#pragma GCC optimize ("O3") #pragma GCC target ("avx") #include "bits/stdc++.h" // define macro "/D__MAI" using namespace std; typedef long long int ll; #define xprintf(fmt,...) fprintf(stderr,fmt,__VA_ARGS__) #define debugv(v) {printf("L%d %s > ",__LINE__,#v);for(auto e:v){cout< ",__LINE__,#m);for(int x=0;x<(w);x++){cout<<(m)[x]<<" ";}cout<\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){cout<<(m)[y][x]<<" ";}cout< ostream& operator <<(ostream &o, const pair p) { o << "(" << p.first << ":" << p.second << ")"; return o; } template inline size_t argmin(iterator begin, iterator end) { return distance(begin, min_element(begin, end)); } template inline size_t argmax(iterator begin, iterator end) { return distance(begin, max_element(begin, end)); } template T& maxset(T& to, const T& val) { return to = max(to, val); } template T& minset(T& to, const T& val) { return to = min(to, val); } void bye(string s, int code = 0) { cout << s << endl; exit(0); } mt19937_64 randdev(8901016); inline ll rand_range(ll l, ll h) { return uniform_int_distribution(l, h)(randdev); } #ifdef __MAI #define getchar_unlocked getchar #define putchar_unlocked putchar #endif #ifdef __VSCC #define getchar_unlocked _getchar_nolock #define putchar_unlocked _putchar_nolock #endif namespace { #define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E) class MaiScanner { public: template void input_integer(T& var) { var = 0; T sign = 1; int cc = getchar_unlocked(); for (; cc<'0' || '9'>(int& var) { input_integer(var); return *this; } inline MaiScanner& operator>>(long long& var) { input_integer(var); return *this; } inline MaiScanner& operator>>(string& var) { int cc = getchar_unlocked(); for (; !isvisiblechar(cc); cc = getchar_unlocked()); for (; isvisiblechar(cc); cc = getchar_unlocked()) var.push_back(cc); return *this; } template void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; } }; } MaiScanner scanner; typedef int boolean; class EasyLP { public: const int dimension; // 左辺 vector> equation; // 定数項 vector offset; // 目的関数 vector objective; // 求まった目的関数の値 double objective_c; EasyLP(int n) :dimension(n), objective(n) { } // 目的関数を最小化する. // 式の情報は書き換えられる. double minimize() { while (true) { // printTableau(); // 目的関数の値を減少させることができる変数を探す int idx = 0; { double val = objective[0]; for (int i = 1; i < dimension; ++i) { if (val > objective[i]) { val = objective[i]; idx = i; } } // 無いなら最適解が得られた if (val >= 0) break; } // どの程度まで増やせば良いだろうか int target = -1; { double val, lim = 0; for (int i = 0; i < equation.size(); ++i) { if (equation[i][idx] == 0) continue; // 0除算防止 val = offset[i] / equation[i][idx]; if (0 < val && (target == -1 || val < lim)) { lim = val; target = i; } } }; if (target == -1) break; { // ピボット係数 double p = equation[target][idx]; // ピボット係数を p で除算 for (double& e : equation[target]) e /= p; offset[target] /= p; // ピボット列の掃き出し for (int i = 0; i < equation.size(); ++i) { if (i == target) continue; double d = equation[i][idx]; for (int j = 0; j < dimension; j++) { if (j != idx) equation[i][j] -= d * equation[target][j]; else equation[i][j] = 0; } offset[i] -= d * offset[target]; } { double d = objective[idx]; for (int j = 0; j < dimension; j++) { if (j != idx) objective[j] -= d * equation[target][j]; else objective[j] = 0; } objective_c += d * offset[target]; } } } return -objective_c; } void printTableau() { for (int i = 0; i < equation.size(); ++i) { for (double a : equation[i]) { printf(" %7.2f", a); } printf(" | %7.2f\n", offset[i]); } for (int i = equation.size(); 0 <= i; --i) { printf("---------"); } printf("\n"); for (double a : objective) { printf(" %7.2f", a); } printf(" %7.2f\n#####\n", objective_c); } }; int main() { { // EasyLP lp(5); // lp.equation.push_back({ 60.0, 40.0, 1.0, 0.0, 0.0 }); lp.offset.push_back(3800.0); // lp.equation.push_back({ 20.0, 30.0, 0.0, 1.0, 0.0 }); lp.offset.push_back(2100.0); // lp.equation.push_back({ 20.0, 10.0, 0.0, 0.0, 1.0 }); lp.offset.push_back(1200.0); // lp.objective = { -400.0, -300.0, 0.0, 0.0, 0.0 }; lp.objective_c = 0.0; // // printf("%.7f\n", lp.minimize()); } int ic, id; scanner >> ic >> id; double c, d; c = ic; d = id; EasyLP lp(4); lp.equation.push_back({ 21.0, 8.0, 1.0, 0.0 }); lp.offset.push_back(28.0*c); lp.equation.push_back({ 7.0, 20.0, 0.0, 1.0 }); lp.offset.push_back(28.0*d); lp.objective = { -1000.0, -2000.0, 0.0, 0.0 }; lp.objective_c = 0.0; printf("%.7f\n", lp.minimize()); //lp.printTableau(); return 0; }