// clang-format off
#include<bits/stdc++.h>
using namespace std;
using LL=long long;
#define FOR(i,l,r) for(auto i=(l);i<=(r);++i)
#define REP(i,n) FOR(i,0,(n)-1)
#define ssize(x) int(x.size())
template<class A,class B>auto&operator<<(ostream&o,pair<A,B>p){return o<<"("<<p.first<<", "<<p.second<<")";}
template<class T>auto operator<<(ostream&o,T x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<(", ")+2*!i++<<e;return o<<"}";}
#ifdef DEBUG
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<"\n";}(X)
#else
#define debug(...) {}
#endif
// clang-format on
#include <ext/pb_ds/assoc_container.hpp>
using htable_t = __gnu_pbds::gp_hash_table<LL, int>;
const int nbase = 10;
const int max_digits = 18;
// Representation of digits multiplication
#define GET_BIT(a, i) (((a) >> i) & 1)
#define SET_BIT(a, i) (a ^= (1 << (i)))
using fact_t = array<short, 4>;
using hash_t = uint32_t;
const array<LL, 4> fact_primes = {2, 3, 5, 7};
const array<hash_t, 4> fact_nexps = {55, 37, 19, 19};
const array<hash_t, 4> fact_pos
= {1,
fact_nexps[0],
fact_nexps[0] * fact_nexps[1],
fact_nexps[0] * fact_nexps[1] * fact_nexps[2]};
const array<fact_t, nbase> fact_digits = {{
{0, 0, 0, 0}, // 0
{0, 0, 0, 0}, // 1
{1, 0, 0, 0}, // 2
{0, 1, 0, 0}, // 3
{2, 0, 0, 0}, // 4
{0, 0, 1, 0}, // 5
{1, 1, 0, 0}, // 6
{0, 0, 0, 1}, // 7
{3, 0, 0, 0}, // 8
{0, 2, 0, 0} // 9
}};
#define HDELTA_ROW(c) \
fact_pos[0] * fact_digits[c][0] + fact_pos[1] * fact_digits[c][1] \
+ fact_pos[2] * fact_digits[c][2] + fact_pos[3] * fact_digits[c][3]
const array<hash_t, nbase> fact_hdelta = {HDELTA_ROW(0),
HDELTA_ROW(1),
HDELTA_ROW(2),
HDELTA_ROW(3),
HDELTA_ROW(4),
HDELTA_ROW(5),
HDELTA_ROW(6),
HDELTA_ROW(7),
HDELTA_ROW(8),
HDELTA_ROW(9)};
const int nhashes = 695971;
const int zero_id = 36100;
const int nids = zero_id + 1;
LL fact_to_mul(const fact_t& fact);
hash_t fact_to_hash(const fact_t& fact);
fact_t hash_to_fact(const hash_t& hash);
fact_t mul_to_fact(LL mul);
int mul_to_id(const LL& mul);
LL digit_mul(LL mul);
array<int, nhashes> hash_to_id;
array<hash_t, nids> id_to_hash;
array<short, nids> id_to_group;
void gen_muls();
void gen_id_to_group();
using decimal_t = vector<pair<int, LL>>;
decimal_t N_to_decimal(LL N);
array<array<array<LL, nbase>, nids>, max_digits> dp;
array<array<LL, nids>, max_digits> dp2;
void calc_dp();
LL lower_with_id(const decimal_t& N, int id);
int
main()
{
cin.tie(0)->sync_with_stdio(0);
gen_muls();
gen_id_to_group();
calc_dp();
// Get ids that don't belong to group 0
vector<int> non0ids;
REP (id, nids)
if (id_to_group[id] != 0) non0ids.emplace_back(id);
int t;
cin >> t;
while (t--) {
LL N;
cin >> N;
array<LL, nbase> score;
score.fill(0);
// Handle 10^18
score[id_to_group[mul_to_id(digit_mul(N))]] += 1;
if (N == 1000000000000000000)
score[id_to_group[mul_to_id(digit_mul(--N))]] += 1;
// Add influence to score of each id
LL add_to_0 = N - 1;
auto dec = N_to_decimal(N);
