#include <cstdio> #include <algorithm> #include <set> #include <vector> #include <list> #include <cassert> #include <sstream> #include <string> #ifndef DEBUG #define DEBUG 0 #endif #define dprint(fmt, ...) do { if (DEBUG) printf(fmt, ##__VA_ARGS__); } while (0) using namespace std; typedef long long LL; struct Upcoming_merge; /** * Klienci dla ktorych zapiekanki beda pieczone jedna po drugiej sa grupowani. */ struct Group { LL k; LL wait; LL wait_updated_at_d; LL t_first; // czas kiedy przychodzi pierwszy klient z tej grupy LL t_last; // kiedy przychodzi ostatni set<Upcoming_merge>::iterator my_merge; Group () {} Group (LL k_, LL wait_, LL tf, LL tl) : k(k_), wait(wait_), wait_updated_at_d(0), t_first(tf), t_last(tl) {} string to_string() const { stringstream ss; ss << k << " " << wait << " (at " << wait_updated_at_d << ") " << t_first << ".." << t_last; return ss.str(); } LL k2() const { if (k & 1L) { return (k - 1L) / 2L * k; } return k / 2L * (k - 1L); } LL d_first(LL d) { return t_first - d; } LL d_last(LL d) { return t_first + (k - 1L) * d; } }; // Grupy moga sie laczyc przy dostatecznie duzej zmianie d. Chemy wiedziec kiedy to bedzie. struct Upcoming_merge { LL at_d; // wskaznik do wczesniejszej grupy list<Group>::iterator group; Upcoming_merge(LL at_d_, list<Group>::iterator group_) : at_d(at_d_), group(group_) {} string to_string() const { stringstream ss; ss << "m at " << at_d << " t0 " << group->t_first; return ss.str(); } bool operator<(const Upcoming_merge& other) const { if (at_d != other.at_d) { return at_d < other.at_d; } return group->t_first < other.group->t_first; } }; struct World { list<Group> groups; set<Upcoming_merge> merges; LL sum_k2; // suma po k(k+1)/2 po kazdej grupie LL res; LL d; // czas pieczenia w piekarniku LL next_merge() const { if (merges.empty()) { return 9223372036854775807L; } else { return merges.cbegin()->at_d; } } void print() { dprint("res %Ld sum_k2 %Ld d %Ld\n", res, sum_k2, d); dprint("groups: (%lu)\n", groups.size()); for (auto& group : groups) { dprint("%s\n", group.to_string().c_str()); } dprint("merges: (%lu)\n", merges.size()); for (auto& merge : merges) { dprint("%s\n", merge.to_string().c_str()); } dprint("---\n"); } set<Upcoming_merge>::iterator upcoming_merge_with_next(list<Group>::iterator it) { if (it == --(groups.end())) { return merges.end(); } list<Group>::iterator next = it; ++next; LL k = it->k; LL next_merge_at = (next->t_first - it->t_first + k - 1) / k; dprint("a merge between %s and %s will be at %Ld\n", it->to_string().c_str(), next->to_string().c_str(), next_merge_at); return merges.insert(Upcoming_merge(next_merge_at, it)).first; } LL merge_with_next(list<Group>::iterator it, LL dd) { list<Group>::iterator next_it = it; ++next_it; assert (it != groups.end()); assert (next_it != groups.end()); assert (it->my_merge != merges.end()); dprint("merging %s with %s\n", it->to_string().c_str(), next_it->to_string().c_str()); LL rv = it->k2() + next_it->k2(); LL rv_without_updated_at_this_d = (it->wait_updated_at_d != d + dd ? it->k2() : 0) + next_it->k2(); dprint("rv %Ld rv without %Ld\n", rv, rv_without_updated_at_this_d); Group next = *next_it; dprint("res bef %Ld\n", res); res -= it->wait + it->k2() * (max(LL(0), d - it->wait_updated_at_d)); dprint("res mid %Ld\n", res); res -= next_it->wait + next_it->k2() * (max(LL(0), d - next_it->wait_updated_at_d)); dprint("res aft %Ld\n", res); // uwzglednij wszystkie zmiany implicite it->wait += it->k2() * (d + dd - it->wait_updated_at_d); next_it->wait += next_it->k2() * (d + dd - next_it->wait_updated_at_d); dprint("waits now %Ld %Ld\n", it->wait, next_it->wait); LL offset = it->d_last(d + dd) - next_it->d_first(d + dd); assert (offset >= 0); next_it->wait += next_it->k * offset; dprint("after offset next waits now %Ld\n", next_it->wait); it->k += next_it->k; it->wait += next_it->wait; it->t_last = next_it->t_last; it->wait_updated_at_d = d + dd; sum_k2 -= rv; sum_k2 += it->k2(); res += it->wait; if (next_it->my_merge != merges.end()) { merges.erase(next_it->my_merge); } merges.erase(it->my_merge); groups.erase(next_it); // nowy merge it->my_merge = upcoming_merge_with_next(it); return rv_without_updated_at_this_d; } // roznica w d void update(LL dd) { if (dd == 0) { dprint("SKIPPING\n"); return; } dprint("UPDATING by %Ld to %Ld\n", dd, d + dd); // fprintf(stderr, "here\n"); // fflush(stderr); LL affected = sum_k2; while (!merges.empty() && merges.cbegin()->at_d <= d + dd) { affected -= merge_with_next(merges.cbegin()->group, dd); // dprint("after update:\n"); // print(); } res += affected * dd; d += dd; dprint("affected: %Ld new res %Ld new d %Ld\n", affected, res, d); dprint("\n"); } }; struct Query { LL val; LL result; int pos; }; bool by_val(const Query& q1, const Query& q2) { return q1.val < q2.val; } bool by_pos(const Query& q1, const Query& q2) { return q1.pos < q2.pos; } int main() { World world; int n, m; scanf("%d%d", &n, &m); world.groups.emplace_back(1, 0, 0, 0); for (int i = 0; i < n; ++i) { LL t; scanf("%Ld", &t); if (t == world.groups.back().t_first) { ++world.groups.back().k; } else { world.groups.emplace_back(1, 0, t, t); } } world.res = 0; world.sum_k2 = 0; for (const auto& g : world.groups) { world.sum_k2 += g.k2(); } world.d = 0; for (list<Group>::iterator it = world.groups.begin(); it != world.groups.end(); ++it) { it->my_merge = world.upcoming_merge_with_next(it); } world.print(); vector<Query> ds(m); for (int i = 0; i < m; ++i) { scanf("%Ld", &ds[i].val); ds[i].pos = i; } sort(ds.begin(), ds.end(), by_val); LL last = 0; for (int i = 0; i < m; ++i) { LL next_merge = world.next_merge(); dprint("next_merge: %Ld\n", next_merge); if (ds[i].val <= next_merge) { world.update(ds[i].val - last); ds[i].result = world.res; last = ds[i].val; } else { world.update(next_merge - last); last = next_merge; --i; } } sort(ds.begin(), ds.end(), by_pos); for (int i = 0; i < m; ++i) { printf("%Ld\n", ds[i].result); } }
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 | #include <cstdio> #include <algorithm> #include <set> #include <vector> #include <list> #include <cassert> #include <sstream> #include <string> #ifndef DEBUG #define DEBUG 0 #endif #define dprint(fmt, ...) do { if (DEBUG) printf(fmt, ##__VA_ARGS__); } while (0) using namespace std; typedef long long LL; struct Upcoming_merge; /** * Klienci dla ktorych zapiekanki beda pieczone jedna po drugiej sa grupowani. */ struct Group { LL k; LL wait; LL wait_updated_at_d; LL t_first; // czas kiedy przychodzi pierwszy klient z tej grupy LL t_last; // kiedy przychodzi ostatni set<Upcoming_merge>::iterator my_merge; Group () {} Group (LL k_, LL wait_, LL tf, LL tl) : k(k_), wait(wait_), wait_updated_at_d(0), t_first(tf), t_last(tl) {} string to_string() const { stringstream ss; ss << k << " " << wait << " (at " << wait_updated_at_d << ") " << t_first << ".." << t_last; return ss.str(); } LL k2() const { if (k & 1L) { return (k - 1L) / 2L * k; } return k / 2L * (k - 1L); } LL d_first(LL d) { return t_first - d; } LL d_last(LL d) { return t_first + (k - 1L) * d; } }; // Grupy moga sie laczyc przy dostatecznie duzej zmianie d. Chemy wiedziec kiedy to bedzie. struct Upcoming_merge { LL at_d; // wskaznik do wczesniejszej grupy list<Group>::iterator group; Upcoming_merge(LL at_d_, list<Group>::iterator group_) : at_d(at_d_), group(group_) {} string to_string() const { stringstream ss; ss << "m at " << at_d << " t0 " << group->t_first; return ss.str(); } bool operator<(const Upcoming_merge& other) const { if (at_d != other.at_d) { return at_d < other.at_d; } return group->t_first < other.group->t_first; } }; struct World { list<Group> groups; set<Upcoming_merge> merges; LL sum_k2; // suma po k(k+1)/2 po kazdej grupie LL res; LL d; // czas pieczenia w piekarniku LL next_merge() const { if (merges.empty()) { return 9223372036854775807L; } else { return merges.cbegin()->at_d; } } void print() { dprint("res %Ld sum_k2 %Ld d %Ld\n", res, sum_k2, d); dprint("groups: (%lu)\n", groups.size()); for (auto& group : groups) { dprint("%s\n", group.to_string().c_str()); } dprint("merges: (%lu)\n", merges.size()); for (auto& merge : merges) { dprint("%s\n", merge.to_string().c_str()); } dprint("---\n"); } set<Upcoming_merge>::iterator upcoming_merge_with_next(list<Group>::iterator it) { if (it == --(groups.end())) { return merges.end(); } list<Group>::iterator next = it; ++next; LL k = it->k; LL next_merge_at = (next->t_first - it->t_first + k - 1) / k; dprint("a merge between %s and %s will be at %Ld\n", it->to_string().c_str(), next->to_string().c_str(), next_merge_at); return merges.insert(Upcoming_merge(next_merge_at, it)).first; } LL merge_with_next(list<Group>::iterator it, LL dd) { list<Group>::iterator next_it = it; ++next_it; assert (it != groups.end()); assert (next_it != groups.end()); assert (it->my_merge != merges.end()); dprint("merging %s with %s\n", it->to_string().c_str(), next_it->to_string().c_str()); LL rv = it->k2() + next_it->k2(); LL rv_without_updated_at_this_d = (it->wait_updated_at_d != d + dd ? it->k2() : 0) + next_it->k2(); dprint("rv %Ld rv without %Ld\n", rv, rv_without_updated_at_this_d); Group next = *next_it; dprint("res bef %Ld\n", res); res -= it->wait + it->k2() * (max(LL(0), d - it->wait_updated_at_d)); dprint("res mid %Ld\n", res); res -= next_it->wait + next_it->k2() * (max(LL(0), d - next_it->wait_updated_at_d)); dprint("res aft %Ld\n", res); // uwzglednij wszystkie zmiany implicite it->wait += it->k2() * (d + dd - it->wait_updated_at_d); next_it->wait += next_it->k2() * (d + dd - next_it->wait_updated_at_d); dprint("waits now %Ld %Ld\n", it->wait, next_it->wait); LL offset = it->d_last(d + dd) - next_it->d_first(d + dd); assert (offset >= 0); next_it->wait += next_it->k * offset; dprint("after offset next waits now %Ld\n", next_it->wait); it->k += next_it->k; it->wait += next_it->wait; it->t_last = next_it->t_last; it->wait_updated_at_d = d + dd; sum_k2 -= rv; sum_k2 += it->k2(); res += it->wait; if (next_it->my_merge != merges.end()) { merges.erase(next_it->my_merge); } merges.erase(it->my_merge); groups.erase(next_it); // nowy merge it->my_merge = upcoming_merge_with_next(it); return rv_without_updated_at_this_d; } // roznica w d void update(LL dd) { if (dd == 0) { dprint("SKIPPING\n"); return; } dprint("UPDATING by %Ld to %Ld\n", dd, d + dd); // fprintf(stderr, "here\n"); // fflush(stderr); LL affected = sum_k2; while (!merges.empty() && merges.cbegin()->at_d <= d + dd) { affected -= merge_with_next(merges.cbegin()->group, dd); // dprint("after update:\n"); // print(); } res += affected * dd; d += dd; dprint("affected: %Ld new res %Ld new d %Ld\n", affected, res, d); dprint("\n"); } }; struct Query { LL val; LL result; int pos; }; bool by_val(const Query& q1, const Query& q2) { return q1.val < q2.val; } bool by_pos(const Query& q1, const Query& q2) { return q1.pos < q2.pos; } int main() { World world; int n, m; scanf("%d%d", &n, &m); world.groups.emplace_back(1, 0, 0, 0); for (int i = 0; i < n; ++i) { LL t; scanf("%Ld", &t); if (t == world.groups.back().t_first) { ++world.groups.back().k; } else { world.groups.emplace_back(1, 0, t, t); } } world.res = 0; world.sum_k2 = 0; for (const auto& g : world.groups) { world.sum_k2 += g.k2(); } world.d = 0; for (list<Group>::iterator it = world.groups.begin(); it != world.groups.end(); ++it) { it->my_merge = world.upcoming_merge_with_next(it); } world.print(); vector<Query> ds(m); for (int i = 0; i < m; ++i) { scanf("%Ld", &ds[i].val); ds[i].pos = i; } sort(ds.begin(), ds.end(), by_val); LL last = 0; for (int i = 0; i < m; ++i) { LL next_merge = world.next_merge(); dprint("next_merge: %Ld\n", next_merge); if (ds[i].val <= next_merge) { world.update(ds[i].val - last); ds[i].result = world.res; last = ds[i].val; } else { world.update(next_merge - last); last = next_merge; --i; } } sort(ds.begin(), ds.end(), by_pos); for (int i = 0; i < m; ++i) { printf("%Ld\n", ds[i].result); } } |