結果
問題 | No.2122 黄金比で擬似乱数生成 |
ユーザー | hitonanode |
提出日時 | 2022-11-04 22:23:52 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 2 ms / 2,000 ms |
コード長 | 23,085 bytes |
コンパイル時間 | 2,323 ms |
コンパイル使用メモリ | 189,624 KB |
実行使用メモリ | 5,376 KB |
最終ジャッジ日時 | 2024-07-18 22:11:34 |
合計ジャッジ時間 | 3,188 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge5 |
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ファイルパターン | 結果 |
---|---|
other | AC * 26 |
ソースコード
#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <chrono>#include <cmath>#include <complex>#include <deque>#include <forward_list>#include <fstream>#include <functional>#include <iomanip>#include <ios>#include <iostream>#include <limits>#include <list>#include <map>#include <numeric>#include <queue>#include <random>#include <set>#include <sstream>#include <stack>#include <string>#include <tuple>#include <type_traits>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>using namespace std;using lint = long long;using pint = pair<int, int>;using plint = pair<lint, lint>;struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;#define ALL(x) (x).begin(), (x).end()#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)#define REP(i, n) FOR(i,0,n)#define IREP(i, n) IFOR(i,0,n)template <typename T, typename V>void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os <<']'; return os; }template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v<< ','; os << ']'; return os; }#if __cplusplus >= 201703Ltemplate <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);},tpl); return is; }template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) {((os << args << ','), ...);}, tpl); return os << ')'; }#endiftemplate <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os<< v << ','; os << '}'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os <<']'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}';return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os <<'}'; return os; }template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v <<','; os << '}'; return os; }template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for(auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }#ifdef HITONANODE_LOCALconst string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET<< std::endl#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " <<__FILE__ << COLOR_RESET << std::endl : std::cerr)#else#define dbg(x) ((void)0)#define dbgif(cond, x) ((void)0)#endifstruct ModIntRuntime {private:static int md;public:using lint = long long;static int mod() { return md; }int val_;static std::vector<ModIntRuntime> &facs() {static std::vector<ModIntRuntime> facs_;return facs_;}static int &get_primitive_root() {static int primitive_root_ = 0;if (!primitive_root_) {primitive_root_ = [&]() {std::set<int> fac;int v = md - 1;for (lint i = 2; i * i <= v; i++)while (v % i == 0) fac.insert(i), v /= i;if (v > 1) fac.insert(v);for (int g = 1; g < md; g++) {bool ok = true;for (auto i : fac)if (ModIntRuntime(g).power((md - 1) / i) == 1) {ok = false;break;}if (ok) return g;}return -1;}();}return primitive_root_;}static void set_mod(const int &m) {if (md != m) facs().clear();md = m;get_primitive_root() = 0;}ModIntRuntime &_setval(lint v) {val_ = (v >= md ? v - md : v);return *this;}int val() const noexcept { return val_; }ModIntRuntime() : val_(0) {}ModIntRuntime(lint v) { _setval(v % md + md); }explicit operator bool() const { return val_ != 0; }ModIntRuntime operator+(const ModIntRuntime &x) const {return ModIntRuntime()._setval((lint)val_ + x.val_);}ModIntRuntime operator-(const ModIntRuntime &x) const {return ModIntRuntime()._setval((lint)val_ - x.val_ + md);}ModIntRuntime operator*(const