#include <cstdio> #include <cstdlib> #include <cassert> #include <cstring> #include <array> #include <vector> using llu = long long unsigned int; using histogram_t = std::array<llu, 10>; static const llu POWERS_OF_TEN[] = { 1ULL, 10ULL, 100ULL, 1000ULL, 10000ULL, 100000ULL, 1000000ULL, 10000000ULL, 100000000ULL, 1000000000ULL, 10000000000ULL, 100000000000ULL, 1000000000000ULL, 10000000000000ULL, 100000000000000ULL, 1000000000000000ULL, 10000000000000000ULL, 100000000000000000ULL, 1000000000000000000ULL, }; static llu BINOM[20][20]; // TODO: Precompute this llu binom(llu n, llu k) { if (k > n) { return 0; } if (2 * k > n) { return binom(n, n - k); } if (k == 0) { return 1; } return binom(n - 1, k - 1) * n / k; } int play(llu num) { while (num >= 10) { llu new_num = 1; while (num > 0) { new_num *= (num % 10); num /= 10; } num = new_num; } return num; } void enumerate(std::array<std::vector<histogram_t>, 10>& result, histogram_t& histogram, int idx, int prev_digit) { if (idx == 0) { llu num = 0; for (int i = 1; i < 10; i++) { for (int j = 0; j < histogram[i]; j++) { num = 10 * num + (llu)i; } } int play_result = play(num); if (play_result != 0) { result[play_result].push_back(histogram); } return; } for (int d = prev_digit; d < 10; d++) { if (d % 2 == 0 && histogram[5] > 0) { continue; } if (d == 5 && (histogram[2] > 0 || histogram[4] > 0)) { continue; } histogram[d]++; enumerate(result, histogram, idx - 1, d); histogram[d]--; } } histogram_t compute(std::array<std::vector<histogram_t>, 10> precomputed, llu upto) { histogram_t ret = {{0}}; char digits[32]; sprintf(digits, "%llu", upto); int len = std::strlen(digits); for (int i = 0; i < len; i++) { // printf("Position %d (%c)\n", i, digits[i]); digits[i] -= '0'; // For all non-zero digits up to the current one, count the configurations // which start with 'd' for (int d = 1; d < digits[i]; d++) { // printf("Processing digit %d\n", d); for (int remainder = 1; remainder < 10; remainder++) { const auto& histos = precomputed[remainder]; for (const histogram_t& histo : histos) { if (histo[d] > 0) { // printf(" Including"); // for (int i = 0; i < 10; i++) { // printf(" %llu", histo[i]); // } // printf("\n"); llu counts = 1; llu sum = 0; for (int x = 1; x < 10; x++) { sum += histo[x] - (x == d ? 1 : 0); counts *= BINOM[sum][histo[x] - (x == d ? 1 : 0)]; } ret[remainder] += counts; } } } } // Filter out the histograms - leave only those which are possible // after the current digit is added // printf("Continuing to the next digit (%d)\n", digits[i]); for (auto& histos : precomputed) { int pos = 0; while (pos < histos.size()) { if (histos[pos][digits[i]] == 0) { // Remove this histogram - doesn't have the necessary digits // printf(" Rejecting"); // for (int x = 0; x < 10; x++) { // printf(" %llu", histos[pos][x]); // } // printf("\n"); histos[pos] = histos.back(); histos.pop_back(); } else { // printf(" Keeping "); // for (int i = 0; i < 10; i++) { // printf(" %llu", histos[pos][i]); // } // printf("\n"); histos[pos][digits[i]]--; pos++; } } } } // There might be one remaining histogram that we need to include for (int i = 1; i < 10; i++) { if (!precomputed[i].empty()) { // printf("Adding leftover histogram with remainder %d\n", i); ret[i]++; } } ret[0] = upto + 1 - POWERS_OF_TEN[len - 1]; for (int i = 1; i < 10; i++) { ret[0] -= ret[i]; } return ret; }; int main() { for (int n = 0; n < 20; n++) { for (int k = 0; k < 20; k++) { BINOM[n][k] = binom(n, k); } } int t; scanf("%d\n", &t); std::array<std::array<std::vector<histogram_t>, 10>, 20> precomputed; std::array<histogram_t, 20> baselines = {{0}}; for (int i = 1; i < 20; i++) { histogram_t tmp; enumerate(precomputed[i], tmp, i, 1); } llu tenpow = 1; for (int i = 1; i < 20; i++) { baselines[i] = compute(precomputed[i - 1], tenpow - 1); for (int j = 0; j < 10; j++) { baselines[i][j] += baselines[i - 1][j]; } tenpow *= 10; } while (t --> 0) { llu n; scanf("%llu", &n); char digits[32]; sprintf(digits, "%llu", n); int len = std::strlen(digits); histogram_t counts = compute(precomputed[len], n); for (int i = 0; i < 10; i++) { if (i == 9) { printf("%llu\n", baselines[len][i] + counts[i]); } else { printf("%llu ", baselines[len][i] + counts[i]); } } } 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 | #include <cstdio> #include <cstdlib> #include <cassert> #include <cstring> #include <array> #include <vector> using llu = long long unsigned int; using histogram_t = std::array<llu, 10>; static const llu POWERS_OF_TEN[] = { 1ULL, 10ULL, 100ULL, 1000ULL, 10000ULL, 100000ULL, 1000000ULL, 10000000ULL, 100000000ULL, 1000000000ULL, 10000000000ULL, 100000000000ULL, 1000000000000ULL, 10000000000000ULL, 100000000000000ULL, 1000000000000000ULL, 10000000000000000ULL, 100000000000000000ULL, 1000000000000000000ULL, }; static llu BINOM[20][20]; // TODO: Precompute this llu binom(llu n, llu k) { if (k > n) { return 0; } if (2 * k > n) { return binom(n, n - k); } if (k == 0) { return 1; } return binom(n - 1, k - 1) * n / k; } int play(llu num) { while (num >= 10) { llu new_num = 1; while (num > 0) { new_num *= (num % 10); num /= 10; } num = new_num; } return num; } void enumerate(std::array<std::vector<histogram_t>, 10>& result, histogram_t& histogram, int idx, int prev_digit) { if (idx == 0) { llu num = 0; for (int i = 1; i < 10; i++) { for (int j = 0; j < histogram[i]; j++) { num = 10 * num + (llu)i; } } int play_result = play(num); if (play_result != 0) { result[play_result].push_back(histogram); } return; } for (int d = prev_digit; d < 10; d++) { if (d % 2 == 0 && histogram[5] > 0) { continue; } if (d == 5 && (histogram[2] > 0 || histogram[4] > 0)) { continue; } histogram[d]++; enumerate(result, histogram, idx - 1, d); histogram[d]--; } } histogram_t compute(std::array<std::vector<histogram_t>, 10> precomputed, llu upto) { histogram_t ret = {{0}}; char digits[32]; sprintf(digits, "%llu", upto); int len = std::strlen(digits); for (int i = 0; i < len; i++) { // printf("Position %d (%c)\n", i, digits[i]); digits[i] -= '0'; // For all non-zero digits up to the current one, count the configurations // which start with 'd' for (int d = 1; d < digits[i]; d++) { // printf("Processing digit %d\n", d); for (int remainder = 1; remainder < 10; remainder++) { const auto& histos = precomputed[remainder]; for (const histogram_t& histo : histos) { if (histo[d] > 0) { // printf(" Including"); // for (int i = 0; i < 10; i++) { // printf(" %llu", histo[i]); // } // printf("\n"); llu counts = 1; llu sum = 0; for (int x = 1; x < 10; x++) { sum += histo[x] - (x == d ? 1 : 0); counts *= BINOM[sum][histo[x] - (x == d ? 1 : 0)]; } ret[remainder] += counts; } } } } // Filter out the histograms - leave only those which are possible // after the current digit is added // printf("Continuing to the next digit (%d)\n", digits[i]); for (auto& histos : precomputed) { int pos = 0; while (pos < histos.size()) { if (histos[pos][digits[i]] == 0) { // Remove this histogram - doesn't have the necessary digits // printf(" Rejecting"); // for (int x = 0; x < 10; x++) { // printf(" %llu", histos[pos][x]); // } // printf("\n"); histos[pos] = histos.back(); histos.pop_back(); } else { // printf(" Keeping "); // for (int i = 0; i < 10; i++) { // printf(" %llu", histos[pos][i]); // } // printf("\n"); histos[pos][digits[i]]--; pos++; } } } } // There might be one remaining histogram that we need to include for (int i = 1; i < 10; i++) { if (!precomputed[i].empty()) { // printf("Adding leftover histogram with remainder %d\n", i); ret[i]++; } } ret[0] = upto + 1 - POWERS_OF_TEN[len - 1]; for (int i = 1; i < 10; i++) { ret[0] -= ret[i]; } return ret; }; int main() { for (int n = 0; n < 20; n++) { for (int k = 0; k < 20; k++) { BINOM[n][k] = binom(n, k); } } int t; scanf("%d\n", &t); std::array<std::array<std::vector<histogram_t>, 10>, 20> precomputed; std::array<histogram_t, 20> baselines = {{0}}; for (int i = 1; i < 20; i++) { histogram_t tmp; enumerate(precomputed[i], tmp, i, 1); } llu tenpow = 1; for (int i = 1; i < 20; i++) { baselines[i] = compute(precomputed[i - 1], tenpow - 1); for (int j = 0; j < 10; j++) { baselines[i][j] += baselines[i - 1][j]; } tenpow *= 10; } while (t --> 0) { llu n; scanf("%llu", &n); char digits[32]; sprintf(digits, "%llu", n); int len = std::strlen(digits); histogram_t counts = compute(precomputed[len], n); for (int i = 0; i < 10; i++) { if (i == 9) { printf("%llu\n", baselines[len][i] + counts[i]); } else { printf("%llu ", baselines[len][i] + counts[i]); } } } return 0; } |