#include <algorithm> #include <cmath> #include <complex> #include <cstdint> #include <functional> #include <iomanip> #include <iostream> #include <iterator> #include <numeric> #include <string> #include <utility> #include <tuple> #include <vector> constexpr int big_int_base = 1 << 30; constexpr std::size_t naive_multiplication_limit = 20; class big_unsigned { public: big_unsigned() = default; big_unsigned(int value) { *this = value; } bool operator!() const { return digits.empty(); } friend bool operator==(const big_unsigned& lhs, const big_unsigned& rhs) { return lhs.digits == rhs.digits; } friend bool operator!=(const big_unsigned& lhs, const big_unsigned& rhs) { return !(lhs == rhs); } friend bool operator<(const big_unsigned& lhs, const big_unsigned& rhs) { if (lhs.digits.size() < rhs.digits.size()) return true; if (lhs.digits.size() > rhs.digits.size()) return false; return std::lexicographical_compare(lhs.digits.rbegin(), lhs.digits.rend(), rhs.digits.rbegin(), rhs.digits.rend()); } friend bool operator>(const big_unsigned& lhs, const big_unsigned& rhs) { return rhs < lhs; } friend bool operator<=(const big_unsigned& lhs, const big_unsigned& rhs) { return !(rhs < lhs); } friend bool operator>=(const big_unsigned& lhs, const big_unsigned& rhs) { return !(lhs < rhs); } big_unsigned& operator=(int other) { if (other != 0) digits = {other}; else digits.clear(); return *this; } big_unsigned& operator*=(int other) { long long n = other; long long carry = 0; for (auto&& digit : digits) { long long new_digit = digit * n + carry; digit = new_digit % big_int_base; carry = new_digit / big_int_base; } while (carry > 0) { digits.push_back(carry % big_int_base); carry /= big_int_base; } return *this; } big_unsigned& operator+=(const big_unsigned& other) { if (&other == this) return *this *= 2; if (other.digits.size() > digits.size()) { digits.reserve(other.digits.size() + 1); digits.resize(other.digits.size()); } add(other.digits.begin(), other.digits.end()); return *this; } big_unsigned& operator-=(const big_unsigned& other) { if (&other == this) return *this = 0; bool carry = false; auto this_it = digits.begin(); for (auto it = other.digits.begin(); it != other.digits.end(); ++it, ++this_it) { auto& digit = *this_it; digit -= *it + carry; carry = digit < 0; if (carry) digit += big_int_base; } for (; carry && this_it != digits.end(); ++this_it) { auto& digit = *this_it; digit--; carry = digit < 0; if (carry) digit += big_int_base; } while (!digits.empty() && digits.back() == 0) { digits.pop_back(); } return *this; } big_unsigned& operator*=(const big_unsigned& other) { return *this = multiply(digits.begin(), digits.end(), other.digits.begin(), other.digits.end()); } friend big_unsigned operator*(big_unsigned&& lhs, int rhs) { big_unsigned result = std::move(lhs); return result *= rhs; } friend big_unsigned operator*(int lhs, big_unsigned&& rhs) { big_unsigned result = std::move(rhs); return result *= lhs; } friend big_unsigned operator+(const big_unsigned& lhs, const big_unsigned& rhs) { if (lhs.digits.size() < rhs.digits.size()) { big_unsigned result = rhs; return result += lhs; } big_unsigned result = lhs; return result += rhs; } friend big_unsigned operator+(const big_unsigned& lhs, big_unsigned&& rhs) { big_unsigned result = std::move(rhs); return result += lhs; } friend big_unsigned operator+(big_unsigned&& lhs, const big_unsigned& rhs) { big_unsigned result = std::move(lhs); return result += rhs; } friend big_unsigned operator+(big_unsigned&& lhs, big_unsigned&& rhs) { if (lhs.digits.capacity() < rhs.digits.capacity()) { big_unsigned result = std::move(rhs); return result += lhs; } big_unsigned result = std::move(lhs); return result += rhs; } friend big_unsigned operator-(const big_unsigned& lhs, const big_unsigned& rhs) { big_unsigned result = lhs; return result -= rhs; } friend big_unsigned operator-(big_unsigned&& lhs, const big_unsigned& rhs) { big_unsigned result = std::move(lhs); return result -= rhs; } friend big_unsigned operator*(const big_unsigned& lhs, const big_unsigned& rhs) { return multiply(lhs.digits.begin(), lhs.digits.end(), rhs.digits.begin(), rhs.digits.end()); } private: template<class ForwardIt> void add(ForwardIt first, ForwardIt last) { bool carry = false; auto this_it = digits.begin(); for (auto it = first; it != last; ++it, ++this_it) { auto& digit = *this_it; digit += *it + carry; carry = digit >= big_int_base; if (carry) digit -= big_int_base; } for (; carry && this_it != digits.end(); ++this_it) { auto& digit = *this_it; digit++; carry = digit >= big_int_base; if (carry) digit -= big_int_base; } if (carry) { digits.push_back(1); } else { while (!digits.empty() && digits.back() == 0) { digits.pop_back(); } } } template<class ForwardIt1, class ForwardIt2> static big_unsigned add(ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2) { big_unsigned result; auto size1 = std::distance(first1, last1); auto size2 = std::distance(first2, last2); if (size1 < size2) { result.digits.reserve(size2 + 1); result.digits.assign(first2, last2); result.add(first1, last1); } else { result.digits.reserve(size1 + 1); result.digits.assign(first1, last1); result.add(first2, last2); } return result; } template<class ForwardIt1, class ForwardIt2> static big_unsigned multiply(ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2) { auto size1 = std::distance(first1, last1); auto size2 = std::distance(first2, last2); if (size1 == 0 || size2 == 0) return {}; if (size1 < naive_multiplication_limit || size2 < naive_multiplication_limit) return naive_multiply(first1, last1, first2, last2); return karatsuba(first1, last1, first2, last2); } template<class ForwardIt1, class ForwardIt2> static big_unsigned naive_multiply(ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2) { big_unsigned result; result.digits.resize(std::distance(first1, last1) + std::distance(first2, last2)); auto out = result.digits.begin(); for (auto it = first1; it != last1; ++it, ++out) { long long digit = *it; long long carry = 0; auto out2 = out; for (auto it2 = first2; it2 != last2; ++it2, ++out2) { long long new_digit = *out2; new_digit += digit * *it2 + carry; *out2 = new_digit % big_int_base; carry = new_digit / big_int_base; } *out2 = (int)carry; } while (!result.digits.empty() && result.digits.back() == 0) { result.digits.pop_back(); } return result; } template<class ForwardIt1, class ForwardIt2> static big_unsigned karatsuba(ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2) { auto size1 = std::distance(first1, last1); auto size2 = std::distance(first2, last2); auto half = std::max(size1, size2) / 2; auto middle1 = first1; auto middle2 = first2; std::advance(middle1, std::min(size1, half)); std::advance(middle2, std::min(size2, half)); auto z0 = multiply(first1, middle1, first2, middle2); auto z2 = multiply(middle1, last1, middle2, last2); auto z1 = add(first1, middle1, middle1, last1) * add(first2, middle2, middle2, last2) - z0 - z2; z1.digits.insert(z1.digits.begin(), half, 0); z2.digits.insert(z2.digits.begin(), half * 2, 0); return std::move(z0) + std::move(z1) + std::move(z2); } std::vector<int> digits; }; constexpr std::size_t fib_count = 75'000; big_unsigned fib[fib_count] {1, 1}; big_unsigned to_big_unsigned(const std::vector<int>& x) { int n = (int)x.size(); int s = std::max(2, (int)std::sqrt(n)); std::vector<big_unsigned> y((n - 1) / s + 1); std::vector<big_unsigned> z((n - 1) / s + 1); for (int i = 0; i < n; i++) { if (x[i]) { if (i % s == 0) { y[i / s] = 1; } else if (i % s == 1) { z[i / s] = 1; } else { y[i / s] += fib[i % s - 2]; z[i / s] += fib[i % s - 1]; } } } for (auto i = y.size(); --i;) { y[i - 1] += y[i] * fib[s - 2] + z[i] * fib[s - 1]; z[i - 1] += y[i] * fib[s - 1] + z[i] * fib[s]; } return y[0] + z[0] * 2; } big_unsigned load() { int n; std::cin >> n; std::vector<int> x(n); for (auto&& b : x) { std::cin >> b; } return to_big_unsigned(x); } void write(big_unsigned&& x) { std::vector<int> result; int bound = fib_count; while (!!x) { int a = 0; int b = bound; while (b - a > 1) { auto mid = a + (b - a) / 2; if (fib[mid] <= x) a = mid; else b = mid; } x -= fib[a]; if ((int)result.size() < a) result.resize(a); result[a - 1] = 1; bound = a - 1; } std::cout << result.size(); for (const auto& b : result) { std::cout << ' ' << b; } std::cout << '\n'; } int main() { for (std::size_t i = 2; i < fib_count; i++) { fib[i] = fib[i - 1] + fib[i - 2]; } std::ios_base::sync_with_stdio(false); std::cin.tie(nullptr); int t; std::cin >> t; while (t--) { write(load() * load()); } return 0; }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 | #include <algorithm> #include <cmath> #include <complex> #include <cstdint> #include <functional> #include <iomanip> #include <iostream> #include <iterator> #include <numeric> #include <string> #include <utility> #include <tuple> #include <vector> constexpr int big_int_base = 1 << 30; constexpr std::size_t naive_multiplication_limit = 20; class big_unsigned { public: big_unsigned() = default; big_unsigned(int value) { *this = value; } bool operator!