for (const auto& id : non0ids) {
const auto &val = lower_with_id(dec, id);
score[id_to_group[id]] += val, add_to_0 -= val;
}
score[0] += add_to_0;
// Output
REP (i, nbase) cout << score[i] << " ";
cout << "\n";
}
return 0;
}
LL
lower_with_id(const decimal_t& N, int id)
{
LL results = 0;
bool dont_care_about_tz = false;
for (int n = ssize(N) - 1; n >= 0; --n, dont_care_about_tz = true) {
const auto& [digit, pref] = N[n];
// Handle digit multiplying to 0
if (id == zero_id) {
if (digit == 0) {
results += pref;
break;
}
if (digit - 1 >= 1) results += dp[n][zero_id][digit - 1];
if (dont_care_about_tz)
results += dp[n][zero_id][0];
else
results += dp2[n][zero_id];
continue;
}
// It's impossible to have non-zero id with digit == 0
if (digit == 0) break;
// Smaller digit here, so definitely smaller in the future
if (digit - 1 >= 1) results += dp[n][id][digit - 1];
if (!dont_care_about_tz) results += dp2[n][id];
const auto& h = id_to_hash[id];
if (!GET_BIT(h, digit)) break;
id = hash_to_id[(h >> nbase) - fact_hdelta[digit]];
}
return results;
}
void
calc_dp()
{
LL pow10 = 10;
dp2[0].fill(0);
REP (c, nbase) dp[0][mul_to_id(c)][c] = 1;
FOR (n, 1, max_digits - 1) {
dp2[n] = dp2[n - 1];
REP (id, nids - 1) {
const auto& h = id_to_hash[id];
dp[n][id].fill(0);
FOR (c, 1, nbase - 1) {
if (!GET_BIT(h, c)) continue;
auto idp = hash_to_id[(h >> nbase) - fact_hdelta[c]];
REP (cp, nbase) dp[n][id][c] += dp[n - 1][idp][cp];
dp2[n][id] += dp[n - 1][id][c];
}
}
// Handle zero_id
LL dpzerosum = 0;
FOR (c, 1, nbase - 1) dpzerosum += dp[n - 1][zero_id][c];
dp2[n][zero_id] += dpzerosum;
dp[n][zero_id].fill(0);
dp[n][zero_id][0] = pow10;
FOR (c, 1, nbase - 1)
dp[n][zero_id][c] = dpzerosum + dp[n - 1][zero_id][0];
pow10 *= 10;
}
// Make dp[n][id][c] = sum k 1...c dp[n][id][k]
REP (n, max_digits) {
REP (id, nids) {
auto& d = dp[n][id];
FOR (c, 2, nbase - 1) d[c] += d[c - 1];
}
}
}
decimal_t
N_to_decimal(LL N)
{
decimal_t dec;
for (LL pow10 = 1, pref = 0; N; N /= 10, pow10 *= 10) {
const auto& digit = N % 10;
dec.emplace_back(digit, pref);
pref += pow10 * digit;
}
return dec;
}
short
get_group_rec(int id)
{
if (id_to_group[id] == -1)
id_to_group[id] = get_group_rec(mul_to_id(
digit_mul(fact_to_mul(hash_to_fact(id_to_hash[id] >> nbase)))));
return id_to_group[id];
}
void
gen_id_to_group()
{
id_to_group.fill(-1);
REP (x, nbase) id_to_group[mul_to_id(x)] = x;
REP (id, nids) id_to_group[id] = get_group_rec(id);
}
bool
mul_achievable(LL mul)
{
if (mul == 0) return 0;
int digits = 0;
for (int c = nbase - 1; c > 1; --c)
while (mul % c == 0) ++digits, mul /= c;
return digits <= max_digits;
}
bool
fact_have_c(const fact_t& fact, const int& c)
{
return fact[0] >= fact_digits[c][0] && fact[1] >= fact_digits[c][1]
&& fact[2] >= fact_digits[c][2] && fact[3] >= fact_digits[c][3];
}
void
gen_muls()
{
LL max_val = 1;
int id = 0;
REP (i, 18) max_val *= 9;
for (LL val2 = 1; val2 <= max_val; val2 *= 2) {
