#ifndef DEBUG_MODE #define NDEBUG #endif #include <vector> #include <string> #include <iostream> #include <algorithm> #include <cstdio> #include <time.h> #include <assert.h> using namespace std; typedef long long ll; int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); } ll brute(vector<int> money, string cycle, int limit, bool print) { int player_id = 0, step = 0; while(step < limit) { char value = cycle[step % cycle.size()]; int player_id = step % money.size(); if(print) { for(int i = 0; i < (int)money.size(); i++) printf("%d%c ", (int)money[i], player_id == i ? '.' : ' '); printf("\n"); } money[player_id] += value == 'W' ? 1 : -1; step++; if(money[player_id] == 0) break; } return step == limit ? -1 : step; } struct ValueMap { void init(const vector<int> &values) { min = values.front(); max = values.front(); for(int n = 0; n < (int)values.size(); n++) { min = std::min(min, values[n]); max = std::max(max, values[n]); } int count = max - min + 1; keys.clear(); keys.resize(count, make_pair(0, 0)); for(int n = 0; n < (int)values.size(); n++) { int value_id = values[n] - min; keys[value_id].first++; } int cur_pos = 0; for(int n = 0; n < (int)keys.size(); n++) { keys[n].second = cur_pos; cur_pos += keys[n].first; keys[n].first = 0; } positions.resize(values.size()); for(int n = 0; n < (int)values.size(); n++) { int key_id = values[n] - min; positions[keys[key_id].second + keys[key_id].first++] = n; } } int findValue(int value, int min_pos, int max_pos) const { if(value < min || value > max) return -1; pair<int, int> key = keys[value - min]; int a = key.second, b = key.second + key.first; while(a < b) { int mid = (a + b) / 2; int val = positions[mid]; if(val < min_pos) a = mid + 1; else b = mid; } int out = positions[a]; if(out < min_pos || out > max_pos) return -1; return out; } void print() const { for(int n = 0; n < (int)keys.size(); n++) { if(!keys[n].first) continue; printf("%d: ", min + n); for(int i = 0; i < keys[n].first; i++) printf(" %d", positions[keys[n].second + i]); printf("\n"); } } // pairs: count / offset into positions vector<pair<int, int>> keys; vector<int> positions; int min, max; }; // make sure it's not 0 int lsbPos(int value) { int bit = 0; while(((1 << bit) & value) == 0) bit++; return bit; } // make sure it's not 0 int msbPos(int value) { int bit = 24; while(((1 << bit) & value) == 0) bit--; return bit; } struct ValueMins { void init(const vector<int> &values) { minimums[0] = values; int level = 0; while(minimums[level].size() > 1) { vector<int> &cur = minimums[level], &next = minimums[level + 1]; next.resize((cur.size() + 1) / 2); for(int n = 0; n + 1 < (int)next.size(); n++) next[n] = std::min(cur[n * 2 + 0], cur[n * 2 + 1]); if(cur.size() % 2 == 0) next.back() = std::min(cur.back(), cur[cur.size() - 2]); else next.back() = cur.back(); level++; } } int findMin(int start, int count, bool print) const { int min = 0; #ifdef DEBUG_MODE if(print) printf("start: %d count: %d\n", start, count); #endif if(start == 0 && count > 0) { int level = msbPos(count); #ifdef DEBUG_MODE if(print) printf("lev: %d\n", level); #endif min = std::min(min, minimums[level][start >> level]); start += 1 << level; count -= 1 << level; } int sbit = 0, cbit = 24; while(count > 0) { while(!(start & (1 << sbit))) sbit++; while(!