#include <iostream> #include <cmath> #include <vector> #include <algorithm> const int MD = 20; int64_t F[MD]; int64_t S[MD][MD]; // (n over k) char C[MD]; char C2[MD]; int C2l; const int MAX = 14000000; char N[MAX][MD]; char B[MAX]; int D[MAX]; int Z[MAX]; int nc = 0; int64_t CCV[MD][10]; std::vector<int> DDN[MD]; void toD2(int64_t v) { C2l = 0; while (v > 0) { C2[C2l] = v%10; v/=10; ++C2l; } C2[C2l] = 0; std::reverse(C2, C2+C2l); } void toD(int64_t x, int z = 0) { int& d = D[nc]; Z[nc] = z; char *NN = N[nc]; while (z > 0) { NN[d] = 0; ++d; --z; } while (x > 0) { NN[d] = x%10; x/=10; ++d; } DDN[d].push_back(nc); ++nc; } // int64_t mul(int64_t x) { // int64_t y = 1; // for (char c : std::to_string(x)) { // y *= c-'0'; // } // return y; // } int64_t mul2(int64_t x) { int64_t y = 1; while (x > 0) { y*=x%10; x/=10; } return y; } int64_t brute(int64_t x) { int64_t y = mul2(x); if (y > 9) return brute(y); else return y; } int64_t count = 0; void gen(int k, int d, std::string prefix) { if (d>9) return; if (k == 0) { ++count; // std::clog << prefix << std::endl; } else { if (d == -1) gen(k-1, d, prefix); else gen(k-1, d, prefix + char('0'+d)); gen(k, d+1, prefix); } } struct CC { int fc, fd, fz; int64_t ff; // CC(): fc(0), fd(0), ff(1) {} CC add(int d) { if (d == 0) return {fc, fd, fz+1, ff}; else return {fc+1, fd+1, fz, ff}; } CC apply() { return {fc, 0, fz, ff*F[fd]}; } int64_t total() { // if (fz > 0) std::clog << fz << " :: " << F[fc]/ff << " vs " << (F[fc]/ff) / (F[fc-1]/ff/F[fz-1]) << std::endl; // if (fz == 0) return F[fc]/ff; // else return (F[fc]/ff)/(F[fc-1]/ff/F[fz-1]); // return fz*F[fc-1]/ff/F[fd]; if (fc == 0) return 0; // return F[fc]/ff/F[fd]*(F[fc+fz-1]/F[fc-1]/F[fz]); return F[fc]/(ff*F[fd])*S[fc+fz-1][fz]; } }; int64_t vvv; struct CC2 { static CC2 make(int n) { CC2 cc; cc.n = n; cc.d = D[n]; cc.C[0] = Z[n]; for (int i=0;i<10;++i) cc.C[i] = 0; for (int i;i<cc.d;++i) { ++cc.C[N[n][i]]; } cc.fd = 1; for (int i=0;i<10;++i) cc.fd *= F[cc.C[i]]; return cc; } CC2 without(int digit) const { CC2 cc2 = *this; cc2.fd /= cc2.C[digit]; --cc2.C[digit]; --cc2.d; return cc2; } int64_t total() const { if (d == 0) return 1; // int64_t ttl = F[d]; // for (int i=0;i<10;++i) ttl /= F[C[i]]; // return ttl; return F[d] / fd; } // // C2 <= this int64_t count_le(int nv, bool start = false) { if (d == 0) return 0; int d1 = start ? 1 : 0; int64_t total = 0; while (d1 < C2[nv]) { if (C[d1] > 0) { // std::clog << d1 << "(" << N[n][d] << ")" << " : " << without(d1).total() << std::endl; total += without(d1).total(); } ++d1; } // std::clog << "::: ::: " << total << " " << d1 << " " << int(C2[nv]) << std::endl; // d1 == C2[nv] if (d == 1) return total + C[d1]; else if (C[d1] > 0) return total + without(d1).count_le(nv+1); else return total; } char C[10]; int64_t fd; int d; int n; }; // int64_t C[10]; void gen(int k, int d, int64_t p, int z, CC cc) { if (k == 0) { if (p == 0) { ++count; return; } else if (z > 0) { B[nc] = 0; toD(p, z); CCV[cc.fc + z][0] += cc.total(); // C[0] += cc.total(); } else { int bb = B[nc] = brute(p); toD(p); CCV[cc.fc + z][bb] += cc.total(); //C[brute(p)] += cc.total(); } // std::clog << std::string(z, '0') << p << " = " << brute(p) << " x " << cc.total() << std::endl; } else { if (d == -1) gen(k-1, d, p, z, cc); else if (d == 0) gen(k-1, d, p*10+d, z+1, cc.add(d)); else gen(k-1, d, p*10+d, z, cc.add(d)); if (d<9) gen(k, d+1, p, z, cc.apply()); } } int64_t count_le(int n) { CC2 cc = CC2::make(n); return cc.count_le(0, true); } int64_t CV[10]; void solve(int64_t v) { vvv = v; toD2(v); for (int i=0;i<10;++i) CV[i] = 0; int d = 0; while (v > 9) { ++d; for (int i=0;i<10;++i) CV[i] += CCV[d][i]; v /= 10; } for (int n : DDN[d+1]) { int64_t cl = count_le(n); // std::clog << B[n] << " :: " << std::string(Z[n], '0'); // for (int i=0;i<D[n];++i) std::clog << int(N[n][i]); // std::clog << " <= " << v << " = " << cl << std::endl; CV[B[n]] += cl; } } int64_t T[1001]; int main() { std::ios_base::sync_with_stdio(0); F[0] = 1; for (int i=1;i<MD;++i) F[i] = F[i-1]*i; for (int i=0;i<MD;++i) S[i][0] = S[i][i] = 1; for (int i=1;i<MD;++i) for (int j=1;j<MD;++j) S[i][j] = S[i-1][j-1] + S[i-1][j]; // C[0] = 1; CCV[0][0] = 1; int t; std::cin >> t; int digits = 1; for (int i=0;i<t;++i) { int64_t v; std::cin >> T[i]; toD2(T[i]); digits = std::max(digits, C2l); } gen(std::min(digits, 18), -1, 0, 0, {0,0,0,1}); gen(0, 19, 1, 18, {1, 1, 18, 1}); for (int i=0;i<t;++i) { solve(T[i]); std::cout << CV[0]; for (int i=1;i<10;++i) std::cout << " " << CV[i]; // std::cout << "\n"; std::cout << std::endl; } // std::cin >> n; // gen(n, -1, 0, 0, {0,0,0,1}); // for (int i=0;i<10;++i) std::cout << " " << C[i]; // std::cout << std::endl; // std::cout.precision(4); // for (int i=0;i<10;++i) std::cout << " " << std::fixed << double(C[i])/pow(10,n)*100; // std::cout << std::endl; // int64_t total = 0; // for (int i=0;i<10;++i) total += C[i]; // std::cout << "Total = " << std::fixed << double(total)/pow(10,n)*100; // std::clog << "COUNT OF ZEROS = " << count << std::endl; // std::cin >> n; // for (int i= 0;i<n;++i) { // std::cout << i << " = " << brute(i) << " %= " << mul(i)%10 << 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 | #include <iostream> #include <cmath> #include <vector> #include <algorithm> const int MD = 20; int64_t F[MD]; int64_t S[MD][MD]; // (n over k) char C[MD]; char C2[MD]; int C2l; const int MAX = 14000000; char N[MAX][MD]; char B[MAX]; int D[MAX]; int Z[MAX]; int nc = 0; int64_t CCV[MD][10]; std::vector<int> DDN[MD]; void toD2(int64_t v) { C2l = 0; while (v > 0) { C2[C2l] = v%10; v/=10; ++C2l; } C2[C2l] = 0; std::reverse(C2, C2+C2l); } void toD(int64_t x, int z = 0) { int& d = D[nc]; Z[nc] = z; char *NN = N[nc]; while (z > 0) { NN[d] = 0; ++d; --z; } while (x > 0) { NN[d] = x%10; x/=10; ++d; } DDN[d].push_back(nc); ++nc; } // int64_t mul(int64_t x) { // int64_t y = 1; // for (char c : std::to_string(x)) { // y *= c-'0'; // } // return y; // } int64_t mul2(int64_t x) { int64_t y = 1; while (x > 0) { y*=x%10; x/=10; } return y; } int64_t brute(int64_t x) { int64_t y = mul2(x); if (y > 9) return brute(y); else return y; } int64_t count = 0; void gen(int k, int d, std::string prefix) { if (d>9) return; if (k == 0) { ++count; // std::clog << prefix << std::endl; } else { if (d == -1) gen(k-1, d, prefix); else gen(k-1, d, prefix + char('0'+d)); gen(k, d+1, prefix); } } struct CC { int fc, fd, fz; int64_t ff; // CC(): fc(0), fd(0), ff(1) {} CC add(int d) { if (d == 0) return {fc, fd, fz+1, ff}; else return {fc+1, fd+1, fz, ff}; } CC apply() { return {fc, 0, fz, ff*F[fd]}; } int64_t total() { // if (fz > 0) std::clog << fz << " :: " << F[fc]/ff << " vs " << (F[fc]/ff) / (F[fc-1]/ff/F[fz-1]) << std::endl; // if (fz == 0) return F[fc]/ff; // else return (F[fc]/ff)/(F[fc-1]/ff/F[fz-1]); // return fz*F[fc-1]/ff/F[fd]; if (fc == 0) return 0; // return F[fc]/ff/F[fd]*(F[fc+fz-1]/F[fc-1]/F[fz]); return