for (LL val3 = val2; val3 <= max_val; val3 *= 3) {
for (LL val5 = val3; val5 <= max_val; val5 *= 5) {
for (LL val7 = val5; val7 <= max_val; val7 *= 7) {
if (!mul_achievable(val7)) continue;
auto fact = mul_to_fact(val7);
auto h = fact_to_hash(fact);
hash_to_id[h] = id;
id_to_hash[id] = h << nbase;
REP (c, nbase)
if (fact_have_c(fact, c)) SET_BIT(id_to_hash[id], c);
++id;
}
}
}
}
}
LL
fact_to_mul(const fact_t& fact)
{
LL mul = 1;
REP (pi, ssize(fact_primes))
REP (exp, fact[pi]) mul *= fact_primes[pi];
return mul;
}
hash_t
fact_to_hash(const fact_t& fact)
{
return fact_pos[0] * fact[0] + fact_pos[1] * fact[1] + fact_pos[2] * fact[2]
+ fact_pos[3] * fact[3];
}
fact_t
hash_to_fact(const hash_t& hash)
{
return {static_cast<short>((hash % fact_pos[1])),
static_cast<short>((hash % fact_pos[2]) / fact_pos[1]),
static_cast<short>((hash % fact_pos[3]) / fact_pos[2]),
static_cast<short>((hash) / fact_pos[3])};
}
fact_t
mul_to_fact(LL mul)
{
// FIXME: handle this
assert(mul != 0);
fact_t fact = {0, 0, 0, 0};
REP (pi, ssize(fact_primes)) {
const auto& prime = fact_primes[pi];
while (mul % prime == 0) mul /= prime, ++fact[pi];
}
return fact;
}
int
mul_to_id(const LL& mul)
{
return (mul == 0 ? zero_id : hash_to_id[fact_to_hash(mul_to_fact(mul))]);
}
LL
digit_mul(LL mul)
{
if (mul == 0) return 0;
LL nxt = 1;
for (; mul; mul /= 10) nxt *= mul % 10;
return nxt;
}
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 | // clang-format off #include<bits/stdc++.h> using namespace std; using LL=long long; #define FOR(i,l,r) for(auto i=(l);i<=(r);++i) #define REP(i,n) FOR(i,0,(n)-1) #define ssize(x) int(x.size()) template<class A,class B>auto&operator<<(ostream&o,pair<A,B>p){return o<<"("<<p.first<<", "<<p.second<<")";} template<class T>auto operator<<(ostream&o,T x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<(", ")+2*!i++<<e;return o<<"}";} #ifdef DEBUG #define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<"\n";}(X) #else #define debug(...) {} #endif // clang-format on #include <ext/pb_ds/assoc_container.hpp> using htable_t = __gnu_pbds::gp_hash_table<LL, int>; const int nbase = 10; const int max_digits = 18; // Representation of digits multiplication #define GET_BIT(a, i) (((a) >> i) & 1) #define SET_BIT(a, i) (a ^= (1 << (i))) using fact_t = array<short, 4>; using hash_t = uint32_t; const array<LL, 4> fact_primes = {2, 3, 5, 7}; const array<hash_t, 4> fact_nexps = {55, 37, 19, 19}; const array<hash_t, 4> fact_pos = {1, fact_nexps[0], fact_nexps[0] * fact_nexps[1], fact_nexps[0] * fact_nexps[1] * fact_nexps[2]}; const array<fact_t, nbase> fact_digits = {{ {0, 0, 0, 0}, // 0 {0, 0, 0, 0}, // 1 {1, 0, 0, 0}, // 2 {0, 1, 0, 0}, // 3 {2, 0, 0, 0}, // 4 {0, 0, 1, 0}, // 5 {1, 1, 0, 0}, // 6 {0, 0, 0, 1}, // 7 {3, 0, 0, 0}, // 8 {0, 2, 0, 0} // 9 }}; #define HDELTA_ROW(c) \ fact_pos[0] * fact_digits[c][0] + fact_pos[1] * fact_digits[c][1] \ + fact_pos[2] * fact_digits[c][2] + fact_pos[3] * fact_digits[c][3] const array<hash_t, nbase> fact_hdelta = {HDELTA_ROW(0), HDELTA_ROW(1), HDELTA_ROW(2), HDELTA_ROW(3), HDELTA_ROW(4), HDELTA_ROW(5), HDELTA_ROW(6), HDELTA_ROW(7), HDELTA_ROW(8), HDELTA_ROW(9)}; const int nhashes = 695971; const int zero_id = 36100; const int nids = zero_id + 1; LL fact_to_mul(const fact_t& fact); hash_t fact_to_hash(const fact_t& fact); fact_t hash_to_fact(const hash_t& hash); fact_t mul_to_fact(LL mul); int mul_to_id(const LL& mul); LL digit_mul(LL mul); array<int, nhashes> hash_to_id; array<hash_t, nids> id_to_hash; array<short, nids> id_to_group; void gen_muls(); void gen_id_to_group(); using decimal_t = vector<pair<int, LL>>; decimal_t N_to_decimal(LL N); array<array<array<LL, nbase>, nids>, max_digits> dp; array<array<LL, nids>, max_digits> dp2; void calc_dp(); LL lower_with_id(const decimal_t& N, int id); int main() { cin.tie(0)->sync_with_stdio(0); gen_muls(); gen_id_to_group(); calc_dp(); // Get ids that don't belong to group 0 vector<int> non0ids; REP (id, nids) if (id_to_group[id] != 0) non0ids.emplace_back(id); int t; cin >> t; while (t--) { LL N; cin >> N; array<LL, nbase> score; score.fill(0); // Handle 10^18 score[id_to_group[mul_to_id(digit_mul(N))]] += 1; if (N == 1000000000000000000) score[id_to_group[mul_to_id(digit_mul(--N))]] += 1; // Add influence to score of each id LL add_to_0 = N - 1; auto dec = N_to_decimal(N); for (const auto& id : non0ids) { const auto &val = lower_with_id(dec, id); score[id_to_group[id]] += val, add_to_0 -= val; } score[0] += add_to_0; // Output REP (i, nbase) cout << score[i] << " "; cout << "\n"; } return 0; } LL lower_with_id(const decimal_t& N, int id) { LL results = 0; bool dont_care_about_tz = false; for (int n = ssize(N) - 1; n >= 0; --n, dont_care_about_tz = true) { const auto& [digit, pref] = N[n]; // Handle digit multiplying to 0 if (id == zero_id) { if (digit == 0) { results += pref; break; } if (digit - 1 >= 1) results += dp[n][zero_id][digit - 1]; if (dont_care_about_tz) results += dp[n][zero_id][0]; else results += dp2[n][zero_id]; continue; } // It's impossible to have non-zero id with digit == 0 if (digit == 0) break; // Smaller digit here, so definitely smaller in the future if (digit - 1 >= 1) results += dp[n][id][digit - 1]; if (!dont_care_about_tz) results += dp2[n][id]; const auto& h = id_to_hash[id]; if (!GET_BIT(h, digit)) break; id = hash_to_id[(h >> nbase) - fact_hdelta[digit]]; } return results; } void calc_dp() { LL pow10 = 10; dp2[0].fill(0); REP (c, nbase) dp[0][mul_to_id(c)][c] = 1; FOR (n, 1, max_digits - 1) { dp2[n] = dp2[n - 1]; REP (id, nids - 1) { const auto& h = id_to_hash[id]; dp[n][id].fill(0); FOR (c, 1, nbase - 1) { if (!GET_BIT(h, c)) continue; auto idp = hash_to_id[(h >> nbase) - fact_hdelta[c]]; REP (cp, nbase) dp[n][id][c] += dp[n - 1][idp][cp]; dp2[n][id] += dp[n - 1][id][c]; } } // Handle zero_id LL dpzerosum = 0; FOR (c, 1, nbase - 1) dpzerosum += dp[n - 1][zero_id][c]; dp2[n][zero_id] += dpzerosum; dp[n][zero_id].fill(0); dp[n][zero_id][0] = pow10; FOR (c, 1, nbase - 1) dp[n][zero_id][c] = dpzerosum + dp[n - 1][zero_id][0]; pow10 *= 10; } // Make dp[n][id][c] = sum k 1...c dp[n][id][k] REP (n, max_digits) { REP (id, nids) { auto& d = dp[n][id]; FOR (c, 2, nbase - 1) d[c] += d[c - 1]; } } } decimal_t N_to_decimal(LL N) { decimal_t dec; for (LL pow10 = 1, pref = 0; N; N /= 10, pow10 *= 10) { const auto& digit = N % 10; dec.emplace_back(digit, pref); pref += pow10 * digit; } return dec; } short get_group_rec(int id) { if (id_to_group[id] == -1) id_to_group[id] = get_group_rec(mul_to_id( digit_mul(fact_to_mul(hash_to_fact(id_to_hash[id] >> nbase))))); return id_to_group[id]; } void gen_id_to_group() { id_to_group.fill(-1); REP (x, nbase) id_to_group[mul_to_id(x)] = x; REP (id, nids) id_to_group[id] = get_group_rec(id); } bool mul_achievable(LL mul) { if (mul == 0) return 0; int digits = 0; for (int c = nbase - 1; c > 1; --c) while (mul % c == 0) ++digits, mul /= c; return digits <= max_digits; } bool fact_have_c(const fact_t& fact, const int& c) { return fact[0] >= fact_digits[c][0] && fact[1] >= fact_digits[c][1] && fact[2] >= fact_digits[c][2] && fact[3] >= fact_digits[c][3]; } void gen_muls() { LL max_val = 1; int id = 0; REP (i, 18) max_val *= 9; for (LL val2 = 1; val2 <= max_val; val2 *= 2) { for (LL val3 = val2; val3 <= max_val; val3 *= 3) { for (LL val5 = val3; val5 <= max_val; val5 *= 5) { for (LL val7 = val5; val7 <= max_val; val7 *= 7) { if (!mul_achievable(val7)) continue; auto fact = mul_to_fact(val7); auto h = fact_to_hash(fact); hash_to_id[h] = id; id_to_hash[id] = h << nbase; REP (c, nbase) if (fact_have_c(fact, c)) SET_BIT(id_to_hash[id], c); ++id; } } } } } LL fact_to_mul(const fact_t& fact) { LL mul = 1; REP (pi, ssize(fact_primes)) REP (exp, fact[pi]) mul *= fact_primes[pi]; return mul; } hash_t fact_to_hash(const fact_t& fact) { return fact_pos[0] * fact[0] + fact_pos[1] * fact[1] + fact_pos[2] * fact[2] + fact_pos[3] * fact[3]; } fact_t hash_to_fact(const hash_t& hash) { return {static_cast<short>((hash % fact_pos[1])), static_cast<short>((hash % fact_pos[2]) / fact_pos[1]), static_cast<short>((hash % fact_pos[3]) / fact_pos[2]), static_cast<short>((hash) / fact_pos[3])}; } fact_t mul_to_fact(LL mul) { // FIXME: handle this assert(mul != 0); fact_t fact = {0, 0, 0, 0}; REP (pi, ssize(fact_primes)) { const auto& prime = fact_primes[pi]; while (mul % prime == 0) mul /= prime, ++fact[pi]; } return fact; } int mul_to_id(const LL& mul) { return (mul == 0 ? zero_id : hash_to_id[fact_to_hash(mul_to_fact(mul))]); } LL digit_mul(LL mul) { if (mul == 0) return 0; LL nxt = 1; for (; mul; mul /= 10) nxt *= mul % 10; return nxt; } |
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