(count & (1 << cbit))) cbit--; int level = std::min(sbit, cbit); #ifdef DEBUG_MODE if(print) printf("s: %d lev: %d\n", start, level); #endif min = std::min(min, minimums[level][start >> level]); start += 1 << level; count -= 1 << level; } return min; } vector<int> minimums[24]; }; int findMin(const vector<int> &sums, int offset, int count) { int min = 0; for(int i = 0; i < count; i++) { int value = sums[i + offset]; min = std::min(min, value); } if(offset > 0) min -= sums[offset - 1]; return min; } int findMin(const vector<int> &sums, const ValueMins &vmins, int offset, int count) { int min = vmins.findMin(offset, count, 0); if(offset > 0) min -= sums[offset - 1]; return min; } int findFirstValue(const vector<int> &sums, int offset, int count, int key) { if(offset > 0) key += sums[offset - 1]; int ret = -1; for(int i = 0; i < count; i++) { int value = sums[i + offset]; if(value == key) { ret = i; break; } } return ret; } int findFirstValue(const vector<int> &sums, const ValueMap &vmap, int offset, int count, int key) { if(offset > 0) key += sums[offset - 1]; int ret = vmap.findValue(key, offset, offset + count - 1); if(ret != -1) ret -= offset; return ret; } ll solve(const vector<int> &money, const string &cycle, bool print) { int cycle_size = (int)cycle.size(), count = (int)money.size(); int gcd = ::gcd(cycle_size, count); int sub_cycle_size = cycle_size / gcd; vector<int> cycle_pos(cycle.size(), -1); vector<char> sub_cycle(sub_cycle_size); vector<int> sub_sum(sub_cycle_size * 2); ValueMap vmaps; ValueMins vmins; #ifdef DEBUG_MODE if(print) { printf("cycle: %s\n", cycle.c_str()); printf("count:%d cycle:%d gcd:%d\n", count, cycle_size, gcd); } #endif ll out = -1ll; for(int s = 0; s < gcd; s++) { int prev = 0, min = 0, pos = s % cycle_size; for(int i = 0; i < sub_cycle_size; i++) { char value = cycle[pos]; assert(cycle_pos[pos] == -1); cycle_pos[pos] = i; pos = (pos + count) % cycle_size; sub_cycle[i] = value; int ivalue = value == 'W' ? 1 : -1; prev = sub_sum[i] = ivalue + prev; } for(int i = sub_cycle_size; i < sub_cycle_size * 2; i++) { int ivalue = sub_cycle[i - sub_cycle_size] == 'W' ? 1 : -1; prev = sub_sum[i] = ivalue + prev; } int sub_total = sub_sum[sub_cycle_size - 1]; vmaps.init(sub_sum); vmins.init(sub_sum); #ifdef DEBUG_MODE if(print) { printf("Sub-cycle %d: total:%d min:%d ", s, sub_total, min); for(int i = 0; i < sub_cycle_size; i++) printf("%c", sub_cycle[i]); printf("\n"); for(int i = 0; i < sub_cycle_size * 2; i++) printf("%d ", sub_sum[i]); printf("\n"); } #endif for(int n = s; n < count; n += gcd) { int sub_id = n % gcd; int cycle_start_pos = cycle_pos[n % cycle_size]; assert(cycle_start_pos != -1); #ifdef DEBUG_MODE if(print) printf("%d cycle:%d cpos:%d money:%d ", n, sub_id, cycle_start_pos, money[n]); #endif ll full_cycles = 0, cur_money = money[n]; ll cycle_gain = sub_total; int cycle_min = findMin(sub_sum, vmins, cycle_start_pos, sub_cycle_size); #ifdef DEBUG_MODE if(print) printf("cmin:%d ", cycle_min); #endif if(cycle_gain < 0) { // Last cycle doesn't have to be complete full_cycles = std::max(0ll, (cur_money + cycle_min) / -cycle_gain); cur_money += full_cycles * cycle_gain; if(cur_money > -cycle_min) { cur_money += cycle_gain; full_cycles++; } assert(cur_money <= -cycle_min); // printf("%d/%d/%d ", cur_money, min, cycle_gain); } ll simple_steps = 0; ll last_money = cur_money; ll iters = 0; if(cur_money + cycle_min > 0) continue; int pos = findFirstValue(sub_sum, vmaps, cycle_start_pos, sub_cycle_size, -cur_money); if(pos != -1) { simple_steps = pos + 1; cur_money = 0; } ll total_steps = -1; if(cur_money == 0) { total_steps = (simple_steps + full_cycles * sub_cycle_size - 1) * count + n + 1; if(total_steps < out || out == -1) out = total_steps; } #ifdef DEBUG_MODE if(print) printf(" full:%lld*%d simple:%lld -> %lld\n", full_cycles, sub_cycle_size, simple_steps, total_steps); #endif } #ifdef DEBUG_MODE if(print) printf("\n"); #endif } return out; } pair<vector<int>, string> randomize(int size) { vector<int> money(rand() % size + 1); string cycle(rand() % size + 1, ' '); for(int n = 0; n < (int)money.size(); n++) money[n] = (rand() / 10) % size + 1; for(int n = 0; n < (int)cycle.size(); n++) cycle[n] = rand() % 2 ? 