//PROBLEM 3B #pragma GCC optimize("O3") #include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for(int i = a; i < (b); ++i) #define all(x) begin(x), end(x) #define sz(x) (int)(x).size() typedef long long ll; typedef pair<int, int> pii; typedef vector<int> vi; const ll maxN = ll(1e18) + ll(1e9); ll compute(ll x) { while(x > 9) { string s = to_string(x); x = 1; for(auto &i : s) x *= (i - '0'); } return x; } const int MAX_LEN = 19; int num_id[60][38][26][22]; ll dp[MAX_LEN + 2][66666][10];//dp[length][product][digit], digit turned into prefix sum ll result[66666]; int main() { cin.tie(0)->sync_with_stdio(0); vector<array<ll, 5>> numbers; vector<ll> possible_nonzero; for(ll p2 = 0, mock2 = maxN; mock2; p2++, mock2 /= 2) { for(ll p3 = 0, mock3 = mock2; mock3; p3++, mock3 /= 3) { for(ll p5 = 0, mock5 = mock3; mock5; p5++, mock5 /= 5) { for(ll p7 = 0, mock7 = mock5; mock7; p7++, mock7 /= 7) { ll val = 1; for(ll t = p2; t--;) val *= 2; for(ll t = p3; t--;) val *= 3; for(ll t = p5; t--;) val *= 5; for(ll t = p7; t--;) val *= 7; num_id[p2][p3][p5][p7] = numbers.size(); result[numbers.size()] = compute(val); if(result[numbers.size()]) possible_nonzero.push_back(numbers.size()); numbers.push_back({val, p2, p3, p5, p7}); } } } } auto transition = [&](int cur_len, int p2, int p3, int p5, int p7, int digit, ll val) { assert(digit); { int tmp = digit; while(tmp % 2 == 0) tmp /= 2, p2++; while(tmp % 3 == 0) tmp /= 3, p3++; while(tmp % 5 == 0) tmp /= 5, p5++; while(tmp % 7 == 0) tmp /= 7, p7++; } if(p2 >= 60 || p3 >= 38 || p5 >= 26 || p7 >= 22) return; int new_id = num_id[p2][p3][p5][p7]; dp[cur_len + 1][new_id][digit] += val; }; dp[0][0][0] = 1; for(int len = 0; len <= MAX_LEN; len++) { for(auto [num, p2, p3, p5, p7] : numbers) { int cur_id = num_id[p2][p3][p5][p7]; for(int digit = 1; digit < 10; digit++) dp[len][cur_id][digit] += dp[len][cur_id][digit - 1]; ll sum = dp[len][cur_id][9]; if(!sum) continue; for(int digit = 1; digit < 10; digit++) transition(len, p2, p3, p5, p7, digit, sum); } } // for(int len = 0; len <= 2; len++) { // for(auto [num, p2, p3, p5, p7] : numbers) { // int cur_id = num_id[p2][p3][p5][p7]; // if(!dp[len][cur_id][9]) continue; // cout << len << " " << setw(5) << num << " "; // for(int digit = 1; digit < 10; digit++) { // cout << setw(3) << dp[len][cur_id][digit] << " "; // } // cout << endl; // } // } auto solve = [&](ll n) -> array<ll, 10> { array<ll, 10> answer; answer.fill(0); string strn = to_string(n); int len = strn.size(); for(auto target_id : possible_nonzero) { ll count = 0; auto [num, p2, p3, p5, p7] = numbers[target_id]; [&]() { for(int shorter = 1; shorter < len; shorter++) count += dp[shorter][target_id][9]; for(int matched = 0; matched < len; matched++) { int tmp = strn[matched] - '0'; if(tmp == 0) return; // cout << num_id[p2][p3][p5][p7] << endl; count += dp[len - matched][num_id[p2][p3][p5][p7]][tmp - 1]; while(tmp % 2 == 0) tmp /= 2, p2--; while(tmp % 3 == 0) tmp /= 3, p3--; while(tmp % 5 == 0) tmp /= 5, p5--; while(tmp % 7 == 0) tmp /= 7, p7--; if(min({p2, p3, p5, p7}) < 0) return; } //matched == len count += dp[len - len][num_id[p2][p3][p5][p7]][9]; }(); answer[result[target_id]] += count; } for(auto &i : answer) answer[0] -= i; answer[0] += n; return answer; }; int T; cin >> T; while(T--) { ll n; cin >> n; auto answer = solve(n); for(int i = 0; i < 10; i++) { cout << answer[i]; if(i == 9) cout << '\n'; else cout << ' '; } } }
