結果
問題 | No.1073 無限すごろく |
ユーザー |
![]() |
提出日時 | 2020-06-05 23:09:08 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 2 ms / 2,000 ms |
コード長 | 18,187 bytes |
コンパイル時間 | 2,868 ms |
コンパイル使用メモリ | 228,436 KB |
最終ジャッジ日時 | 2025-01-10 22:56:54 |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 30 |
ソースコード
#pragma region preprocessor#ifdef LOCAL//*#define _GLIBCXX_DEBUG // gcc/*/#define _LIBCPP_DEBUG 0 // clang//*/#define __clock__// #define __buffer_check__#else#pragma GCC optimize("Ofast")// #define __buffer_check__// #define NDEBUG#endif#define __precision__ 15#define iostream_untie true#include <bits/stdc++.h>#include <ext/rope>#define __all(v) std::begin(v), std::end(v)#define __rall(v) std::rbegin(v), std::rend(v)#define __popcount(n) __builtin_popcountll(n)#define __clz32(n) __builtin_clz(n)#define __clz64(n) __builtin_clzll(n)#define __ctz32(n) __builtin_ctz(n)#define __ctz64(n) __builtin_ctzll(n)#ifdef __clock__#include "clock.hpp"#else#define build_clock() ((void)0)#define set_clock() ((void)0)#define get_clock() ((void)0)#endif#ifdef LOCAL#include "dump.hpp"#define mesg(str) std::cerr << "[ " << __LINE__ << " : " << __FUNCTION__ << " ] " << str << "\n"#else#define dump(...) ((void)0)#define mesg(str) ((void)0)#endif#pragma endregion // preprocessor#pragma region std-overloadnamespace std{// hashtemplate <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); } };// iostreamtemplate <class T, class U> istream &operator>>(istream &is, pair<T, U> &p) { return is >> p.first >> p.second; }template <class T, class U> ostream &operator<<(ostream &os, const pair<T, U> &p) { return os << p.first << ' ' << p.second; }template <class tuple_t, size_t index> struct tupleis { static istream &apply(istream &is, tuple_t &t) { tupleis<tuple_t, index - 1>::apply(is, t); return is >> get<index>(t); } };template <class tuple_t> struct tupleis<tuple_t, SIZE_MAX> { static istream &apply(istream &is, tuple_t &t) { return is; } };template <class... T> istream &operator>>(istream &is, tuple<T...> &t) { return tupleis<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(is, t); }template <> istream &operator>>(istream &is, tuple<> &t) { return is; }template <class tuple_t, size_t index> struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos<tuple_t, index - 1>::apply(os, t); return os << ' ' << get<index>(t); } };template <class tuple_t> struct tupleos<tuple_t, 0> { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } };template <class... T> ostream &operator<<(ostream &os, const tuple<T...> &t) { return tupleos<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(os, t); }template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; }template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> =nullptr>istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; }template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> =nullptr>ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; returnos; }} // namespace std#pragma endregion // std-overload#pragma region executive-settingnamespace setting{using namespace std;using namespace chrono;system_clock::time_point start_time, end_time;long long get_elapsed_time() { end_time = system_clock::now(); return duration_cast<milliseconds>(end_time - start_time).count(); }void print_elapsed_time() { cerr << "\n----- Exec time : " << get_elapsed_time() << " ms -----\n\n"; }void buffer_check() { char bufc; if(cin >> bufc) cerr << "\n\033[1;35mwarning\033[0m: buffer not empty.