ModIntRuntime &x) const {return ModIntRuntime()._setval((lint)val_ * x.val_ % md);}ModIntRuntime operator/(const ModIntRuntime &x) const {return ModIntRuntime()._setval((lint)val_ * x.inv().val() % md);}ModIntRuntime operator-() const { return ModIntRuntime()._setval(md - val_); }ModIntRuntime &operator+=(const ModIntRuntime &x) { return *this = *this + x; }ModIntRuntime &operator-=(const ModIntRuntime &x) { return *this = *this - x; }ModIntRuntime &operator*=(const ModIntRuntime &x) { return *this = *this * x; }ModIntRuntime &operator/=(const ModIntRuntime &x) { return *this = *this / x; }friend ModIntRuntime operator+(lint a, const ModIntRuntime &x) {return ModIntRuntime()._setval(a % md + x.val_);}friend ModIntRuntime operator-(lint a, const ModIntRuntime &x) {return ModIntRuntime()._setval(a % md - x.val_ + md);}friend ModIntRuntime operator*(lint a, const ModIntRuntime &x) {return ModIntRuntime()._setval(a % md * x.val_ % md);}friend ModIntRuntime operator/(lint a, const ModIntRuntime &x) {return ModIntRuntime()._setval(a % md * x.inv().val() % md);}bool operator==(const ModIntRuntime &x) const { return val_ == x.val_; }bool operator!=(const ModIntRuntime &x) const { return val_ != x.val_; }bool operator<(const ModIntRuntime &x) const {return val_ < x.val_;} // To use std::map<ModIntRuntime, T>friend std::istream &operator>>(std::istream &is, ModIntRuntime &x) {lint t;return is >> t, x = ModIntRuntime(t), is;}friend std::ostream &operator<<(std::ostream &os, const ModIntRuntime &x) {return os << x.val_;}lint power(lint n) const {lint ans = 1, tmp = this->val_;while (n) {if (n & 1) ans = ans * tmp % md;tmp = tmp * tmp % md;n /= 2;}return ans;}ModIntRuntime pow(lint n) const { return power(n); }ModIntRuntime inv() const { return this->pow(md - 2); }ModIntRuntime fac() const {int l0 = facs().size();if (l0 > this->val_) return facs()[this->val_];facs().resize(this->val_ + 1);for (int i = l0; i <= this->val_; i++)facs()[i] = (i == 0 ? ModIntRuntime(1) : facs()[i - 1] * ModIntRuntime(i));return facs()[this->val_];}ModIntRuntime doublefac() const {lint k = (this->val_ + 1) / 2;return (this->val_ & 1)? ModIntRuntime(k * 2).fac() / (ModIntRuntime(2).pow(k) * ModIntRuntime(k).fac()): ModIntRuntime(k).fac() * ModIntRuntime(2).pow(k);}ModIntRuntime nCr(const ModIntRuntime &r) const {return (this->val_ < r.val_) ? ModIntRuntime(0): this->fac() / ((*this - r).fac() * r.fac());}ModIntRuntime sqrt() const {if (val_ == 0) return 0;if (md == 2) return val_;if (power((md - 1) / 2) != 1) return 0;ModIntRuntime b = 1;while (b.power((md - 1) / 2) == 1) b += 1;int e = 0, m = md - 1;while (m % 2 == 0) m >>= 1, e++;ModIntRuntime x = power((m - 1) / 2), y = (*this) * x * x;x *= (*this);ModIntRuntime z = b.power(m);while (y != 1) {int j = 0;ModIntRuntime t = y;while (t != 1) j++, t *= t;z = z.power(1LL << (e - j - 1));x *= z, z *= z, y *= z;e = j;}return ModIntRuntime(std::min(x.val_, md - x.val_));}};int ModIntRuntime::md = 1;using mint = ModIntRuntime;namespace matrix_ {struct has_id_method_impl {template <class T_> static auto check(T_ *) -> decltype(T_::id(), std::true_type());template <class T_> static auto check(...) -> std::false_type;};template <class T_> struct has_id : decltype(has_id_method_impl::check<T_>(nullptr)) {};} // namespace matrix_template <typename T> struct matrix {int H, W;std::vector<T> elem;typename std::vector<T>::iterator operator[](int i) { return elem.begin() + i * W; }inline T &at(int i, int j) { return elem[i * W + j]; }inline T get(int i, int j) const { return elem[i * W + j]; }int height() const { return H; }int width() const { return W; }std::vector<std::vector<T>> vecvec() const {std::vector<std::vector<T>> ret(H);for (int i = 0; i < H; i++) {std::copy(elem.begin() + i * W, elem.begin() + (i + 1) * W, std::back_inserter(ret[i]));}return ret;}operator std::vector<std::vector<T>>() const { return vecvec(); }matrix() = default;matrix(int H, int W) : H(H), W(W), elem(H * W) {}matrix(const std::vector<std::vector<T>> &d) : H(d.size()), W(d.size() ? d[0].size() : 0) {for (auto &raw : d) std::copy(raw.begin(), raw.end(), std::back_inserter(elem));}template <typename T2, typename std::enable_if<matrix_::has_id<T2>::value>::type * = nullptr>static T2 _T_id() {return T2::id();}template <typename T2, typename std::enable_if<!matrix_::has_id<T2>::value>::type * = nullptr>static T2 _T_id() {return T2(1);}static matrix Identity(int N) {matrix ret(N, N);for (int i = 0; i < N; i++) ret.at(i, i) = _T_id<T>();return ret;}matrix operator-() const {matrix ret(H, W);for (int i = 0; i < H * W; i++) ret.elem[i] = -elem[i];return ret;}matrix operator*(const T &v) const {matrix ret = *this;for (auto &x : ret.elem) x *= v;return ret;}matrix operator/(const T &v) const {matrix ret = *this;const T vinv = _T_id<T>() / v;for (auto &x : ret.elem) x *= vinv;return ret;}matrix operator+(const matrix &r) const {matrix ret = *this;for (int i = 0; i < H * W; i++) ret.elem[i] += r.elem[i];return ret;}matrix operator-(const matrix &r) const {matrix ret = *this;for (int i = 0; i < H * W; i++) ret.elem[i] -= r.elem[i];return ret;}matrix operator*(const matrix &r) const {matrix ret(H, r.W);for (int i = 0; i < H; i++) {for (int k = 0; k < W; k++) {for (int j = 0; j < r.W; j++) ret.at(i, j) += this->get(i, k) * r.get(k, j);}}return ret;}matrix &operator*=(const T &v) { return *this = *this * v; }matrix &operator/=(const T &v) { return *this = *this / v; }matrix &operator+=(const matrix &r) { return *this = *this + r; }matrix &operator-=(const matrix &r) { return *this = *this - r; }matrix &operator*=(const matrix &r) { return *this = *this * r; }bool operator==(const matrix &r) const { return H == r.H and W == r.W and elem == r.elem; }bool operator!=(const matrix &r) const { return H != r.H or W != r.W or elem != r.elem; }bool operator<(const matrix &r) const { return elem < r.elem; }matrix pow(int64_t n) const {matrix ret = Identity(H);bool ret_is_id = true;if (n == 0) return ret;for (int i = 63 - __builtin_clzll(n); i >= 0; i--) {if (!ret_is_id) ret *= ret;if ((n >> i) & 1) ret *= (*this), ret_is_id = false;}return ret;}std::vector<T> pow_vec(int64_t n, std::vector<T> vec) const {matrix x = *this;while (n) {if (n & 1) vec = x * vec;x *= x;n >>= 1;}return vec;};matrix transpose() const {matrix ret(W, H);for (int i = 0; i < H; i++) {for (int j = 0; j < W; j++) ret.at(j, i) = this->get(i, j);}return ret;}// Gauss-Jordan elimination// - Require inverse for every non-zero element// - Complexity: O(H^2 W)template <typename T2, typename std::enable_if<std::is_floating_point<T2>::value>::type * = nullptr>static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {int piv = -1;for (int j = h; j < mtr.H; j++) {if (mtr.get(j, c) and (piv < 0 or std::abs(mtr.get(j, c)) > std::abs(mtr.get(piv, c))))piv = j;}return piv;}template <typename T2, typename std::enable_if<!std::is_floating_point<T2>::value>::type * = nullptr>static int choose_pivot(const matrix<T2> &mtr, int h, int c) noexcept {for (int j = h; j < mtr.H; j++) {if (mtr.get(j, c) != T2()) return j;}return -1;}matrix gauss_jordan() const {int c = 0;matrix mtr(*this);std::vector<int> ws;ws.reserve(W);for (int h = 0; h < H; h++) {if (c == W) break;int piv = choose_pivot(mtr, h, c);if (piv == -1) {c++;h--;continue;}if (h != piv) {for (int w = 0; w < W; w++) {std::swap(mtr[piv][w], mtr[h][w]);mtr.at(piv, w) *= -_T_id<T>(); // To