#include <bits/stdc++.h>
using namespace std;
#define FOR(i, l, r) for(int i = (l); i <= (r); ++i)
#define REP(i, n) FOR(i, 0, (n) - 1)
#define ssize(x) int(x.size())
#ifdef DEBUG
auto &operator << (auto &o, pair<auto, auto> p) {
return o << "(" << p.first << ", " << p.second << ")";
}
auto operator << (auto &o, auto x) -> decltype(x.end(), o) {
o << "{"; int i = 0;
for (auto e : x) o << ","+!i++ << e;
return o << "}";
}
#define debug(X...) cerr << "["#X"]: ", [](auto ...$) {((cerr << $ << "; "), ...) << endl;}(X)
#else
#define debug(...) {}
#endif
constexpr int LEN = 18;
constexpr long long INF = (long long)3e18 + 100;
constexpr int P2 = 3 * LEN + 1;
constexpr int P3 = 2 * LEN + 1;
constexpr int P5 = LEN + 1;
constexpr int P7 = LEN + 1;
constexpr int ALL_STATES = 904810;
constexpr int BASE = 64;
constexpr int MAX_STATE = BASE * BASE * BASE * (P7 + 1);
constexpr int ZERO =
P2 +
(P3 - 1) * BASE +
(P5 - 1) * BASE * BASE +
(P7 - 1) * BASE * BASE * BASE;
static array<int, 4> primes = {2, 3, 5, 7};
long long get_digit_product(long long n) {
long long ret = 1;
while (n > 0) {
int digit = n % 10;
n /= 10;
ret *= digit;
}
return ret;
}
int state_from_array(const array<int, 4> &state) {
int ret = 0;
int mult = 1;
REP (i, 4) {
int e = state[i];
assert(e < BASE);
ret += mult * e;
mult *= BASE;
}
return ret;
}
int convert_to_state(long long value) {
static array<int, 10> base_states = {
ZERO,
0,
1,
BASE * 1,
2,
BASE * BASE * 1,
BASE * 1 + 1,
BASE * BASE * BASE * 1,
3,
BASE * 2
};
if (value < 10)
return base_states[value];
int state = 0;
int mult = 1;
REP (i, 4) {
int p = primes[i];
int e = 0;
while (value % p == 0) {
++e;
value /= p;
}
assert(e < BASE);
state += mult * e;
mult *= BASE;
}
return state;
}
int get_next_state(int state) {
if (state == ZERO) return state;
long long value = 1;
REP (i, 4) {
int state_i = state % BASE;
state /= BASE;
long long take = (long long)pow(primes[i], state_i);
if (take > INF / value)
return ZERO;
value *= take;
}
long long next_value = get_digit_product(value);
return convert_to_state(next_value);
}
short final_digit[MAX_STATE + 1];
vector<int> all_states;
array<int, MAX_STATE + 5> state_id = {};
long long dp[LEN + 1][2][ALL_STATES];
array<long long, 10> starting_dp[LEN + 1];
short dfs(int state) {
if (final_digit[state] != -1)
return final_digit[state];
int next_state = get_next_state(state);
return final_digit[state] = dfs(next_state);
}
void preprocessing() {
REP (i, MAX_STATE + 5)
state_id[i] = -1;
REP (state, MAX_STATE + 1) {
final_digit[state] = -1;
}
REP (digit, 10) {
int state = convert_to_state(digit);
final_digit[state] = digit;
}
REP (p2, P2) REP (p3, P3) REP (p5, P5) REP (p7, P7) {
int state = state_from_array({p2, p3, p5, p7});
final_digit[state] = dfs(state);
}
all_states.emplace_back(ZERO);
REP (p2, P2) REP (p3, P3) REP (p5, P5) REP (p7, P7) {
int state = state_from_array({p2, p3, p5, p7});
state_id[state] = ssize(all_states);
all_states.emplace_back(state);
}
REP (i, LEN + 1) REP (j, 2) REP (k, ssize(all_states))
dp[i][j][k] = -1;
vector<array<int, 3>> visited = {};
deque<array<int, 3>> Q = {};
FOR (digit, 1, 9) {
int state = convert_to_state(digit);
int id = state_id[state];
dp[0][0][id] = 1;
Q.push_back({0, 0, id});
}
array<long long, 10> answer = {};
int current_length = 0;
while (!Q.empty()) {
auto [len, smaller, id] = Q.front();
visited.push_back({len, smaller, id});
Q.pop_front();
if (len > current_length) {
starting_dp[len] = answer;
current_length = len;
}
if (len == LEN)
continue;
int current_state = all_states[id];
if (current_state == ZERO) continue;
long long d = dp[len][0][id];
int my_final_digit = final_digit[current_state];
answer[my_final_digit] += d;
FOR (digit, 1, 9) {
int new_state = current_state + convert_to_state(digit);
int new_id = state_id[new_state];
if (new_id == -1)
continue;
if (dp[len + 1][0][new_id] == -1) {
dp[len + 1][0][new_id] = 0;
Q.push_back({len + 1, 0, new_id});
}
dp[len + 1][0][new_id] += d;
}
}
