#include <bits/stdc++.h> using namespace std; constexpr int MAX_DIGITS = 18; struct Number; long long factorial[MAX_DIGITS + 1]; vector<Number> pre_numbers; int t; long long n; struct Number { int final_digit; int length = 0; int digit_count[10] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; long long numerator, denominator; Number(long long num, int num_digitified) { final_digit = num_digitified; while(num) { length++, digit_count[num % 10]++; num /= 10; } numerator = factorial[length]; denominator = 1; for(int i = 1; i <= 9; i++) { denominator *= factorial[digit_count[i]]; } } long long combinations() { return numerator / denominator; } void add_digit(int digit) { numerator = factorial[++length]; denominator *= ++digit_count[digit]; } void remove_digit(int digit) { numerator = factorial[--length]; denominator /= digit_count[digit]--; } }; long long digitify(long long num) { while(num > 9) { long long new_num = 1; while(num) { new_num *= num % 10; num /= 10; } num = new_num; } return num; } void precompute() { factorial[0] = 1; for(int i = 1; i <= MAX_DIGITS; i++) { factorial[i] = factorial[i - 1] * i; } vector<pair<long long, long long>> candidates; for(int i = 1; i <= 9; i++) { candidates.push_back({i, i}); pre_numbers.push_back(Number(i, i)); } for(int lth = 2; lth <= MAX_DIGITS; lth++) { vector<pair<long long, long long>> new_candidates; for(pair<long long, long long> candidate : candidates) { for(int i = candidate.first % 10; i <= 9; i++) { new_candidates.push_back({(candidate.first * 10) + i, candidate.second * i}); if(!new_candidates.back().second) { new_candidates.pop_back(); continue; } int final_digit = digitify(new_candidates.back().second); if(final_digit) { pre_numbers.push_back(Number(new_candidates.back().first, final_digit)); } } } swap(candidates, new_candidates); } } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); precompute(); cin >> t; while(t--) { cin >> n; string n_str = to_string(n); vector<long long> ans(10); for(Number number : pre_numbers) { if(number.length > (int)n_str.length()) { continue; } if(number.length < (int)n_str.length()) { ans[number.final_digit] += number.combinations(); continue; } bool entire = true; for(char c : n_str) { if(c == '0') { entire = false; break; } for(int i = 1; i < c - '0'; i++) { if(number.digit_count[i] > 0) { number.remove_digit(i); ans[number.final_digit] += number.combinations(); number.add_digit(i); } } if(number.digit_count[c - '0'] > 0) { number.remove_digit(c - '0'); } else { entire = false; break; } } if(entire) { ans[number.final_digit]++; } } ans[0] = n - accumulate(ans.begin(), ans.end(), 0LL); for(long long i : ans) { cout << i << ' '; } cout << '\n'; } }
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 | #include <bits/stdc++.h> using namespace std; constexpr int MAX_DIGITS = 18; struct Number; long long factorial[MAX_DIGITS + 1]; vector<Number> pre_numbers; int t; long long n; struct Number { int final_digit; int length = 0; int digit_count[10] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; long long numerator, denominator; Number(long long num, int num_digitified) { final_digit = num_digitified; while(num) { length++, digit_count[num % 10]++; num /= 10; } numerator = factorial[length]; denominator = 1; for(int i = 1; i <= 9; i++) { denominator *= factorial[digit_count[i]]; } } long long combinations() { return numerator / denominator; } void add_digit(int digit) { numerator = factorial[++length]; denominator *= ++digit_count[digit]; } void remove_digit(int digit) { numerator = factorial[--length]; denominator /= digit_count[digit]--; } }; long long digitify(long long num) { while(num > 9) { long long new_num = 1; while(num) { new_num *= num % 10; num /= 10; } num = new_num; } return num; } void precompute() { factorial[0] = 1; for(int i = 1; i <= MAX_DIGITS; i++) { factorial[i] = factorial[i - 1] * i; } vector<pair<long long, long long>> candidates; for(int i = 1; i <= 9; i++) { candidates.push_back({i, i}); pre_numbers.push_back(Number(i, i)); } for(int lth = 2; lth <= MAX_DIGITS; lth++) { vector<pair<long long, long long>> new_candidates; for(pair<long long, long long> candidate : candidates) { for(int i = candidate.first % 10; i <= 9; i++) { new_candidates.push_back({(candidate.first * 10) + i, candidate.second * i}); if(!new_candidates.back().second) { new_candidates.pop_back(); continue; } int final_digit = digitify(new_candidates.back().second); if(final_digit) { pre_numbers.push_back(Number(new_candidates.back().first, final_digit)); } } } swap(candidates, new_candidates); } } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); precompute(); cin >> t; while(t--) { cin >> n; string n_str = to_string(n); vector<long long> ans(10); for(Number number : pre_numbers) { if(number.length > (int)n_str.length()) { continue; } if(number.length < (int)n_str.length()) { ans[number.final_digit] += number.combinations(); continue; } bool entire = true; for(char c : n_str) { if(c == '0') { entire = false; break; } for(int i = 1; i < c - '0'; i++) { if(number.digit_count[i] > 0) { number.remove_digit(i); ans[number.final_digit] += number.combinations(); number.add_digit(i); } } if(number.digit_count[c - '0'] > 0) { number.remove_digit(c - '0'); } else { entire = false; break; } } if(entire) { ans[number.final_digit]++; } } ans[0] = n - accumulate(ans.begin(), ans.end(), 0LL); for(long long i : ans) { cout << i << ' '; } cout << '\n'; } } |