#include <cstdio> #include <cstdlib> #include <cstdint> #include <cmath> #include <cassert> #include <iostream> #include <vector> // LCM of all digits static const uint64_t DIGIT_LCM = 2520; static const uint8_t LIMIT_DIGITSET = 4 * 4 * 2 * 2; uint64_t intpow(uint64_t x, uint64_t n) { if (n == 0) { return 1; } uint64_t result = intpow(x, n / 2); result *= result; if (n & 1) { result *= x; } return result; } struct digitset { uint8_t packed = 0; void add_digit(uint8_t digit) { switch (digit) { case 0: // Make invalid packed = 0xFF; break; case 1: break; case 2: add_two(1); break; case 3: add_three(1); break; case 4: add_two(2); break; case 5: packed |= 1 << 4; break; case 6: add_two(1); add_three(1); break; case 7: packed |= 1 << 5; break; case 8: add_two(3); break; case 9: add_three(2); break; default: break; } } void add_two(uint8_t level) { uint8_t two = std::max((uint8_t)(packed & 0x3), level); packed = (packed & ~0x3) | two; } void add_three(uint8_t level) { uint8_t three = std::max((uint8_t)(packed & 0xC), (uint8_t)(level << 2)); packed = (packed & ~0xC) | three; } digitset united(digitset other) const { uint8_t two = std::max((uint8_t)(packed & 0x3), (uint8_t)(other.packed & 0x3)); uint8_t three = std::max((uint8_t)(packed & 0xC), (uint8_t)(other.packed & 0xC)); uint8_t five_seven = (packed | other.packed) & 0x30; return digitset{(uint8_t)(two | three | five_seven)}; } unsigned int get_lcm() const { // TODO: we could use a lookup table for that unsigned int two = intpow(2, packed & 0x3); unsigned int three = intpow(3, (packed >> 2) & 0x3); unsigned int five = (packed & 0x10) ? 5 : 1; unsigned int seven = (packed & 0x20) ? 7 : 1; return two * three * five * seven; } bool is_valid() const { return (packed & 0xC) != 0xC; } bool is_divisible_by_ten() const { unsigned int two = packed & 0x3; unsigned int five = packed & 0x10; return two && five; } static digitset from_num(uint64_t num) { digitset ret{0}; while (num > 0) { ret.add_digit(num % 10); num /= 10; } return ret; } }; std::ostream& operator<<(std::ostream& os, const digitset& dset) { unsigned int two = dset.packed & 0x3; unsigned int three = (dset.packed >> 2) & 0x3; unsigned int five = (dset.packed & 0x10) ? 1 : 0; unsigned int seven = (dset.packed & 0x20) ? 1 : 0; os << "{[2]:" << two << " [3]:" << three << " [5]:" << five << " [7]:" << seven << " lcm:" << dset.get_lcm() << "}"; return os; } uint64_t data[20][LIMIT_DIGITSET][DIGIT_LCM] = { 0 }; uint64_t numlen(uint64_t num) { uint64_t len = 0; do { num /= 10; len++; } while (num > 0); return len; } std::vector<uint8_t> to_digits(uint64_t num) { std::vector<uint8_t> ret; do { ret.push_back(num % 10); num /= 10; } while (num > 0); return ret; } void precompute_up_to_level(const uint64_t max_level) { // Prepare the zeroth level data[0][0][0] = 1; // Others are zeros // Other levels uint64_t tenpow = 1; for (uint64_t level = 1; level <= max_level; level++) { for (uint64_t d = 1; d <= 9; d++) { const uint64_t offset = (d * tenpow) % DIGIT_LCM; for (uint8_t raw_source_dset = 0; raw_source_dset < LIMIT_DIGITSET; raw_source_dset++) { digitset dset{raw_source_dset}; if (!dset.is_valid()) { continue; } dset.add_digit(d); const uint8_t raw_dest_dset = dset.packed; for (uint64_t i = 0; i < DIGIT_LCM - offset; i++) { data[level][raw_dest_dset][i + offset] += data[level - 1][raw_source_dset][i]; } for (uint64_t i = DIGIT_LCM - offset; i < DIGIT_LCM; i++) { data[level][raw_dest_dset][i - DIGIT_LCM + offset] += data[level - 1][raw_source_dset][i]; } } } tenpow *= 10; } } // Computes how many uint64_t count_with_offset(uint64_t level, uint64_t offset, digitset base_dset) { // std::cout << "count_with_offset: " << level << " " << offset << " " << base_dset << std::endl; if (base_dset.is_divisible_by_ten()) { // std::cout << " divisible by ten, skipping" << std::endl; return 0; } uint64_t count = 0; offset %= DIGIT_LCM; for (uint8_t raw_dset = 0; raw_dset < LIMIT_DIGITSET; raw_dset++) { digitset dset = digitset{raw_dset}; if (!dset.is_valid()) { continue; } // std::cout << " united: " << dset << std::endl; dset = dset.united(base_dset); if (dset.is_divisible_by_ten()) { continue; } unsigned int lcm = dset.get_lcm(); for (unsigned int i = (DIGIT_LCM - offset) % lcm; i < DIGIT_LCM; i += lcm) { // if (data[level][raw_dset][i] > 