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 | //PROBLEM 3B #pragma GCC optimize("O3") #include <bits/stdc++.h> using namespace std; #define rep(i, a, b) for(int i = a; i < (b); ++i) #define all(x) begin(x), end(x) #define sz(x) (int)(x).size() typedef long long ll; typedef pair<int, int> pii; typedef vector<int> vi; const ll maxN = ll(1e18) + ll(1e9); ll compute(ll x) { while(x > 9) { string s = to_string(x); x = 1; for(auto &i : s) x *= (i - '0'); } return x; } const int MAX_LEN = 19; int num_id[60][38][26][22]; ll dp[MAX_LEN + 2][66666][10];//dp[length][product][digit], digit turned into prefix sum ll result[66666]; int main() { cin.tie(0)->sync_with_stdio(0); vector<array<ll, 5>> numbers; vector<ll> possible_nonzero; for(ll p2 = 0, mock2 = maxN; mock2; p2++, mock2 /= 2) { for(ll p3 = 0, mock3 = mock2; mock3; p3++, mock3 /= 3) { for(ll p5 = 0, mock5 = mock3; mock5; p5++, mock5 /= 5) { for(ll p7 = 0, mock7 = mock5; mock7; p7++, mock7 /= 7) { ll val = 1; for(ll t = p2; t--;) val *= 2; for(ll t = p3; t--;) val *= 3; for(ll t = p5; t--;) val *= 5; for(ll t = p7; t--;) val *= 7; num_id[p2][p3][p5][p7] = numbers.size(); result[numbers.size()] = compute(val); if(result[numbers.size()]) possible_nonzero.push_back(numbers.size()); numbers.push_back({val, p2, p3, p5, p7}); } } } } auto transition = [&](int cur_len, int p2, int p3, int p5, int p7, int digit, ll val) { assert(digit); { int tmp = digit; while(tmp % 2 == 0) tmp /= 2, p2++; while(tmp % 3 == 0) tmp /= 3, p3++; while(tmp % 5 == 0) tmp /= 5, p5++; while(tmp % 7 == 0) tmp /= 7, p7++; } if(p2 >= 60 || p3 >= 38 || p5 >= 26 || p7 >= 22) return; int new_id = num_id[p2][p3][p5][p7]; dp[cur_len + 1][new_id][digit] += val; }; dp[0][0][0] = 1; for(int len = 0; len <= MAX_LEN; len++) { for(auto [num, p2, p3, p5, p7] : numbers) { int cur_id = num_id[p2][p3][p5][p7]; for(int digit = 1; digit < 10; digit++) dp[len][cur_id][digit] += dp[len][cur_id][digit - 1]; ll sum = dp[len][cur_id][9]; if(!sum) continue; for(int digit = 1; digit < 10; digit++) transition(len, p2, p3, p5, p7, digit, sum); } } // for(int len = 0; len <= 2; len++) { // for(auto [num, p2, p3, p5, p7] : numbers) { // int cur_id = num_id[p2][p3][p5][p7]; // if(!dp[len][cur_id][9]) continue; // cout << len << " " << setw(5) << num << " "; // for(int digit = 1; digit < 10; digit++) { // cout << setw(3) << dp[len][cur_id][digit] << " "; // } // cout << endl; // } // } auto solve = [&](ll n) -> array<ll, 10> { array<ll, 10> answer; answer.fill(0); string strn = to_string(n); int len = strn.size(); for(auto target_id : possible_nonzero) { ll count = 0; auto [num, p2, p3, p5, p7] = numbers[target_id]; [&]() { for(int shorter = 1; shorter < len; shorter++) count += dp[shorter][target_id][9]; for(int matched = 0; matched < len; matched++) { int tmp = strn[matched] - '0'; if(tmp == 0) return; // cout << num_id[p2][p3][p5][p7] << endl; count += dp[len - matched][num_id[p2][p3][p5][p7]][tmp - 1]; while(tmp % 2 == 0) tmp /= 2, p2--; while(tmp % 3 == 0) tmp /= 3, p3--; while(tmp % 5 == 0) tmp /= 5, p5--; while(tmp % 7 == 0) tmp /= 7, p7--; if(min({p2, p3, p5, p7}) < 0) return; } //matched == len count += dp[len - len][num_id[p2][p3][p5][p7]][9]; }(); answer[result[target_id]] += count; } for(auto &i : answer) answer[0] -= i; answer[0] += n; return answer; }; int T; cin >> T; while(T--) { ll n; cin >> n; auto answer = solve(n); for(int i = 0; i < 10; i++) { cout << answer[i]; if(i == 9) cout << '\n'; else cout << ' '; } } } |