\n"; }struct setupper{setupper(){if(iostream_untie) ios::sync_with_stdio(false), cin.tie(nullptr);cout << fixed << setprecision(__precision__);#ifdef stderr_pathfreopen(stderr_path, "a", stderr);#endif#ifdef LOCALcerr << fixed << setprecision(__precision__) << boolalpha << "\n----- stderr at LOCAL -----\n\n";#endif#ifdef __clock__start_time = system_clock::now();atexit(print_elapsed_time);#endif#ifdef __buffer_check__atexit(buffer_check);#endif}} __setupper; // struct setupper} // namespace setting#pragma endregion // executive-setting#pragma region fucntion-utility// lambda wrapper for recursive method.template <class lambda_type>class make_recursive{lambda_type func;public:make_recursive(lambda_type &&f) : func(std::move(f)) {}template <class... Args> auto operator()(Args &&... args) const { return func(*this, std::forward<Args>(args)...); }};template <class T, class... types> T read(types... args) noexcept { typename std::remove_const<T>::type obj(args...); std::cin >> obj; return obj; }// #define input(type, var, ...) type var{read<type>(__VA_ARGS__)}// substitute y for x if x > y.template <class T> inline bool chmin(T &x, const T &y) { return x > y ? x = y, true : false; }// substitute y for x if x < y.template <class T> inline bool chmax(T &x, const T &y) { return x < y ? x = y, true : false; }// binary search on discrete range.template <class iter_type, class pred_type>iter_type binary(iter_type __ok, iter_type __ng, pred_type pred){assert(__ok != __ng);std::ptrdiff_t dist(__ng - __ok);while(std::abs(dist) > 1){iter_type mid(__ok + dist / 2);if(pred(mid)) __ok = mid, dist -= dist / 2;else __ng = mid, dist /= 2;}return __ok;}// binary search on real numbers.template <class pred_type>long double binary(long double __ok, long double __ng, const long double eps, pred_type pred){assert(__ok != __ng);while(std::abs(__ok - __ng) > eps){long double mid{(__ok + __ng) / 2};(pred(mid) ? __ok : __ng) = mid;}return __ok;}// trinary search on discrete range.template <class iter_type, class comp_type>iter_type trinary(iter_type __first, iter_type __last, comp_type comp){assert(__first < __last);std::ptrdiff_t dist(__last - __first);while(dist > 2){iter_type __left(__first + dist / 3), __right = (__first + dist * 2 / 3);if(comp(__left, __right)) __last = __right, dist = dist * 2 / 3;else __first = __left, dist -= dist / 3;}if(dist > 1 && comp(next(__first), __first)) ++__first;return __first;}// trinary search on real numbers.template <class comp_type>long double trinary(long double __first, long double __last, const long double eps, comp_type comp){assert(__first < __last);while(__last - __first > eps){long double __left{(__first * 2 + __last) / 3}, __right{(__first + __last * 2) / 3};if(comp(__left, __right)) __last = __right;else __first = __left;}return __first;}// size of array.template <class A, size_t N> size_t size(A (&array)[N]) { return N; }// be careful that val is type-sensitive.template <class T, class A, size_t N> void init(A (&array)[N], const T &val) { std::fill((T*)array, (T*)(array + N), val); }#pragma endregion // function-utility#pragma region using-aliasusing namespace std;using i32 = int_least32_t; using i64 = int_least64_t; using u32 = uint_least32_t; using u64 = uint_least64_t;using p32 = pair<i32, i32>; using p64 = pair<i64, i64>;template <class T, class Comp = less<T>> using heap = priority_queue<T, vector<T>, Comp>;template <class T> using hashset = unordered_set<T>;template <class Key, class Value> using hashmap = unordered_map<Key, Value>;using namespace __gnu_cxx;#pragma endregion // using-alias#pragma region library#include <cassert>#include <iostream>#include <valarray>template <class Ring>class matrix{struct identity_wrapper{template <bool arith, class = void>struct check { static Ring identity() { return Ring::identity(); } };template <class void_t>struct check<true, void_t> { static Ring identity() { return 1; } };operator Ring() { return check<std::is_arithmetic<Ring>::value>::identity(); }};using row_type = std::valarray<Ring>;using data_type = std::valarray<row_type>;data_type data;friend std::istream &operator>>(std::istream &is, matrix &mat){for(size_t i = 0; i != mat.rows(); ++i)for(size_t j = 0; j != mat.columns(); ++j)is >> mat[i][j];return is;}friend std::ostream &operator<<(std::ostream &os, const matrix &mat){for(size_t i = 0; i != mat.rows(); ++i){if(i) os << "\n";for(size_t j = 0; j != mat.columns(); ++j) os << (j ? " " : "") << mat[i][j];}return os;}friend matrix transpose(const matrix &mat){matrix res(mat.columns(), mat.rows());for(size_t i{mat.columns()}; i--;)for(size_t j{mat.rows()}; j--;)res[i][j] = mat[j][i];return res;}public:explicit matrix(size_t _n = 1) : matrix(_n, _n) {}matrix(size_t _r, size_t _c) : data(row_type(_c), _r) {}matrix(const data_type &_data) : data(_data) {}size_t rows() const { return data.size(); }size_t columns() const { return data[0].size(); }row_type &operator[](const size_t i) { assert(i < data.size()); return data[i]; }const row_type &operator[](const size_t i) const { assert(i < data.size()); return data[i]; }matrix operator-() const { return {-data}; }matrix &operator+=(const matrix &rhs) { data += rhs.data; return *this; }matrix &operator-=(const matrix &rhs) { data -= rhs.data; return *this; }matrix &operator*=(matrix rhs) noexcept{assert(columns() == rhs.rows());rhs = transpose(rhs);for(row_type &row : data){const row_type copied{row};for(size_t j{rhs.rows()}; j--;) row[j] = (copied * rhs[j]).sum();}return *this;}matrix operator+(const matrix &rhs) const { return matrix{*this} += rhs; }matrix operator-(const matrix &rhs) const { return matrix{*this} -= rhs; }matrix operator*(const matrix &rhs) const { return matrix{*this} *= rhs; }friend row_type &operator*=(row_type &lhs, const matrix &rhs) { return lhs = lhs * rhs; }friend row_type operator*(row_type &lhs, const matrix &rhs){assert(lhs.size() == rhs.rows());row_type res(rhs.columns());for(size_t k{lhs.size()}; k--;)for(size_t j{rhs.columns()}; j--;)res[j] += lhs[k] * rhs[k][j];return res;}static matrix identity(const size_t _n){matrix ide(_n);for(size_t i{_n}; i--;) ide[i][i] = identity_wrapper();return ide;}friend matrix pow(matrix mat, unsigned long long exp){matrix res{identity(mat.rows())};for(assert(mat.rows() == mat.columns()); exp; mat *= mat, exp >>= 1) if(exp & 1) res *= mat;return res;}}; // class matrix#ifndef modint_hpp#define modint_hpp#include <cassert>#include <iostream>template <int mod>class modint{int val;public:static constexpr modint identity() noexcept { return 1; }constexpr modint() noexcept : val{0} {}constexpr modint(long long x) noexcept : val((x %= mod) < 0 ? mod + x : x) {}constexpr long long value() const noexcept { return val; }constexpr modint operator++(int) noexcept { modint t = *this; return ++val, t; }constexpr modint operator--(int) noexcept { modint t = *this; return --val, t; }constexpr modint &operator++() noexcept { return ++val, *this; }constexpr modint &operator--() noexcept { return --val, *this; }constexpr modint operator-() const noexcept { return modint(-val); }constexpr modint &operator+=(const modint &other) noexcept { return (val += other.val) < mod ? 0 : val -= mod, *this; }constexpr modint &operator-=(const modint &other) noexcept { return (val += mod - other.val) < mod ? 0 : val -= mod, *this; }constexpr modint &operator*=(const modint &other) noexcept { return val = (long long)val * other.val % mod, *this; }constexpr modint &operator/=(const modint &other) noexcept { return *this *= inverse(other); }constexpr modint operator+(const modint &other) const noexcept { return modint(*this) += other; }constexpr modint operator-(const modint &other) const noexcept { return modint(*this) -= other; }constexpr modint operator*(const modint &other) const noexcept { return modint(*this) *= other; }constexpr modint operator/(const modint &other) const noexcept { return modint(*this) /= other; }constexpr bool operator==(const modint &other) const noexcept { return val == other.val; }constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; }constexpr bool operator!