0) { // std::cout << " adding [" << i << "] = " << data[level][raw_dset][i] << std::endl; // } count += data[level][raw_dset][i]; } } // std::cout << " return " << count << std::endl; return count; } uint64_t count_in_range(uint64_t begin, uint64_t end) { if (begin >= end) { return 0; } auto begin_digits = to_digits(begin); auto end_digits = to_digits(end); // Make both representations have the same size begin_digits.resize(end_digits.size(), 0); // Compute length of the prefix without the common part int uncommon = end_digits.size(); // No need to check uncommon > 0, because both vectors are // guaranteed to be different while (begin_digits[uncommon - 1] == end_digits[uncommon - 1]) { uncommon--; } uint64_t base = begin; uint64_t count = 0; uint64_t tenpow = 1; if (begin_digits[0] == 0) { begin_digits[0]++; base++; } for (int i = 0; i < uncommon - 1; i++) { for (uint8_t d = begin_digits[i]; d <= 9; d++) { // std::cout << " base: " << base << ", end: " << end << std::endl; digitset dset = digitset::from_num(base / tenpow); if (dset.is_valid()) { count += count_with_offset(i, base, dset); } base += tenpow; } tenpow *= 10; begin_digits[i + 1]++; } for (uint8_t d = std::max(begin_digits[uncommon - 1], (uint8_t)1); d < end_digits[uncommon - 1]; d++) { // std::cout << " base: " << base << ", end: " << end << std::endl; digitset dset = digitset::from_num(base / tenpow); if (dset.is_valid()) { count += count_with_offset(uncommon - 1, base, dset); } base += tenpow; } for (int i = uncommon - 2; i >= 0; i--) { tenpow /= 10; for (uint8_t d = 0; d < end_digits[i]; d++) { // std::cout << " base: " << base << ", end: " << end << std::endl; digitset dset = digitset::from_num(base / tenpow); if (dset.is_valid()) { count += count_with_offset(i, base, dset); } base += tenpow; } } // std::cout << " base: " << base << ", end: " << end << std::endl; assert(base == end); return count; } int main() { std::ios::sync_with_stdio(false); uint64_t l, r; std::cin >> l >> r; precompute_up_to_level(numlen(r)); const uint64_t count = count_in_range(l, r + 1); std::cout << count << std::endl; 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 | #include <cstdio> #include <cstdlib> #include <cstdint> #include <cmath> #include <cassert> #include <iostream> #include <vector> // LCM of all digits static const uint64_t DIGIT_LCM = 2520; static const uint8_t LIMIT_DIGITSET = 4 * 4 * 2 * 2; uint64_t intpow(uint64_t x, uint64_t n) { if (n == 0) { return 1; } uint64_t result = intpow(x, n / 2); result *= result; if (n & 1) { result *= x; } return result; } struct digitset { uint8_t packed = 0; void add_digit(uint8_t digit) { switch (digit) { case 0: // Make invalid packed = 0xFF; break; case 1: break; case 2: add_two(1); break; case 3: add_three(1); break; case 4: add_two(2); break; case 5: packed |= 1 << 4; break; case 6: add_two(1); add_three(1); break; case 7: packed |= 1 << 5; break; case 8: add_two(3); break; case 9: add_three(2); break; default: break; } } void add_two(uint8_t level) { uint8_t two = std::max((uint8_t)(packed & 0x3), level); packed = (packed & ~0x3) | two; } void add_three(uint8_t level) { uint8_t three = std::max((uint8_t)(packed & 0xC), (uint8_t)(level << 2)); packed = (packed & ~0xC) | three; } digitset united(digitset other) const { uint8_t two = std::max((uint8_t)(packed & 0x3), (uint8_t)(other.packed & 0x3)); uint8_t three = std::max((uint8_t)(packed & 0xC), (uint8_t)(other.packed & 0xC)); uint8_t five_seven = (packed | other.packed) & 0x30; return digitset{(uint8_t)(two | three | five_seven)}; } unsigned int get_lcm() const { // TODO: we could use a lookup table for that unsigned int two = intpow(2, packed & 0x3); unsigned int three = intpow(3, (packed >> 2) & 0x3); unsigned int five = (packed & 0x10) ? 5 : 1; unsigned int seven = (packed & 0x20) ? 7 : 1; return two * three * five * seven; } bool is_valid() const { return (packed & 0xC) != 0xC; } bool is_divisible_by_ten() const { unsigned int two = packed & 0x3; unsigned int five = packed & 0x10; return two && five; } static digitset from_num(uint64_t num) { digitset ret{0}; while (num > 0) { ret.add_digit(num % 10); num /= 10; } return ret; } }; std::ostream& operator<<(std::ostream& os, const digitset& dset) { unsigned int two = dset.packed & 0x3; unsigned int three = (dset.packed >> 2) & 0x3; unsigned int five = (dset.packed & 0x10) ? 