'W' : 'P'; return make_pair(money, cycle); } void testRandom(int seed, int count) { bool single_test = count > 2000; if(seed <= 0) { seed = time(0); printf("seed: %d\n", seed); } srand(seed); if(single_test) { pair<vector<int>, string> task = randomize(count); ll ret = solve(task.first, task.second, false); printf("%lld\n", ret); return; } for(int n = 0; n < count; n++) { pair<vector<int>, string> task = randomize(10 + n); int size = (int)(task.first.size() + task.second.size()); if(count >= 2000 && n % (count / 10) == 0) { printf("."); fflush(stdout); } ll ret = solve(task.first, task.second, false); ll max_brute = ret < 0 ? size * size * 16 : ret + 100; ll correct = brute(task.first, task.second, max_brute, false); if(ret != correct) { printf("Error: %lld; should be: %lld:\n", ret, correct); if(std::max(correct, ret) < 200) { solve(task.first, task.second, true); brute(task.first, task.second, ll(size) * size * 16, true); } break; } } printf("\n"); } #define RANDOM_TESTING #if defined(DEBUG_MODE) && defined(RANDOM_TESTING) int main(int argc, char **argv) { assert(argc >= 3); int seed = atoi(argv[1]), count = atoi(argv[2]); testRandom(seed, count); return 0; } #else int main() { std::ios_base::sync_with_stdio(false); cin.tie(0); int count; cin >> count; vector<int> money(count, 0); for(int n = 0; n < count; n++) cin >> money[n]; int cycle_size; string cycle; cin >> cycle_size >> cycle; #ifdef DEBUG_MODE cout << brute(money, cycle, 100000, false) << endl; #endif cout << solve(money, cycle, true) << endl; return 0; } #endif
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 | #ifndef DEBUG_MODE #define NDEBUG #endif #include <vector> #include <string> #include <iostream> #include <algorithm> #include <cstdio> #include <time.h> #include <assert.h> using namespace std; typedef long long ll; int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); } ll brute(vector<int> money, string cycle, int limit, bool print) { int player_id = 0, step = 0; while(step < limit) { char value = cycle[step % cycle.size()]; int player_id = step % money.size(); if(print) { for(int i = 0; i < (int)money.size(); i++) printf("%d%c ", (int)money[i], player_id == i ? '.' : ' '); printf("\n"); } money[player_id] += value == 'W' ? 1 : -1; step++; if(money[player_id] == 0) break; } return step == limit ? -1 : step; } struct ValueMap { void init(const vector<int> &values) { min = values.front(); max = values.front(); for(int n = 0; n < (int)values.size(); n++) { min = std::min(min, values[n]); max = std::max(max, values[n]); } int count = max - min + 1; keys.clear(); keys.resize(count, make_pair(0, 0)); for(int n = 0; n < (int)values.size(); n++) { int value_id = values[n] - min; keys[value_id].first++; } int cur_pos = 0; for(int n = 0; n < (int)keys.size(); n++) { keys[n].second = cur_pos; cur_pos += keys[n].first; keys[n].first = 0; } positions.resize(values.size()); for(int n = 0; n < (int)values.size(); n++) { int key_id = values[n] - min; positions[keys[key_id].second + keys[key_id].first++] = n; } } int findValue(int value, int min_pos, int max_pos) const { if(value < min || value > max) return -1; pair<int, int> key = keys[value - min]; int a = key.second, b = key.second + key.first; while(a < b) { int mid = (a + b) / 2; int val = positions[mid]; if(val < min_pos) a = mid + 1; else b = mid; } int out = positions[a]; if(out < min_pos || out > max_pos) return -1; return out; } void print() const { for(int n = 0; n < (int)keys.size(); n++) { if(!keys[n].first) continue; printf("%d: ", min + n); for(int i = 0; i < keys[n].first; i++) printf(" %d", positions[keys[n].second + i]); printf("\n"); } } // pairs: count / offset into positions vector<pair<int, int>> keys; vector<int> positions; int min, max; }; // make sure it's not 0 int lsbPos(int value) { int bit = 0; while(((1 << bit) & value) == 0) bit++; return bit; } // make sure it's not 0 int msbPos(int value) { int bit = 24; while(((1 << bit) & value) == 0) bit--; return bit; } struct ValueMins { void init(const vector<int> &values) { minimums[0] = values; int level = 0; while(minimums[level].size() > 1) { vector<int> &cur = minimums[level], &next = minimums[level + 1]; next.resize((cur.size() + 1) / 2); for(int n = 0; n + 1 < (int)next.size(); n++) next[n] = std::min(cur[n * 2 + 0], cur[n * 2 + 1]); if(cur.size() % 2 == 0) next.back() = std::min(cur.back(), cur[cur.size() - 2]); else next.back() = cur.back(); level++; } } int findMin(int start, int count, bool print) const { int min = 0; #ifdef DEBUG_MODE if(print) printf("start: %d count: %d\n", start, count); #endif if(start == 0 && count > 0) { int level = msbPos(count); #ifdef DEBUG_MODE if(print) printf("lev: %d\n", level); #endif min = std::min(min, minimums[level][start >> level]); start += 1 << level; count -= 1 << level; } int sbit = 0, cbit = 24; while(count > 0) { while(!(start & (1 << sbit))) sbit++; while(!(count & (1 << cbit))) cbit--; int level = std::min(sbit, cbit); #ifdef DEBUG_MODE if(print) printf("s: %d lev: %d\n", start, level); #endif min = std::min(min, minimums[level][start >> level]); start += 1 << level; count -= 1 << level; } return min; } vector<int> minimums[24]; }; int findMin(const vector<int> &sums, int offset, int count) { int min = 0; for(int i = 0; i < count; i++) { int value = sums[i + offset]; min = std::min(min, value); } if(offset > 0) min -= sums[offset - 1]; return min; } int findMin(const vector<int> &sums, const ValueMins &vmins, int offset, int count) { int min = vmins.findMin(offset, count, 0); if(offset > 0) min -= sums[offset - 1]; return min; } int findFirstValue(const vector<int> &sums, int offset, int count, int key) { if(offset > 0) key += sums[offset - 1]; int ret = -1; for(int i = 0; i < count; i++) { int value = sums[i + offset]; if(value == key) { ret = i; break; } } return ret; } int findFirstValue(const vector<int> &sums, const ValueMap &vmap, int offset, int count, int key) { if(offset > 0) key += sums[offset - 1]; int ret = vmap.findValue(key, offset, offset + count - 1); if(ret != -1) ret -= offset; return ret; } ll solve(const vector<int> &money, const string &cycle, bool print) { int cycle_size = (int)cycle.size(), count = (int)money.size(); int gcd = ::gcd(cycle_size, count); int sub_cycle_size = cycle_size / gcd; vector<int> cycle_pos(cycle.size(), -1); vector<char> sub_cycle(sub_cycle_size); vector<int> sub_sum(sub_cycle_size * 2); ValueMap vmaps; ValueMins vmins; #ifdef DEBUG_MODE if(print) { printf("cycle: %s\n", cycle.c_str()); printf("count:%d cycle:%d gcd:%d\n", count, cycle_size, gcd); } #endif ll out = -1ll; for(int s = 0; s < gcd; s++) { int prev = 0, min = 0, pos = s % cycle_size; for(int i = 0; i < sub_cycle_size; i++) { char value = cycle[pos]; assert(cycle_pos[pos] == -1); cycle_pos[pos] = i; pos = (pos + count) % cycle_size; sub_cycle[i] = value; int ivalue = value == 'W' ? 1 : -1; prev = sub_sum[i] = ivalue + prev; } for(int i = sub_cycle_size; i < sub_cycle_size * 2; i++) { int ivalue = sub_cycle[i - sub_cycle_size] == 'W' ? 