() const noexcept { return !val; }friend constexpr modint operator+(long long x, modint y) noexcept { return modint(x) + y; }friend constexpr modint operator-(long long x, modint y) noexcept { return modint(x) - y; }friend constexpr modint operator*(long long x, modint y) noexcept { return modint(x) * y; }friend constexpr modint operator/(long long x, modint y) noexcept { return modint(x) / y; }static constexpr modint inverse(const modint &other) noexcept{assert(other != 0);int a{mod}, b{other.val}, u{}, v{1}, t{};while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v;return {u};}static constexpr modint pow(modint other, long long e) noexcept{if(e < 0) e = e % (mod - 1) + mod - 1;modint res{1};while(e) { if(e & 1) res *= other; other *= other, e >>= 1; }return res;}friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; }friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other = {(is >> val, val)}; return is; }}; // class modinttemplate <>class modint<2>{bool val;public:static constexpr modint identity() noexcept { return 1; }constexpr modint(bool x = false) noexcept : val{x} {}constexpr modint(int x) noexcept : val(x & 1) {}constexpr modint(long long x) noexcept : val(x & 1) {}constexpr operator bool() const noexcept { return val; }constexpr bool value() const noexcept { return val; }constexpr modint &operator+=(const modint &other) noexcept { return val ^= other.val, *this; }constexpr modint &operator-=(const modint &other) noexcept { return val ^= other.val, *this; }constexpr modint &operator*=(const modint &other) noexcept { return val &= other.val, *this; }constexpr modint &operator/=(const modint &other) noexcept { assert(other.val); return *this; }constexpr modint operator!() const noexcept { return !val; }constexpr modint operator-() const noexcept { return *this; }constexpr modint operator+(const modint &other) const noexcept { return val != other.val; }constexpr modint operator-(const modint &other) const noexcept { return val != other.val; }constexpr modint operator*(const modint &other) const noexcept { return val && other.val; }constexpr modint operator/(const modint &other) const noexcept { assert(other.val); return *this; }constexpr bool operator==(const modint &other) const noexcept { return val == other.val; }constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; }friend constexpr modint operator+(long long x, modint y) noexcept { return x & 1 ? !y : y; }friend constexpr modint operator-(long long x, modint y) noexcept { return x & 1 ? !y : y; }friend constexpr modint operator*(long long x, modint y) noexcept { return x & 1 ? y : modint<2>{0}; }friend constexpr modint operator/(long long x, modint y) noexcept { assert(y.val); return x & 1 ? y : modint<2>{0}; }friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; }friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other.val = (is >> val, val & 1); return is; }}; // class modint specialization#endif // modint_hpp#pragma endregion // library#pragma region main-codestruct solver; template <class> void main_(); int main() { main_<solver>(); }template <class solver> void main_(){unsigned t = 1;#ifdef LOCALt = 1;#endif// t = -1; // infinite loop// cin >> t; // case number givenwhile(t--) solver();}struct solver{solver(){i64 n; cin>>n;using mint=modint<(int)1e9+7>;matrix<modint<(int)1e9+7>> a(6,6);for(int i=0; i<6; ++i) a[0][i]=mint(1)/6;for(int i=1; i<6; ++i) a[i][i-1]=1;a=pow(a,n);mint p[6]={1};mint ans;for(int i=0; i<6; ++i){ans+=a[5][5-i]*p[i];for(int j=1; j<6; ++j){if(i+j<6) p[i+j]+=p[i]/6;}}cout << ans << "\n";}};#pragma endregion // main-code