1 : 0; unsigned int seven = (dset.packed & 0x20) ? 1 : 0; os << "{[2]:" << two << " [3]:" << three << " [5]:" << five << " [7]:" << seven << " lcm:" << dset.get_lcm() << "}"; return os; } uint64_t data[20][LIMIT_DIGITSET][DIGIT_LCM] = { 0 }; uint64_t numlen(uint64_t num) { uint64_t len = 0; do { num /= 10; len++; } while (num > 0); return len; } std::vector<uint8_t> to_digits(uint64_t num) { std::vector<uint8_t> ret; do { ret.push_back(num % 10); num /= 10; } while (num > 0); return ret; } void precompute_up_to_level(const uint64_t max_level) { // Prepare the zeroth level data[0][0][0] = 1; // Others are zeros // Other levels uint64_t tenpow = 1; for (uint64_t level = 1; level <= max_level; level++) { for (uint64_t d = 1; d <= 9; d++) { const uint64_t offset = (d * tenpow) % DIGIT_LCM; for (uint8_t raw_source_dset = 0; raw_source_dset < LIMIT_DIGITSET; raw_source_dset++) { digitset dset{raw_source_dset}; if (!dset.is_valid()) { continue; } dset.add_digit(d); const uint8_t raw_dest_dset = dset.packed; for (uint64_t i = 0; i < DIGIT_LCM - offset; i++) { data[level][raw_dest_dset][i + offset] += data[level - 1][raw_source_dset][i]; } for (uint64_t i = DIGIT_LCM - offset; i < DIGIT_LCM; i++) { data[level][raw_dest_dset][i - DIGIT_LCM + offset] += data[level - 1][raw_source_dset][i]; } } } tenpow *= 10; } } // Computes how many uint64_t count_with_offset(uint64_t level, uint64_t offset, digitset base_dset) { // std::cout << "count_with_offset: " << level << " " << offset << " " << base_dset << std::endl; if (base_dset.is_divisible_by_ten()) { // std::cout << " divisible by ten, skipping" << std::endl; return 0; } uint64_t count = 0; offset %= DIGIT_LCM; for (uint8_t raw_dset = 0; raw_dset < LIMIT_DIGITSET; raw_dset++) { digitset dset = digitset{raw_dset}; if (!dset.is_valid()) { continue; } // std::cout << " united: " << dset << std::endl; dset = dset.united(base_dset); if (dset.is_divisible_by_ten()) { continue; } unsigned int lcm = dset.get_lcm(); for (unsigned int i = (DIGIT_LCM - offset) % lcm; i < DIGIT_LCM; i += lcm) { // if (data[level][raw_dset][i] > 0) { // std::cout << " adding [" << i << "] = " << data[level][raw_dset][i] << std::endl; // } count += data[level][raw_dset][i]; } } // std::cout << " return " << count << std::endl; return count; } uint64_t count_in_range(uint64_t begin, uint64_t end) { if (begin >= end) { return 0; } auto begin_digits = to_digits(begin); auto end_digits = to_digits(end); // Make both representations have the same size begin_digits.resize(end_digits.size(), 0); // Compute length of the prefix without the common part int uncommon = end_digits.size(); // No need to check uncommon > 0, because both vectors are // guaranteed to be different while (begin_digits[uncommon - 1] == end_digits[uncommon - 1]) { uncommon--; } uint64_t base = begin; uint64_t count = 0; uint64_t tenpow = 1; if (begin_digits[0] == 0) { begin_digits[0]++; base++; } for (int i = 0; i < uncommon - 1; i++) { for (uint8_t d = begin_digits[i]; d <= 9; d++) { // std::cout << " base: " << base << ", end: " << end << std::endl; digitset dset = digitset::from_num(base / tenpow); if (dset.is_valid()) { count += count_with_offset(i, base, dset); } base += tenpow; } tenpow *= 10; begin_digits[i + 1]++; } for (uint8_t d = std::max(begin_digits[uncommon - 1], (uint8_t)1); d < end_digits[uncommon - 1]; d++) { // std::cout << " base: " << base << ", end: " << end << std::endl; digitset dset = digitset::from_num(base / tenpow); if (dset.is_valid()) { count += count_with_offset(uncommon - 1, base, dset); } base += tenpow; } for (int i = uncommon - 2; i >= 0; i--) { tenpow /= 10; for (uint8_t d = 0; d < end_digits[i]; d++) { // std::cout << " base: " << base << ", end: " << end << std::endl; digitset dset = digitset::from_num(base / tenpow); if (dset.is_valid()) { count += count_with_offset(i, base, dset); } base += tenpow; } } // std::cout << " base: " << base << ", end: " << end << std::endl; assert(base == end); return count; } int main() { std::ios::sync_with_stdio(false); uint64_t l, r; std::cin >> l >> r; precompute_up_to_level(numlen(r)); const uint64_t count = count_in_range(l, r + 1); std::cout << count << std::endl; return 0; } |