#include <bits/stdc++.h> using namespace std; #define ll long long #define ull unsigned ll #define pb push_back #define pii pair<int,int> #define pl pair<ll,ll> #define F first #define S second #define pq priority_queue #define rep(x,y) for(ull x = 0; x < y; x++) #define all(x) x.begin(), x.end() #define deb(x) if(debug) cout << #x << " = " << x << '\n'; #define deb2(x,y) if(debug) cout << #x << " = " << x << ", " << #y << " = " << y << '\n'; constexpr ull M = 1e6+7; constexpr int N = 1e6+7; constexpr int C = 10; constexpr bool debug = 0; map<ull,ull> where; //do ktorej cyfry trafia liczby z tym iloczynem map<ull,ull> combo; //[hasz] = liczba kombinacji ull maks, cyfrmaks; ull sc[10]; ull fac[20]; ull Cpow[13]; int q; struct que{ ull ind; ull num; ull ans[10]; }; bool numsort(que a, que b){ return a.num < b.num; } bool indsort(que a, que b){ return a.ind > b.ind; } int goes(ull num){ //raczej dziala if(num < 10){ where[num] = num+1; return where[num]-1; } if(where[num] > 0) return where[num]-1; ull i = 1; while(num > 0){ i *= num%10; num /= 10; } where[num] = goes(i)+1; return where[num]-1; } ull calc_comb(ull hasz){ //sprawdzic if(combo[hasz] == 0){ ull obcomb = 0; ull bob = 1; for(ull i = 0; i < 8; i++){ if((hasz/bob)%C > 0){ obcomb += calc_comb(hasz-bob); } bob *= C; } combo[hasz] = obcomb; return obcomb; } return combo[hasz]; } ull haszuj(vector<ull> kk){ ull hasz = 0; ull ob = 1; for(ull i = 0; i < 8; i++){ hasz += ob*kk[i]; ob *= C; } return hasz; } vector<ull> unhaszuj(ull hasz){ vector<ull> unhasz(8); for(ull i = 0; i < 8; i++){ unhasz[i] = hasz%C; hasz /= C; } return unhasz; } ull choos(ull a, ull b){ //a wybierz b if(a < b) return 0; return fac[a]/(fac[b]*fac[a-b]); } void process(vector<ull> nums){ //zakladamy, ze przerobilismy wszystkie podciagi ull obhasz = haszuj(nums); ull kombs = 0; ull obkombs = calc_comb(obhasz); //for(auto k: nums) cout << k << ' '; if(debug) cout << '\n'; ull cyfr = 0; for(auto k: nums) cyfr += k; //mniejsza ilosc cyfr //deb(cyfr); if(cyfr == 0) return; for(ull i = cyfr; i < cyfrmaks; i++){ kombs += obkombs*choos(i,cyfr); } //deb(kombs); //rowna ilosc cyfr, idzie po prefiksach ull hasz2 = obhasz; ull ex = 0; ull cyf = 2; ull ten = 1; while(obhasz > 0){ //to raczej dziala while(obhasz%C){ ex += ten*cyf; ten *= 10; --obhasz; } obhasz /= C; ++cyf; } ten = pow(10,cyfrmaks-1); ull cel = goes(ex); ull rem = cyfrmaks-1; ull cyfr2 = cyfr; deb(ex); deb(cel); while(ten > 0){ for(int i = 1; i < (maks/ten)%10; i++){ //co jesli zero? deb(i); if(i == 1){ kombs += calc_comb(hasz2)*choos(rem,cyfr2); } else if((hasz2/Cpow[i-2])%C >= 1){ //cout << "BAM " << rem << ' ' << cyfr2 << '\n'; kombs += calc_comb(hasz2-Cpow[i-2])*choos(rem,cyfr2-1); } } if((maks/ten)%10 != 1){ if((maks/ten)%10 == 