_t h = height(), w = width();assert(h == x.height() and w == x.width());for(size_t i = 0; i < h; ++i){for(size_t j = 0; j < w; ++j){mat[i][j] &= x.mat[i][j];}}return *this;}matrix &operator|=(const matrix &x){size_t h = height(), w = width();assert(h == x.height() and w == x.width());for(size_t i = 0; i < h; ++i){for(size_t j = 0; j < w; ++j){mat[i][j] |= x.mat[i][j];}}return *this;}matrix &operator^=(const matrix &x){size_t h = height(), w = width();assert(h == x.height() and w == x.width());for(size_t i = 0; i < h; ++i){for(size_t j = 0; j < w; ++j){mat[i][j] ^= x.mat[i][j];}}return *this;}matrix &operator+=(const matrix &x){size_t h = height(), w = width();assert(h == x.height() and w == x.width());for(size_t i = 0; i < h; ++i){for(size_t j = 0; j < w; ++j){mat[i][j] += x.mat[i][j];}}return *this;}matrix &operator-=(const matrix &x){size_t h = height(), w = width();assert(h == x.height() and w == x.width());for(size_t i = 0; i < h; ++i){for(size_t j = 0; j < w; ++j){mat[i][j] -= x.mat[i][j];}}return *this;}matrix &operator*=(const matrix &x){size_t l = height(), m = width(), n = x.width();assert(m == x.height());matrix res(l, n);for(size_t i = 0; i < l; ++i){for(size_t j = 0; j < m; ++j){for(size_t k = 0; k < n; ++k){res[i][k] += mat[i][j] * x.mat[j][k];}}}return *this = res;}friend matrix pow(matrix x, int_fast64_t n){assert(x.is_square());matrix res = identity(x.height());while(n){if(n & 1) res *= x;x *= x;n >>= 1;}return res;}friend matrix inverse(const matrix &x){assert(x.is_square());size_t n = x.height();matrix ext_x(x), e(identity(n)), res(n);for(size_t i = 0; i < n; ++i)ext_x[i].insert(end(ext_x[i]), begin(e[i]), end(e[i]));ext_x = ext_x.row_canonical_form();for(size_t i = 0; i < n; ++i){if(std::vector<K>(begin(ext_x[i]), begin(ext_x[i]) + n) != e[i])return matrix();res[i] = std::vector<K>(begin(ext_x[i]) + n, end(ext_x[i]));}return res;}matrix row_canonical_form(){size_t h = height(), w = width(), rank = 0;matrix res(*this);for(size_t j = 0; j < w; ++j){bool piv = false;for(size_t i = rank; i < h; ++i){if(res[i][j] != K(0)){if(piv){K r = -res[i][j];for(size_t k = j; k < w; ++k){res[i][k] += res[rank][k] * r;}}else{swap(res[rank], res[i]);K r = res[rank][j];for(size_t k = j; k < w; ++k){res[rank][k] /= r;}for(size_t k = 0; k < rank; ++k){r = -res[k][j];for(size_t l = j; l < w; ++l){res[k][l] += res[rank][l] * r;}}piv = true;}}}if(piv) ++rank;}return res;}K det() const{matrix<K> x(*this);assert(is_square());size_t n = height();K res(1);for(size_t j = 0; j < n; ++j){bool piv = false;for(size_t i = j; i < n; ++i){if(x[i][j] != K(0)){if(piv){const K r = -x[i][j];for(size_t k = j; k < n; ++k){x[i][k] += x[j][k] * r;}}else{swap(x[i], x[j]);if(i != j) res = -res;const K r = x[j][j];res *= r;for(size_t k = j; k < n; ++k){x[j][k] /= r;}piv = true;}}}if(not piv){return K(0);}}return res;}friend std::istream &operator>>(std::istream &s, matrix &x){size_t h = x.height(), w = x.width();for(size_t i = 0; i < h; ++i){for(size_t j = 0; j < w; ++j){s >> x[i][j];}}return s;}friend std::ostream &operator<<(std::ostream &s, const matrix &x){size_t h = x.height(), w = x.width();for(size_t i = 0; i < h; ++i){if(i) s << "\n";for(size_t j = 0; j < w; ++j){s << (j ? " " : "") << x.mat[i][j];}}return s;}};using namespace std;using namespace math;signed main(){void __solve();void __precalc();unsigned int t = 1;// cin >> t;__precalc();#ifdef LOCALt=3;#endifwhile(t--){__solve();}}void __precalc(){}void __solve(){int a,b,n; cin>>a>>b>>n;matrix<modint<1000000007>> m(3,3),v(3,1);m[0]={a,b,0},m[1]={1,0,0},m[2]={0,1,0};m=pow(m,n);v[0][0]=a,v[1][0]=1;v=m*v;std::cout << v[2][0] << "\n";}