() const { return digits.empty(); } friend bool operator==(const big_unsigned& lhs, const big_unsigned& rhs) { return lhs.digits == rhs.digits; } friend bool operator!=(const big_unsigned& lhs, const big_unsigned& rhs) { return !(lhs == rhs); } friend bool operator<(const big_unsigned& lhs, const big_unsigned& rhs) { if (lhs.digits.size() < rhs.digits.size()) return true; if (lhs.digits.size() > rhs.digits.size()) return false; return std::lexicographical_compare(lhs.digits.rbegin(), lhs.digits.rend(), rhs.digits.rbegin(), rhs.digits.rend()); } friend bool operator>(const big_unsigned& lhs, const big_unsigned& rhs) { return rhs < lhs; } friend bool operator<=(const big_unsigned& lhs, const big_unsigned& rhs) { return !(rhs < lhs); } friend bool operator>=(const big_unsigned& lhs, const big_unsigned& rhs) { return !(lhs < rhs); } big_unsigned& operator=(int other) { if (other != 0) digits = {other}; else digits.clear(); return *this; } big_unsigned& operator*=(int other) { long long n = other; long long carry = 0; for (auto&& digit : digits) { long long new_digit = digit * n + carry; digit = new_digit % big_int_base; carry = new_digit / big_int_base; } while (carry > 0) { digits.push_back(carry % big_int_base); carry /= big_int_base; } return *this; } big_unsigned& operator+=(const big_unsigned& other) { if (&other == this) return *this *= 2; if (other.digits.size() > digits.size()) { digits.reserve(other.digits.size() + 1); digits.resize(other.digits.size()); } add(other.digits.begin(), other.digits.end()); return *this; } big_unsigned& operator-=(const big_unsigned& other) { if (&other == this) return *this = 0; bool carry = false; auto this_it = digits.begin(); for (auto it = other.digits.begin(); it != other.digits.end(); ++it, ++this_it) { auto& digit = *this_it; digit -= *it + carry; carry = digit < 0; if (carry) digit += big_int_base; } for (; carry && this_it != digits.end(); ++this_it) { auto& digit = *this_it; digit--; carry = digit < 0; if (carry) digit += big_int_base; } while (!digits.empty() && digits.back() == 0) { digits.pop_back(); } return *this; } big_unsigned& operator*=(const big_unsigned& other) { return *this = multiply(digits.begin(), digits.end(), other.digits.begin(), other.digits.end()); } friend big_unsigned operator*(big_unsigned&& lhs, int rhs) { big_unsigned result = std::move(lhs); return result *= rhs; } friend big_unsigned operator*(int lhs, big_unsigned&& rhs) { big_unsigned result = std::move(rhs); return result *= lhs; } friend big_unsigned operator+(const big_unsigned& lhs, const big_unsigned& rhs) { if (lhs.digits.size() < rhs.digits.size()) { big_unsigned result = rhs; return result += lhs; } big_unsigned result = lhs; return result += rhs; } friend big_unsigned operator+(const big_unsigned& lhs, big_unsigned&& rhs) { big_unsigned result = std::move(rhs); return result += lhs; } friend big_unsigned operator+(big_unsigned&& lhs, const big_unsigned& rhs) { big_unsigned result = std::move(lhs); return result += rhs; } friend big_unsigned operator+(big_unsigned&& lhs, big_unsigned&& rhs) { if (lhs.digits.capacity() < rhs.digits.capacity()) { big_unsigned result = std::move(rhs); return result += lhs; } big_unsigned result = std::move(lhs); return result += rhs; } friend big_unsigned operator-(const big_unsigned& lhs, const big_unsigned& rhs) { big_unsigned result = lhs; return result -= rhs; } friend big_unsigned operator-(big_unsigned&& lhs, const big_unsigned& rhs) { big_unsigned result = std::move(lhs); return result -= rhs; } friend big_unsigned operator*(const big_unsigned& lhs, const big_unsigned& rhs) { return multiply(lhs.digits.begin(), lhs.digits.end(), rhs.digits.begin(), rhs.digits.end()); } private: template<class ForwardIt> void add(ForwardIt first, ForwardIt last) { bool carry = false; auto this_it = digits.begin(); for (auto it = first; it != last; ++it, ++this_it) { auto& digit = *this_it; digit += *it + carry; carry = digit >= big_int_base; if (carry) digit -= big_int_base; } for (; carry && this_it != digits.end(); ++this_it) { auto& digit = *this_it; digit++; carry = digit >= big_int_base; if (carry) digit -= big_int_base; } if (carry) { digits.push_back(1); } else { while (!digits.empty() && digits.back() == 0) { digits.pop_back(); } } } template<class ForwardIt1, class ForwardIt2> static big_unsigned add(ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2) { big_unsigned result; auto size1 = std::distance(first1, last1); auto size2 = std::distance(first2, last2); if (size1 < size2) { result.digits.reserve(size2 + 1); result.digits.assign(first2, last2); result.add(first1, last1); } else { result.digits.reserve(size1 + 1); result.digits.assign(first1, last1); result.add(first2, last2); } return result; } template<class ForwardIt1, class ForwardIt2> static big_unsigned multiply(ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2) { auto size1 = std::distance(first1, last1); auto size2 = std::distance(first2, last2); if (size1 == 0 || size2 == 0) return {}; if (size1 < naive_multiplication_limit || size2 < naive_multiplication_limit) return naive_multiply(first1, last1, first2, last2); return karatsuba(first1, last1, first2, last2); } template<class ForwardIt1, class ForwardIt2> static big_unsigned naive_multiply(ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2) { big_unsigned result; result.digits.resize(std::distance(first1, last1) + std::distance(first2, last2)); auto out = result.digits.begin(); for (auto it = first1; it != last1; ++it, ++out) { long long digit = *it; long long carry = 0; auto out2 = out; for (auto it2 = first2; it2 != last2; ++it2, ++out2) { long long new_digit = *out2; new_digit += digit * *it2 + carry; *out2 = new_digit % big_int_base; carry = new_digit / big_int_base; } *out2 = (int)carry; } while (!result.digits.empty() && result.digits.back() == 0) { result.digits.pop_back(); } return result; } template<class ForwardIt1, class ForwardIt2> static big_unsigned karatsuba(ForwardIt1 first1, ForwardIt1 last1, ForwardIt2 first2, ForwardIt2 last2) { auto size1 = std::distance(first1, last1); auto size2 = std::distance(first2, last2); auto half = std::max(size1, size2) / 2; auto middle1 = first1; auto middle2 = first2; std::advance(middle1, std::min(size1, half)); std::advance(middle2, std::min(size2, half)); auto z0 = multiply(first1, middle1, first2, middle2); auto z2 = multiply(middle1, last1, middle2, last2); auto z1 = add(first1, middle1, middle1, last1) * add(first2, middle2, middle2, last2) - z0 - z2; z1.digits.insert(z1.digits.begin(), half, 0); z2.digits.insert(z2.digits.begin(), half * 2, 0); return std::move(z0) + std::move(z1) + std::move(z2); } std::vector<int> digits; }; constexpr std::size_t fib_count = 75'000; big_unsigned fib[fib_count] {1, 1}; big_unsigned to_big_unsigned(const std::vector<int>& x) { int n = (int)x.size(); int s = std::max(2, (int)std::sqrt(n)); std::vector<big_unsigned> y((n - 1) / s + 1); std::vector<big_unsigned> z((n - 1) / s + 1); for (int i = 0; i < n; i++) { if (x[i]) { if (i % s == 0) { y[i / s] = 1; } else if (i % s == 1) { z[i / s] = 1; } else { y[i / s] += fib[i % s - 2]; z[i / s] += fib[i % s - 1]; } } } for (auto i = y.size(); --i;) { y[i - 1] += y[i] * fib[s - 2] + z[i] * fib[s - 1]; z[i - 1] += y[i] * fib[s - 1] + z[i] * fib[s]; } return y[0] + z[0] * 2; } big_unsigned load() { int n; std::cin >> n; std::vector<int> x(n); for (auto&& b : x) { std::cin >> b; } return to_big_unsigned(x); } void write(big_unsigned&& x) { std::vector<int> result; int bound = fib_count; while (!!x) { int a = 0; int b = bound; while (b - a > 1) { auto mid = a + (b - a) / 2; if (fib[mid] <= x) a = mid; else b = mid; } x -= fib[a]; if ((int)result.size() < a) result.resize(a); result[a - 1] = 1; bound = a - 1; } std::cout << result.size(); for (const auto& b : result) { std::cout << ' ' << b; } std::cout << '\n'; } int main() { for (std::size_t i = 2; i < fib_count; i++) { fib[i] = fib[i - 1] + fib[i - 2]; } std::ios_base::sync_with_stdio(false); std::cin.tie(nullptr); int t; std::cin >> t; while (t--) { write(load() * load()); } return 0; } |