0) break; if( (hasz2/Cpow[((maks/ten)%10)-2])%C >= 1){ hasz2 -= Cpow[((maks/ten)%10)-2]; cyfr2--; if(cyfr2 < 0) break; } else break; } ten /= 10; rem--; //if(rem < cyfr2) break; } deb(kombs); //deb(ex); sc[cel] += kombs; } que solve(){ //musimy policzyc potencjalne grupy fill(sc, sc+10, 0); cyfrmaks = 0; ull low = 1; if(maks % 10 == 0){ sc[0]++; maks--; } while(low <= maks){ //ile cyfr ma maks low *= 10; cyfrmaks++; } deb(cyfrmaks); //process({0,2,1,3,1,1,0,1}); //ile idzie do 0 bool ones = 1; ull tochek = maks; while(tochek > 0){ if(tochek%10 == 0){ ones = 1; break; } else if(tochek%10 != 1){ ones = 0; //break; } tochek /= 10; } if(!ones){ sc[goes(maks)]++; } ull nonz = 0; ull ten = pow(10,cyfrmaks-1); ull nin = pow(9, cyfrmaks-1); bool pref = 1; if(nin == 1) nonz = maks; else{ while(nin > 0){ if(nin > 1) nonz += nin; deb(nonz); //mniej cyfr, doliczamy ostatni if((maks/ten)%10 == 0) pref = 0; if(pref) nonz += ((maks/ten)%10 - 1)*nin; //uzywamy wszystkich cyfr, skipujemy ostatni element? if(pref && nin == 1) nonz++; deb(nin); ten /= 10; nin /= 9; } } deb(nonz); //ile to ciagi jedynek ull ons = 1; while(ons <= maks){ sc[1]++; ons = ons*10 + 1; } //deb(nonz); sc[0] += maks-nonz; rep(k9, cyfrmaks+1){ rep(k8, cyfrmaks+1-k9){ rep(k7, cyfrmaks+1-k9-k8){ rep(k6, cyfrmaks+1-k9-k8-k7){ //for(int k5 = 0; k5 <= 0; k5++){ rep(k5, cyfrmaks+1-k9-k8-k7-k6){ rep(k4, cyfrmaks+1-k9-k8-k7-k6-k5){ rep(k3, cyfrmaks+1-k9-k8-k7-k6-k5-k4){ rep(k2, cyfrmaks+1-k9-k8-k7-k6-k5-k4-k3){ vector<ull> nums = {k2,k3,k4,k5,k6,k7,k8,k9}; process(nums); } } } } } } } } que ok; ok.ind = q; for(int i = 0; i < 10; i++){ ok.ans[i] = sc[i]; } return ok; //cout << '\n'; } int main(){ ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); combo[0] = 1; fac[0] = 1; Cpow[0] = 1; for(ull i = 1; i < 20; i++) fac[i] = fac[i-1]*i; for(ull i = 1; i < 20; i++) Cpow[i] = Cpow[i-1]*C; //cout << calc_comb(haszuj({2,2,0,0,0,0,0,0})); //rep(i,11) deb(choos(10,i)); vector<que> quers, quers2; cin >> q; while(q--){ cin >> maks; //cout << q << ' ' << maks << '\n'; if(maks <= M){ que ok; ok.ind = q; ok.num = maks; quers.pb(ok); } else{ que ok = solve(); quers2.pb(ok); } } if(!quers.empty()){ fill(sc, sc+10, 0); //cout << "don"; sort(all(quers), numsort); ull number = 0; for(ull i = 1; i <= M; i++){ //cout << i << '\n'; //cout << number << '\n'; sc[goes(i)]++; while(i == quers[number].num){ for(int j = 0; j < 10; j++){ quers[number].ans[j] = sc[j]; } number++; if(number >= quers.size()) break; } if(number >= quers.size()) break; } } if(quers.empty()) quers = quers2; else quers.insert(quers.end(), quers2.begin(), quers2.end()); sort(all(quers), indsort); for(auto k: quers){ for(int i = 0; i < 10; i++) cout << k.ans[i] << ' '; cout << '\n'; } /* */ 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 | #include <bits/stdc++.h> using namespace std; #define ll long long #define ull unsigned ll #define pb push_back #define pii pair<int,int> #define pl pair<ll,ll> #define F first #define S second #define pq priority_queue #define rep(x,y) for(ull x = 0; x < y; x++) #define all(x) x.begin(), x.end() #define deb(x) if(debug) cout << #x << " = " << x << '\n'; #define deb2(x,y) if(debug) cout << #x << " = " << x << ", " << #y << " = " << y << '\n'; constexpr ull M = 1e6+7; constexpr int N = 1e6+7; constexpr int C = 10; constexpr bool debug = 0; map<ull,ull> where; //do ktorej cyfry trafia liczby z tym iloczynem map<ull,ull> combo; //[hasz] = liczba kombinacji ull maks, cyfrmaks; ull sc[10]; ull fac[20]; ull Cpow[13]; int q; struct que{ ull ind; ull num; ull ans[10]; }; bool numsort(que a, que b){ return a.num < b.num; } bool indsort(que a, que b){ return a.ind > b.ind; } int goes(ull num){ //raczej dziala if(num < 10){ where[num] = num+1; return where[num]-1; } if(where[num] > 0) return where[num]-1; ull i = 1; while(num > 0){ i *= num%10; num /= 10; } where[num] = goes(i)+1; return where[num]-1; } ull calc_comb(ull hasz){ //sprawdzic if(combo[hasz] == 0){ ull obcomb = 0; ull bob = 1; for(ull i = 0; i < 8; i++){ if((hasz/bob)%C > 0){ obcomb += calc_comb(hasz-bob); } bob *= C; } combo[hasz] = obcomb; return obcomb; } return combo[hasz]; } ull haszuj(vector<ull> kk){ ull hasz = 0; ull ob = 1; for(ull i = 0; i < 8; i++){ hasz += ob*kk[i]; ob *= C; } return hasz; } vector<ull> unhaszuj(ull hasz){ vector<ull> unhasz(8); for(ull i = 0; i < 8; i++){ unhasz[i] = hasz%C; hasz /= C; } return unhasz; } ull choos(ull a, ull b){ //a wybierz b if(a < b) return 0; return fac[a]/(fac[b]*fac[a-b]); } void process(vector<ull> nums){ //zakladamy, ze przerobilismy wszystkie podciagi ull obhasz = haszuj(nums); ull kombs = 0; ull obkombs = calc_comb(obhasz); //for(auto k: nums) cout << k << ' '; if(debug) cout << '\n'; ull cyfr = 0; for(auto k: nums) cyfr += k; //mniejsza ilosc cyfr //deb(cyfr); if(cyfr == 0) return; for(ull i = cyfr; i < cyfrmaks; i++){ kombs += obkombs*choos(i,cyfr); } //deb(kombs); //rowna ilosc cyfr, idzie po prefiksach ull hasz2 = obhasz; ull ex = 0; ull cyf = 2; ull ten = 1; while(obhasz > 0){ //to raczej dziala while(obhasz%C){ ex += ten*cyf; ten *= 10; --obhasz; } obhasz /= C; ++cyf; } ten = pow(10,cyfrmaks-1); ull cel = goes(ex); ull rem = cyfrmaks-1; ull cyfr2 = cyfr; deb(ex); deb(cel); while(ten > 0){ for(int i = 1; i < (maks/ten)%10; i++){ //co jesli zero? deb(i); if(i == 1){ kombs += calc_comb(hasz2)*choos(rem,cyfr2); } else if((hasz2/Cpow[i-2])%C >= 1){ //cout << "BAM " << rem << ' ' << cyfr2 << '\n'; kombs += calc_comb(hasz2-Cpow[i-2])*choos(rem,cyfr2-1); } } if((maks/ten)%10 != 1){ if((maks/ten)%10 == 0) break; if( (hasz2/Cpow[((maks/ten)%10)-2])%C >= 1){ hasz2 -= Cpow[((maks/ten)%10)-2]; cyfr2--; if(cyfr2 < 0) break; } else break; } ten /= 10; rem--; //if(rem < cyfr2) break; } deb(kombs); //deb(ex); sc[cel] += kombs; } que solve(){ //musimy policzyc potencjalne grupy fill(sc, sc+10, 0); cyfrmaks = 0; ull low = 1; if(maks % 10 == 0){ sc[0]++; maks--; } while(low <= maks){ //ile cyfr ma maks low *= 10; cyfrmaks++; } deb(cyfrmaks); //process({0,2,1,3,1,1,0,1}); //ile idzie do 0 bool ones = 1; ull tochek = maks; while(tochek > 0){ if(tochek%10 == 0){ ones = 1; break; } else if(tochek%10 != 1){ ones = 0; //break; } tochek /= 10; } if(!ones){ sc[goes(maks)]++; } ull nonz = 0; ull ten = pow(10,cyfrmaks-1); ull nin = pow(9, cyfrmaks-1); bool pref = 1; if(nin == 1) nonz = maks; else{ while(nin > 0){ if(nin > 1) nonz += nin; deb(nonz); //mniej cyfr, doliczamy ostatni if((maks/ten)%10 == 0) pref = 0; if(pref) nonz += ((maks/ten)%10 - 1)*nin; //uzywamy wszystkich cyfr, skipujemy ostatni element? if(pref && nin == 1) nonz++; deb(nin); ten /= 10; nin /= 9; } } deb(nonz); //ile to ciagi jedynek ull ons = 1; while(ons <= maks){ sc[1]++; ons = ons*10 + 1; } //deb(nonz); sc[0] += maks-nonz; rep(k9, cyfrmaks+1){ rep(k8, cyfrmaks+1-k9){ rep(k7, cyfrmaks+1-k9-k8){ rep(k6, cyfrmaks+1-k9-k8-k7){ //for(int k5 = 0; k5 <= 0; k5++){ rep(k5, cyfrmaks+1-k9-k8-k7-k6){ rep(k4, cyfrmaks+1-k9-k8-k7-k6-k5){ rep(k3, cyfrmaks+1-k9-k8-k7-k6-k5-k4){ rep(k2, cyfrmaks+1-k9-k8-k7-k6-k5-k4-k3){ vector<ull> nums = {k2,k3,k4,k5,k6,k7,k8,k9}; process(nums); } } } } } } } } que ok; ok.ind = q; for(int i = 0; i < 10; i++){ ok.ans[i] = sc[i]; } return ok; //cout << '\n'; } int main(){ ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); combo[0] = 1; fac[0] = 1; Cpow[0] = 1; for(ull i = 1; i < 20; i++) fac[i] = fac[i-1]*i; for(ull i = 1; i < 20; i++) Cpow[i] = Cpow[i-1]*C; //cout << calc_comb(haszuj({2,2,0,0,0,0,0,0})); //rep(i,11) deb(choos(10,i)); vector<que> quers, quers2; cin >> q; while(q--){ cin >> maks; //cout << q << ' ' << maks << '\n'; if(maks <= M){ que ok; ok.ind = q; ok.num = maks; quers.pb(ok); } else{ que ok = solve(); quers2.pb(ok); } } if(!quers.empty()){ fill(sc, sc+10, 0); //cout << "don"; sort(all(quers), numsort); ull number = 0; for(ull i = 1; i <= M; i++){ //cout << i << '\n'; //cout << number << '\n'; sc[goes(i)]++; while(i == quers[number].num){ for(int j = 0; j < 10; j++){ quers[number].ans[j] = sc[j]; } number++; if(number >= quers.size()) break; } if(number >= quers.size()) break; } } if(quers.empty()) quers = quers2; else quers.insert(quers.end(), quers2.begin(), quers2.end()); sort(all(quers), indsort); for(auto k: quers){ for(int i = 0; i < 10; i++) cout << k.ans[i] << ' '; cout << '\n'; } /* */ return 0; } |