File size: 7,501 Bytes
14c9c2b | 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 | #include <iostream>
#include <string>
#include <vector>
#include <map>
#include <algorithm>
#include <array>
#include <nlohmann/json.hpp>
using json = nlohmann::json;
const long long W_MASS = 20000000;
const long long W_VOL = 25000000;
const int N_ITEMS = 12;
struct Item {
std::string name;
int q;
long long v, m, l;
int original_idx;
};
struct State {
long long m = 0, l = 0, v = 0;
std::vector<int> counts;
bool operator<(const State& other) const {
if (m != other.m) return m < other.m;
if (l != other.l) return l < other.l;
return v > other.v; // for sorting, higher value is better
}
};
std::vector<State> prune(std::vector<State>& states) {
if (states.size() <= 1) return states;
std::sort(states.begin(), states.end(), [](const State& a, const State& b){
return a.v > b.v;
});
std::vector<State> final_pruned;
final_pruned.reserve(states.size());
for(const auto& s : states) {
bool dominated = false;
for(const auto& p : final_pruned) {
if (p.m <= s.m && p.l <= s.l) { // p.v >= s.v is guaranteed by sort order
dominated = true;
break;
}
}
if (!dominated) {
final_pruned.push_back(s);
}
}
return final_pruned;
}
std::vector<State> generate_states(const std::vector<Item>& items, int state_limit) {
int n = items.size();
if (n == 0) {
std::vector<State> res;
res.emplace_back();
res.back().counts.resize(0);
return res;
}
std::vector<State> states;
states.emplace_back();
states.back().counts.resize(n, 0);
for (int i = 0; i < n; ++i) {
std::vector<State> next_states;
int q_eff = items[i].q;
// Heuristic cap to prevent state explosion
if (q_eff > 30) q_eff = 30;
next_states.reserve(states.size() * (q_eff + 1));
for (const auto& s : states) {
for (int c = 0; c <= q_eff; ++c) {
long long next_m = s.m + c * items[i].m;
long long next_l = s.l + c * items[i].l;
if (next_m > W_MASS || next_l > W_VOL) {
break;
}
State next_s;
next_s.m = next_m;
next_s.l = next_l;
next_s.v = s.v + c * items[i].v;
next_s.counts = s.counts;
next_s.counts[i] = c;
next_states.push_back(next_s);
}
}
states = prune(next_states);
if (states.size() > state_limit) {
std::sort(states.begin(), states.end(), [](const State& a, const State& b){
return a.v > b.v;
});
states.resize(state_limit);
}
}
return states;
}
int main() {
std::ios_base::sync_with_stdio(false);
std::cin.tie(NULL);
json input_json;
std::cin >> input_json;
std::vector<Item> all_items;
int idx_counter = 0;
for (auto& [name, val] : input_json.items()) {
all_items.push_back({
name,
val[0].get<int>(),
val[1].get<long long>(),
val[2].get<long long>(),
val[3].get<long long>(),
idx_counter++
});
}
std::vector<Item> lumpy_items, dust_items;
for (const auto& item : all_items) {
if (item.q > 50 && (item.m < 100000 || item.l < 100000)) {
dust_items.push_back(item);
} else {
lumpy_items.push_back(item);
}
}
std::sort(dust_items.begin(), dust_items.end(), [](const Item& a, const Item& b) {
double dens_a = (double)a.v / (a.m / (double)W_MASS * 0.5 + a.l / (double)W_VOL * 0.5 + 1e-9);
double dens_b = (double)b.v / (b.m / (double)W_MASS * 0.5 + b.l / (double)W_VOL * 0.5 + 1e-9);
return dens_a > dens_b;
});
std::vector<Item> lumpy_a, lumpy_b;
for (size_t i = 0; i < lumpy_items.size(); ++i) {
if (i < lumpy_items.size() / 2) {
lumpy_a.push_back(lumpy_items[i]);
} else {
lumpy_b.push_back(lumpy_items[i]);
}
}
int state_limit = 4000;
auto states_a = generate_states(lumpy_a, state_limit);
auto states_b = generate_states(lumpy_b, state_limit);
long long max_total_value = -1;
std::vector<int> best_counts(N_ITEMS, 0);
for (const auto& s_a : states_a) {
for (const auto& s_b : states_b) {
long long current_m = s_a.m + s_b.m;
long long current_l = s_a.l + s_b.l;
if (current_m > W_MASS || current_l > W_VOL) continue;
long long current_v = s_a.v + s_b.v;
std::vector<int> current_counts(N_ITEMS, 0);
for (size_t i = 0; i < lumpy_a.size(); ++i) current_counts[lumpy_a[i].original_idx] = s_a.counts[i];
for (size_t i = 0; i < lumpy_b.size(); ++i) current_counts[lumpy_b[i].original_idx] = s_b.counts[i];
long long m_rem = W_MASS - current_m;
long long l_rem = W_VOL - current_l;
long long dust_v = 0;
for (const auto& item : dust_items) {
int num_to_take = item.q;
if (item.m > 0) num_to_take = std::min(num_to_take, (int)(m_rem / item.m));
if (item.l > 0) num_to_take = std::min(num_to_take, (int)(l_rem / item.l));
if (num_to_take > 0) {
m_rem -= (long long)num_to_take * item.m;
l_rem -= (long long)num_to_take * item.l;
dust_v += (long long)num_to_take * item.v;
current_counts[item.original_idx] += num_to_take;
}
}
if (current_v + dust_v > max_total_value) {
max_total_value = current_v + dust_v;
best_counts = current_counts;
}
}
}
// A pure greedy solution on all items as a baseline
{
long long m_rem = W_MASS;
long long l_rem = W_VOL;
long long current_v = 0;
std::vector<int> current_counts(N_ITEMS, 0);
std::vector<Item> sorted_all = all_items;
std::sort(sorted_all.begin(), sorted_all.end(), [](const Item& a, const Item& b) {
double dens_a = (double)a.v / (a.m / (double)W_MASS * 0.5 + a.l / (double)W_VOL * 0.5 + 1e-9);
double dens_b = (double)b.v / (b.m / (double)W_MASS * 0.5 + b.l / (double)W_VOL * 0.5 + 1e-9);
return dens_a > dens_b;
});
for (const auto& item : sorted_all) {
int num_to_take = item.q;
if (item.m > 0) num_to_take = std::min(num_to_take, (int)(m_rem / item.m));
if (item.l > 0) num_to_take = std::min(num_to_take, (int)(l_rem / item.l));
if (num_to_take > 0) {
m_rem -= (long long)num_to_take * item.m;
l_rem -= (long long)num_to_take * item.l;
current_v += (long long)num_to_take * item.v;
current_counts[item.original_idx] = num_to_take;
}
}
if (current_v > max_total_value) {
best_counts = current_counts;
}
}
json output_json;
for (int i = 0; i < N_ITEMS; ++i) {
output_json[all_items[i].name] = best_counts[i];
}
std::cout << output_json.dump(1, '\t') << std::endl;
return 0;
} |