starting_dp[LEN] = answer;
#ifdef DEBUG
REP (len, LEN + 1)
debug(len, starting_dp[len]);
#endif
debug(ssize(visited));
for (auto [i, j, k] : visited)
dp[i][j][k] = -1;
}
vector<int> get_digits(long long n) {
vector<int> ret = {};
while (n) {
int digit = n % 10;
n /= 10;
ret.emplace_back(digit);
}
reverse(ret.begin(), ret.end());
return ret;
}
void solve(long long n) {
vector<array<int, 3>> visited = {};
deque<array<int, 3>> Q = {};
++n;
vector<int> n_digits = get_digits(n);
debug(n_digits);
array<long long, 10> answer = starting_dp[ssize(n_digits) - 1];
FOR (digit, 1, n_digits[0]) {
int state = convert_to_state(digit);
int id = state_id[state];
int smaller = (digit < n_digits[0]);
dp[0][smaller][id] = 1;
Q.push_back({0, smaller, id});
}
while (!Q.empty()) {
auto [len, smaller, id] = Q.front();
visited.push_back({len, smaller, id});
Q.pop_front();
int current_state = all_states[id];
if (current_state == ZERO) continue;
long long d = dp[len][smaller][id];
if (len == ssize(n_digits) - 1) {
if (smaller == 1) {
int digit = final_digit[all_states[id]];
answer[digit] += dp[len][smaller][id];
}
continue;
}
int limit = (smaller ? 9 : n_digits[len + 1]);
FOR (digit, 1, limit) {
int new_state = current_state + convert_to_state(digit);
int new_id = state_id[new_state];
if (new_id == 0) continue;
int new_smaller = (smaller or digit < n_digits[len + 1]);
if (dp[len + 1][new_smaller][new_id] == -1) {
dp[len + 1][new_smaller][new_id] = 0;
Q.push_back({len + 1, new_smaller, new_id});
}
dp[len + 1][new_smaller][new_id] += d;
}
}
debug(ssize(visited));
for (auto [i, j, k] : visited)
dp[i][j][k] = -1;
long long sum = 0;
FOR (i, 1, 9) sum += answer[i];
answer[0] = n - 1 - sum;
REP (i, 10)
cout << answer[i] << ' ';
cout << '\n';
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
preprocessing();
debug(ssize(all_states));
int t; cin >> t;
while (t--) {
long long n;
cin >> n;
solve(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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 | #include <bits/stdc++.h> using namespace std; #define FOR(i, l, r) for(int i = (l); i <= (r); ++i) #define REP(i, n) FOR(i, 0, (n) - 1) #define ssize(x) int(x.size()) #ifdef DEBUG auto &operator << (auto &o, pair<auto, auto> p) { return o << "(" << p.first << ", " << p.second << ")"; } auto operator << (auto &o, auto x) -> decltype(x.end(), o) { o << "{"; int i = 0; for (auto e : x) o << ","+!i++ << e; return o << "}"; } #define debug(X...) cerr << "["#X"]: ", [](auto ...$) {((cerr << $ << "; "), ...) << endl;}(X) #else #define debug(...) {} #endif constexpr int LEN = 18; constexpr long long INF = (long long)3e18 + 100; constexpr int P2 = 3 * LEN + 1; constexpr int P3 = 2 * LEN + 1; constexpr int P5 = LEN + 1; constexpr int P7 = LEN + 1; constexpr int ALL_STATES = 904810; constexpr int BASE = 64; constexpr int MAX_STATE = BASE * BASE * BASE * (P7 + 1); constexpr int ZERO = P2 + (P3 - 1) * BASE + (P5 - 1) * BASE * BASE + (P7 - 1) * BASE * BASE * BASE; static array<int, 4> primes = {2, 3, 5, 7}; long long get_digit_product(long long n) { long long ret = 1; while (n > 0) { int digit = n % 10; n /= 10; ret *= digit; } return ret; } int state_from_array(const array<int, 4> &state) { int ret = 0; int mult = 1; REP (i, 4) { int e = state[i]; assert(e < BASE); ret += mult * e; mult *= BASE; } return ret; } int convert_to_state(long long value) { static array<int, 10> base_states = { ZERO, 0, 1, BASE * 1, 2, BASE * BASE * 1, BASE * 1 + 1, BASE * BASE * BASE * 1, 3, BASE * 2 }; if (value < 10) return base_states[value]; int state = 0; int mult = 1; REP (i, 4) { int p = primes[i]; int e = 0; while (value % p == 0) { ++e; value /= p; } assert(e < BASE); state += mult * e; mult *= BASE; } return state; } int get_next_state(int state) { if (state == ZERO) return state; long long value = 1; REP (i, 4) { int state_i = state % BASE; state /= BASE; long long take = (long long)pow(primes[i], state_i); if (take > INF / value) return