File size: 7,718 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 | #include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <random>
#include <cctype>
#include <cmath>
using namespace std;
const long long M = 20000000; // mg
const long long L = 25000000; // µL
struct Treasure {
string name;
long long q; // max quantity
long long v; // value per item
long long m; // mass per item (mg)
long long l; // volume per item (µL)
double density;
};
vector<Treasure> treasures;
void parseInput() {
string s;
char c;
while (cin.get(c)) s += c;
size_t i = 0;
auto skipWS = [&]() {
while (i < s.size() && isspace(s[i])) i++;
};
skipWS();
if (s[i] != '{') return;
i++;
while (true) {
skipWS();
if (s[i] == '}') break;
if (s[i] == '"') {
i++;
size_t start = i;
while (s[i] != '"') i++;
string key = s.substr(start, i - start);
i++; // skip '"'
skipWS();
if (s[i] != ':') return;
i++;
skipWS();
if (s[i] != '[') return;
i++;
vector<long long> nums;
for (int j = 0; j < 4; j++) {
skipWS();
long long num = 0;
while (i < s.size() && isdigit(s[i])) {
num = num * 10 + (s[i] - '0');
i++;
}
nums.push_back(num);
if (j < 3) {
skipWS();
if (s[i] != ',') return;
i++;
}
}
skipWS();
if (s[i] != ']') return;
i++;
treasures.push_back({key, nums[0], nums[1], nums[2], nums[3], 0.0});
skipWS();
if (s[i] == ',') i++;
else if (s[i] == '}') break;
else return;
}
}
}
vector<long long> greedy(const vector<int>& order) {
vector<long long> cnt(treasures.size(), 0);
long long cur_m = 0, cur_l = 0;
for (int idx : order) {
const Treasure& t = treasures[idx];
long long maxTake = t.q;
if (t.m > 0) maxTake = min(maxTake, (M - cur_m) / t.m);
if (t.l > 0) maxTake = min(maxTake, (L - cur_l) / t.l);
cnt[idx] = maxTake;
cur_m += maxTake * t.m;
cur_l += maxTake * t.l;
}
return cnt;
}
void improve(vector<long long>& cnt, long long& cur_m, long long& cur_l, long long& cur_v) {
bool improved = true;
while (improved) {
improved = false;
// try to add one item
for (int i = 0; i < (int)treasures.size(); i++) {
if (cnt[i] < treasures[i].q) {
long long new_m = cur_m + treasures[i].m;
long long new_l = cur_l + treasures[i].l;
if (new_m <= M && new_l <= L) {
cnt[i]++;
cur_m = new_m;
cur_l = new_l;
cur_v += treasures[i].v;
improved = true;
}
}
}
// try to swap: remove one from j, add one to i
for (int i = 0; i < (int)treasures.size() && !improved; i++) {
for (int j = 0; j < (int)treasures.size(); j++) {
if (i == j) continue;
if (cnt[i] < treasures[i].q && cnt[j] > 0) {
long long delta_m = treasures[i].m - treasures[j].m;
long long delta_l = treasures[i].l - treasures[j].l;
long long delta_v = treasures[i].v - treasures[j].v;
if (delta_v > 0 && cur_m + delta_m <= M && cur_l + delta_l <= L) {
cnt[i]++; cnt[j]--;
cur_m += delta_m;
cur_l += delta_l;
cur_v += delta_v;
improved = true;
break;
}
}
}
if (improved) break;
}
}
}
void finalRefine(vector<long long>& cnt, long long& cur_m, long long& cur_l, long long& cur_v) {
int n = treasures.size();
for (int i = 0; i < n; i++) {
for (int j = i+1; j < n; j++) {
long long cur_xi = cnt[i], cur_xj = cnt[j];
long long base_m = cur_m - cur_xi*treasures[i].m - cur_xj*treasures[j].m;
long long base_l = cur_l - cur_xi*treasures[i].l - cur_xj*treasures[j].l;
long long base_v = cur_v - cur_xi*treasures[i].v - cur_xj*treasures[j].v;
long long best_xi = cur_xi, best_xj = cur_xj;
long long best_m = cur_m, best_l = cur_l, best_v = cur_v;
for (long long xi = max(0LL, cur_xi-10); xi <= min(treasures[i].q, cur_xi+10); xi++) {
for (long long xj = max(0LL, cur_xj-10); xj <= min(treasures[j].q, cur_xj+10); xj++) {
long long new_m = base_m + xi*treasures[i].m + xj*treasures[j].m;
long long new_l = base_l + xi*treasures[i].l + xj*treasures[j].l;
if (new_m <= M && new_l <= L) {
long long new_v = base_v + xi*treasures[i].v + xj*treasures[j].v;
if (new_v > best_v) {
best_v = new_v;
best_m = new_m;
best_l = new_l;
best_xi = xi;
best_xj = xj;
}
}
}
}
if (best_xi != cur_xi || best_xj != cur_xj) {
cnt[i] = best_xi;
cnt[j] = best_xj;
cur_m = best_m;
cur_l = best_l;
cur_v = best_v;
}
}
}
}
int main() {
parseInput();
int n = treasures.size();
// compute density: value per combined resource
for (int i = 0; i < n; i++) {
// density = v_i / (m_i/M + l_i/L) = v_i * M * L / (m_i * L + l_i * M)
double denom = treasures[i].m * L + treasures[i].l * M;
treasures[i].density = (denom > 0) ? (treasures[i].v * M * L / denom) : 1e18;
}
vector<int> order(n);
for (int i = 0; i < n; i++) order[i] = i;
sort(order.begin(), order.end(), [&](int a, int b) {
return treasures[a].density > treasures[b].density;
});
// initial solution from density order
vector<long long> best_cnt = greedy(order);
long long best_m = 0, best_l = 0, best_v = 0;
for (int i = 0; i < n; i++) {
best_m += best_cnt[i] * treasures[i].m;
best_l += best_cnt[i] * treasures[i].l;
best_v += best_cnt[i] * treasures[i].v;
}
improve(best_cnt, best_m, best_l, best_v);
// random permutations
mt19937 rng(123456); // fixed seed for reproducibility
for (int iter = 0; iter < 100; iter++) {
shuffle(order.begin(), order.end(), rng);
vector<long long> cnt = greedy(order);
long long cur_m = 0, cur_l = 0, cur_v = 0;
for (int i = 0; i < n; i++) {
cur_m += cnt[i] * treasures[i].m;
cur_l += cnt[i] * treasures[i].l;
cur_v += cnt[i] * treasures[i].v;
}
improve(cnt, cur_m, cur_l, cur_v);
if (cur_v > best_v) {
best_v = cur_v;
best_m = cur_m;
best_l = cur_l;
best_cnt = cnt;
}
}
// final refinement on pairs
finalRefine(best_cnt, best_m, best_l, best_v);
// output JSON
cout << "{\n";
for (int i = 0; i < n; i++) {
cout << " \"" << treasures[i].name << "\": " << best_cnt[i];
if (i != n-1) cout << ",";
cout << "\n";
}
cout << "}\n";
return 0;
} |