1 : -1; prev = sub_sum[i] = ivalue + prev; } int sub_total = sub_sum[sub_cycle_size - 1]; vmaps.init(sub_sum); vmins.init(sub_sum); #ifdef DEBUG_MODE if(print) { printf("Sub-cycle %d: total:%d min:%d ", s, sub_total, min); for(int i = 0; i < sub_cycle_size; i++) printf("%c", sub_cycle[i]); printf("\n"); for(int i = 0; i < sub_cycle_size * 2; i++) printf("%d ", sub_sum[i]); printf("\n"); } #endif for(int n = s; n < count; n += gcd) { int sub_id = n % gcd; int cycle_start_pos = cycle_pos[n % cycle_size]; assert(cycle_start_pos != -1); #ifdef DEBUG_MODE if(print) printf("%d cycle:%d cpos:%d money:%d ", n, sub_id, cycle_start_pos, money[n]); #endif ll full_cycles = 0, cur_money = money[n]; ll cycle_gain = sub_total; int cycle_min = findMin(sub_sum, vmins, cycle_start_pos, sub_cycle_size); #ifdef DEBUG_MODE if(print) printf("cmin:%d ", cycle_min); #endif if(cycle_gain < 0) { // Last cycle doesn't have to be complete full_cycles = std::max(0ll, (cur_money + cycle_min) / -cycle_gain); cur_money += full_cycles * cycle_gain; if(cur_money > -cycle_min) { cur_money += cycle_gain; full_cycles++; } assert(cur_money <= -cycle_min); // printf("%d/%d/%d ", cur_money, min, cycle_gain); } ll simple_steps = 0; ll last_money = cur_money; ll iters = 0; if(cur_money + cycle_min > 0) continue; int pos = findFirstValue(sub_sum, vmaps, cycle_start_pos, sub_cycle_size, -cur_money); if(pos != -1) { simple_steps = pos + 1; cur_money = 0; } ll total_steps = -1; if(cur_money == 0) { total_steps = (simple_steps + full_cycles * sub_cycle_size - 1) * count + n + 1; if(total_steps < out || out == -1) out = total_steps; } #ifdef DEBUG_MODE if(print) printf(" full:%lld*%d simple:%lld -> %lld\n", full_cycles, sub_cycle_size, simple_steps, total_steps); #endif } #ifdef DEBUG_MODE if(print) printf("\n"); #endif } return out; } pair<vector<int>, string> randomize(int size) { vector<int> money(rand() % size + 1); string cycle(rand() % size + 1, ' '); for(int n = 0; n < (int)money.size(); n++) money[n] = (rand() / 10) % size + 1; for(int n = 0; n < (int)cycle.size(); n++) cycle[n] = rand() % 2 ? 'W' : 'P'; return make_pair(money, cycle); } void testRandom(int seed, int count) { bool single_test = count > 2000; if(seed <= 0) { seed = time(0); printf("seed: %d\n", seed); } srand(seed); if(single_test) { pair<vector<int>, string> task = randomize(count); ll ret = solve(task.first, task.second, false); printf("%lld\n", ret); return; } for(int n = 0; n < count; n++) { pair<vector<int>, string> task = randomize(10 + n); int size = (int)(task.first.size() + task.second.size()); if(count >= 2000 && n % (count / 10) == 0) { printf("."); fflush(stdout); } ll ret = solve(task.first, task.second, false); ll max_brute = ret < 0 ? size * size * 16 : ret + 100; ll correct = brute(task.first, task.second, max_brute, false); if(ret != correct) { printf("Error: %lld; should be: %lld:\n", ret, correct); if(std::max(correct, ret) < 200) { solve(task.first, task.second, true); brute(task.first, task.second, ll(size) * size * 16, true); } break; } } printf("\n"); } #define RANDOM_TESTING #if defined(DEBUG_MODE) && defined(RANDOM_TESTING) int main(int argc, char **argv) { assert(argc >= 3); int seed = atoi(argv[1]), count = atoi(argv[2]); testRandom(seed, count); return 0; } #else int main() { std::ios_base::sync_with_stdio(false); cin.tie(0); int count; cin >> count; vector<int> money(count, 0); for(int n = 0; n < count; n++) cin >> money[n]; int cycle_size; string cycle; cin >> cycle_size >> cycle; #ifdef DEBUG_MODE cout << brute(money, cycle, 100000, false) << endl; #endif cout << solve(money, cycle, true) << endl; return 0; } #endif |