ZERO; value *= take; } long long next_value = get_digit_product(value); return convert_to_state(next_value); } short final_digit[MAX_STATE + 1]; vector<int> all_states; array<int, MAX_STATE + 5> state_id = {}; long long dp[LEN + 1][2][ALL_STATES]; array<long long, 10> starting_dp[LEN + 1]; short dfs(int state) { if (final_digit[state] != -1) return final_digit[state]; int next_state = get_next_state(state); return final_digit[state] = dfs(next_state); } void preprocessing() { REP (i, MAX_STATE + 5) state_id[i] = -1; REP (state, MAX_STATE + 1) { final_digit[state] = -1; } REP (digit, 10) { int state = convert_to_state(digit); final_digit[state] = digit; } REP (p2, P2) REP (p3, P3) REP (p5, P5) REP (p7, P7) { int state = state_from_array({p2, p3, p5, p7}); final_digit[state] = dfs(state); } all_states.emplace_back(ZERO); REP (p2, P2) REP (p3, P3) REP (p5, P5) REP (p7, P7) { int state = state_from_array({p2, p3, p5, p7}); state_id[state] = ssize(all_states); all_states.emplace_back(state); } REP (i, LEN + 1) REP (j, 2) REP (k, ssize(all_states)) dp[i][j][k] = -1; vector<array<int, 3>> visited = {}; deque<array<int, 3>> Q = {}; FOR (digit, 1, 9) { int state = convert_to_state(digit); int id = state_id[state]; dp[0][0][id] = 1; Q.push_back({0, 0, id}); } array<long long, 10> answer = {}; int current_length = 0; while (!Q.empty()) { auto [len, smaller, id] = Q.front(); visited.push_back({len, smaller, id}); Q.pop_front(); if (len > current_length) { starting_dp[len] = answer; current_length = len; } if (len == LEN) continue; int current_state = all_states[id]; if (current_state == ZERO) continue; long long d = dp[len][0][id]; int my_final_digit = final_digit[current_state]; answer[my_final_digit] += d; FOR (digit, 1, 9) { int new_state = current_state + convert_to_state(digit); int new_id = state_id[new_state]; if (new_id == -1) continue; if (dp[len + 1][0][new_id] == -1) { dp[len + 1][0][new_id] = 0; Q.push_back({len + 1, 0, new_id}); } dp[len + 1][0][new_id] += d; } } starting_dp[LEN] = answer; #ifdef DEBUG REP (len, LEN + 1) debug(len, starting_dp[len]); #endif debug(ssize(visited)); for (auto [i, j, k] : visited) dp[i][j][k] = -1; } vector<int> get_digits(long long n) { vector<int> ret = {}; while (n) { int digit = n % 10; n /= 10; ret.emplace_back(digit); } reverse(ret.begin(), ret.end()); return ret; } void solve(long long n) { vector<array<int, 3>> visited = {}; deque<array<int, 3>> Q = {}; ++n; vector<int> n_digits = get_digits(n); debug(n_digits); array<long long, 10> answer = starting_dp[ssize(n_digits) - 1]; FOR (digit, 1, n_digits[0]) { int state = convert_to_state(digit); int id = state_id[state]; int smaller = (digit < n_digits[0]); dp[0][smaller][id] = 1; Q.push_back({0, smaller, id}); } while (!Q.empty()) { auto [len, smaller, id] = Q.front(); visited.push_back({len, smaller, id}); Q.pop_front(); int current_state = all_states[id]; if (current_state == ZERO) continue; long long d = dp[len][smaller][id]; if (len == ssize(n_digits) - 1) { if (smaller == 1) { int digit = final_digit[all_states[id]]; answer[digit] += dp[len][smaller][id]; } continue; } int limit = (smaller ? 9 : n_digits[len + 1]); FOR (digit, 1, limit) { int new_state = current_state + convert_to_state(digit); int new_id = state_id[new_state]; if (new_id == 0) continue; int new_smaller = (smaller or digit < n_digits[len + 1]); if (dp[len + 1][new_smaller][new_id] == -1) { dp[len + 1][new_smaller][new_id] = 0; Q.push_back({len + 1, new_smaller, new_id}); } dp[len + 1][new_smaller][new_id] += d; } } debug(ssize(visited)); for (auto [i, j, k] : visited) dp[i][j][k] = -1; long long sum = 0; FOR (i, 1, 9) sum += answer[i]; answer[0] = n - 1 - sum; REP (i, 10) cout << answer[i] << ' '; cout << '\n'; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); preprocessing(); debug(ssize(all_states)); int t; cin >> t; while (t--) { long long n; cin >> n; solve(n); } } |
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