F[fc]/(ff*F[fd])*S[fc+fz-1][fz]; } }; int64_t vvv; struct CC2 { static CC2 make(int n) { CC2 cc; cc.n = n; cc.d = D[n]; cc.C[0] = Z[n]; for (int i=0;i<10;++i) cc.C[i] = 0; for (int i;i<cc.d;++i) { ++cc.C[N[n][i]]; } cc.fd = 1; for (int i=0;i<10;++i) cc.fd *= F[cc.C[i]]; return cc; } CC2 without(int digit) const { CC2 cc2 = *this; cc2.fd /= cc2.C[digit]; --cc2.C[digit]; --cc2.d; return cc2; } int64_t total() const { if (d == 0) return 1; // int64_t ttl = F[d]; // for (int i=0;i<10;++i) ttl /= F[C[i]]; // return ttl; return F[d] / fd; } // // C2 <= this int64_t count_le(int nv, bool start = false) { if (d == 0) return 0; int d1 = start ? 1 : 0; int64_t total = 0; while (d1 < C2[nv]) { if (C[d1] > 0) { // std::clog << d1 << "(" << N[n][d] << ")" << " : " << without(d1).total() << std::endl; total += without(d1).total(); } ++d1; } // std::clog << "::: ::: " << total << " " << d1 << " " << int(C2[nv]) << std::endl; // d1 == C2[nv] if (d == 1) return total + C[d1]; else if (C[d1] > 0) return total + without(d1).count_le(nv+1); else return total; } char C[10]; int64_t fd; int d; int n; }; // int64_t C[10]; void gen(int k, int d, int64_t p, int z, CC cc) { if (k == 0) { if (p == 0) { ++count; return; } else if (z > 0) { B[nc] = 0; toD(p, z); CCV[cc.fc + z][0] += cc.total(); // C[0] += cc.total(); } else { int bb = B[nc] = brute(p); toD(p); CCV[cc.fc + z][bb] += cc.total(); //C[brute(p)] += cc.total(); } // std::clog << std::string(z, '0') << p << " = " << brute(p) << " x " << cc.total() << std::endl; } else { if (d == -1) gen(k-1, d, p, z, cc); else if (d == 0) gen(k-1, d, p*10+d, z+1, cc.add(d)); else gen(k-1, d, p*10+d, z, cc.add(d)); if (d<9) gen(k, d+1, p, z, cc.apply()); } } int64_t count_le(int n) { CC2 cc = CC2::make(n); return cc.count_le(0, true); } int64_t CV[10]; void solve(int64_t v) { vvv = v; toD2(v); for (int i=0;i<10;++i) CV[i] = 0; int d = 0; while (v > 9) { ++d; for (int i=0;i<10;++i) CV[i] += CCV[d][i]; v /= 10; } for (int n : DDN[d+1]) { int64_t cl = count_le(n); // std::clog << B[n] << " :: " << std::string(Z[n], '0'); // for (int i=0;i<D[n];++i) std::clog << int(N[n][i]); // std::clog << " <= " << v << " = " << cl << std::endl; CV[B[n]] += cl; } } int64_t T[1001]; int main() { std::ios_base::sync_with_stdio(0); F[0] = 1; for (int i=1;i<MD;++i) F[i] = F[i-1]*i; for (int i=0;i<MD;++i) S[i][0] = S[i][i] = 1; for (int i=1;i<MD;++i) for (int j=1;j<MD;++j) S[i][j] = S[i-1][j-1] + S[i-1][j]; // C[0] = 1; CCV[0][0] = 1; int t; std::cin >> t; int digits = 1; for (int i=0;i<t;++i) { int64_t v; std::cin >> T[i]; toD2(T[i]); digits = std::max(digits, C2l); } gen(std::min(digits, 18), -1, 0, 0, {0,0,0,1}); gen(0, 19, 1, 18, {1, 1, 18, 1}); for (int i=0;i<t;++i) { solve(T[i]); std::cout << CV[0]; for (int i=1;i<10;++i) std::cout << " " << CV[i]; // std::cout << "\n"; std::cout << std::endl; } // std::cin >> n; // gen(n, -1, 0, 0, {0,0,0,1}); // for (int i=0;i<10;++i) std::cout << " " << C[i]; // std::cout << std::endl; // std::cout.precision(4); // for (int i=0;i<10;++i) std::cout << " " << std::fixed << double(C[i])/pow(10,n)*100; // std::cout << std::endl; // int64_t total = 0; // for (int i=0;i<10;++i) total += C[i]; // std::cout << "Total = " << std::fixed << double(total)/pow(10,n)*100; // std::clog << "COUNT OF ZEROS = " << count << std::endl; // std::cin >> n; // for (int i= 0;i<n;++i) { // std::cout << i << " = " << brute(i) << " %= " << mul(i)%10 << std::endl; // } return 0; } |