preserve sign of determinant}}ws.clear();for (int w = c; w < W; w++) {if (mtr.at(h, w) != T()) ws.emplace_back(w);}const T hcinv = _T_id<T>() / mtr.at(h, c);for (int hh = 0; hh < H; hh++)if (hh != h) {const T coeff = mtr.at(hh, c) * hcinv;for (auto w : ws) mtr.at(hh, w) -= mtr.at(h, w) * coeff;mtr.at(hh, c) = T();}c++;}return mtr;}int rank_of_gauss_jordan() const {for (int i = H * W - 1; i >= 0; i--) {if (elem[i] != 0) return i / W + 1;}return 0;}int rank() const { return gauss_jordan().rank_of_gauss_jordan(); }T determinant_of_upper_triangle() const {T ret = _T_id<T>();for (int i = 0; i < H; i++) ret *= get(i, i);return ret;}int inverse() {assert(H == W);std::vector<std::vector<T>> ret = Identity(H), tmp = *this;int rank = 0;for (int i = 0; i < H; i++) {int ti = i;while (ti < H and tmp[ti][i] == 0) ti++;if (ti == H) {continue;} else {rank++;}ret[i].swap(ret[ti]), tmp[i].swap(tmp[ti]);T inv = _T_id<T>() / tmp[i][i];for (int j = 0; j < W; j++) ret[i][j] *= inv;for (int j = i + 1; j < W; j++) tmp[i][j] *= inv;for (int h = 0; h < H; h++) {if (i == h) continue;const T c = -tmp[h][i];for (int j = 0; j < W; j++) ret[h][j] += ret[i][j] * c;for (int j = i + 1; j < W; j++) tmp[h][j] += tmp[i][j] * c;}}*this = ret;return rank;}friend std::vector<T> operator*(const matrix &m, const std::vector<T> &v) {assert(m.W == int(v.size()));std::vector<T> ret(m.H);for (int i = 0; i < m.H; i++) {for (int j = 0; j < m.W; j++) ret[i] += m.get(i, j) * v[j];}return ret;}friend std::vector<T> operator*(const std::vector<T> &v, const matrix &m) {assert(int(v.size()) == m.H);std::vector<T> ret(m.W);for (int i = 0; i < m.H; i++) {for (int j = 0; j < m.W; j++) ret[j] += v[i] * m.get(i, j);}return ret;}std::vector<T> prod(const std::vector<T> &v) const { return (*this) * v; }std::vector<T> prod_left(const std::vector<T> &v) const { return v * (*this); }template <class OStream> friend OStream &operator<<(OStream &os, const matrix &x) {os << "[(" << x.H << " * " << x.W << " matrix)";os << "\n[column sums: ";for (int j = 0; j < x.W; j++) {T s = 0;for (int i = 0; i < x.H; i++) s += x.get(i, j);os << s << ",";}os << "]";for (int i = 0; i < x.H; i++) {os << "\n[";for (int j = 0; j < x.W; j++) os << x.get(i, j) << ",";os << "]";}os << "]\n";return os;}template <class IStream> friend IStream &operator>>(IStream &is, matrix &x) {for (auto &v : x.elem) is >> v;return is;}};int run(int n, lint m) {// alpha^m / sqrtd の小数部分は beta^m / sqrtd の小数部分と等しい// double beta = quadratic_solver<double>(1, -n, -1).first;// auto ret = pow(beta, m) / sqrt(D);// if (ret < 0) ret += 1;// return floorl(ret * 10000);static vector<mint> init{0, 1};static matrix<mint> mat(2, 2);mat[0][1] = 1;mat[1][0] = 1;mat[1][1] = mint(n);auto ret = mat.pow_vec(m, init).front();if (m % 2 == 1) ret -= 1;return ret.val();}void jikken(int n) {double d = n * n + 4;double sqrtd = sqrt(d);double p = (n + sqrtd) / 2;double q = (n - sqrtd) / 2;dbg(d);dbg(make_pair(p, q));dbg((p - q) / sqrtd);dbg((p * p - q * q) / sqrtd);dbg((p * p * p - q * q * q) / sqrtd);dbg((p * p * p * p - q * q * q * q) / sqrtd);dbg((p * p * p * p * p - q * q * q * q * q) / sqrtd);}int main() {mint::set_mod(10000);// jikken(2);// jikken(3);// jikken(4);// jikken(5);// jikken(6);int N;lint M, L;cin >> N >> M >> L;vector<lint> memo(10000, -1);vector<int> f(10000, -1);memo.at(N) = 0;bool skipped = false;for (lint t = 1; t <= L; ++t) {if (f.at(N) >= 0) {N = f[N];} else {f.at(N) = run(N, M);N = f.at(N);}if (!skipped and memo.at(N) >= 0) {const lint rec = t - memo.at(N);const lint sk = floor_div(L - t, rec);if (sk > 0) t += sk * rec;skipped = true;}memo.at(N) = t;}string ret = to_string(N);while (ret.size() < 4) ret = "0" + ret;cout << ret << endl;}