#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif #include #include #include #include #include #include // Maximize cx s.t. Ax <= b, x >= 0 // Implementation idea: https://kopricky.github.io/code/Computation_Advanced/simplex.html // Refer to https://hitonanode.github.io/cplib-cpp/combinatorial_opt/simplex.hpp template struct Simplex { const Float EPS = Float(1.0) / (1LL << DEPS); int N, M; std::vector shuffle_idx; std::vector idx; std::vector> mat; int i_ch, j_ch; private: void _initialize(const std::vector> &A, const std::vector &b, const std::vector &c) { N = c.size(), M = A.size(); mat.assign(M + 2, std::vector(N + 2)); i_ch = M; for (int i = 0; i < M; i++) { for (int j = 0; j < N; j++) mat[i][j] = -A[i][j]; mat[i][N] = 1, mat[i][N + 1] = b[i]; if (mat[i_ch][N + 1] > mat[i][N + 1]) i_ch = i; } for (int j = 0; j < N; j++) mat[M][j] = c[j]; mat[M + 1][N] = -1; idx.resize(N + M + 1); std::iota(idx.begin(), idx.end(), 0); } inline Float abs_(Float x) noexcept { return x > -x ? x : -x; } void _solve() { std::vector jupd; for (nb_iter = 0, j_ch = N;; nb_iter++) { if (i_ch < M) { std::swap(idx[j_ch], idx[i_ch + N + 1]); mat[i_ch][j_ch] = Float(1) / mat[i_ch][j_ch]; jupd.clear(); for (int j = 0; j < N + 2; j++) { if (j != j_ch) { mat[i_ch][j] *= -mat[i_ch][j_ch]; if (abs_(mat[i_ch][j]) > EPS) jupd.push_back(j); } } for (int i = 0; i < M + 2; i++) { if (abs_(mat[i][j_ch]) < EPS or i == i_ch) continue; for (auto j : jupd) mat[i][j] += mat[i][j_ch] * mat[i_ch][j]; mat[i][j_ch] *= mat[i_ch][j_ch]; } } j_ch = -1; for (int j = 0; j < N + 1; j++) { if (j_ch < 0 or idx[j_ch] > idx[j]) { if (mat[M + 1][j] > EPS or (abs_(mat[M + 1][j]) < EPS and mat[M][j] > EPS)) j_ch = j; } } if (j_ch < 0) break; i_ch = -1; for (int i = 0; i < M; i++) { if (mat[i][j_ch] < -EPS) { if (i_ch < 0) { i_ch = i; } else if (mat[i_ch][N + 1] / mat[i_ch][j_ch] - mat[i][N + 1] / mat[i][j_ch] < -EPS) { i_ch = i; } else if (mat[i_ch][N + 1] / mat[i_ch][j_ch] - mat[i][N + 1] / mat[i][j_ch] < EPS and idx[i_ch] > idx[i]) { i_ch = i; } } } if (i_ch < 0) { is_infty = true; break; } } if (mat[M + 1][N + 1] < -EPS) { infeasible = true; return; } x.assign(N, 0); for (int i = 0; i < M; i++) { if (idx[N + 1 + i] < N) x[idx[N + 1 + i]] = mat[i][N + 1]; } ans = mat[M][N + 1]; } public: Simplex(std::vector> A, std::vector b, std::vector c) { is_infty = infeasible = false; if (Randomize) { std::mt19937 rng(std::chrono::steady_clock::now().time_since_epoch().count()); std::vector, Float>> Abs; for (unsigned i = 0; i < A.size(); i++) Abs.emplace_back(A[i], b[i]); std::shuffle(Abs.begin(), Abs.end(), rng); A.clear(), b.clear(); for (auto &&Ab : Abs) A.emplace_back(Ab.first), b.emplace_back(Ab.second); shuffle_idx.resize(c.size()); std::iota(shuffle_idx.begin(), shuffle_idx.end(), 0); std::shuffle(shuffle_idx.begin(), shuffle_idx.end(), rng); auto Atmp = A; auto ctmp = c; for (unsigned i = 0; i < A.size(); i++) { for (unsigned j = 0; j < A[i].size(); j++) A[i][j] = Atmp[i][shuffle_idx[j]]; } for (unsigned j = 0; j < c.size(); j++) c[j] = ctmp[shuffle_idx[j]]; } _initialize(A, b, c); _solve(); if (Randomize and x.size() == c.size()) { auto xtmp = x; for (unsigned j = 0; j < c.size(); j++) x[shuffle_idx[j]] = xtmp[j]; } } unsigned nb_iter; bool is_infty; bool infeasible; std::vector x; Float ans; static void dual(std::vector> &A, std::vector &b, std::vector &c) { const int n = b.size(), m = c.size(); std::vector> At(m, std::vector(n)); for (int i = 0; i < n; ++i) { for (int j = 0; j < m; ++j) At[j][i] = -A[i][j]; } A = At; for (int i = 0; i < n; ++i) b[i] = -b[i]; for (int j = 0; j < m; ++j) c[j] = -c[j]; b.swap(c); } }; lint solve() { int A, B, C; cin >> A >> B >> C; vector XYZW(4); cin >> XYZW; vector c; for (int x : XYZW) c.push_back(x); vector> mat(3, vector(4)); mat[0][0] = mat[1][0] = 1; mat[2][1] = mat[1][1] = 1; mat[2][2] = mat[0][2] = 1; mat[0][3] = mat[1][3] = mat[2][3] = 1; vector vec; vec.push_back(A); vec.push_back(B); vec.push_back(C); Simplex simplex(mat, vec, c); dbg(simplex.x); dbg(simplex.infeasible); dbg(simplex.is_infty); lint ret = 0; constexpr int D = 20; dbg(simplex.x); FOR(i0, simplex.x.at(0) - D, simplex.x.at(0) + D + 1) { FOR(i1, simplex.x.at(1) - D, simplex.x.at(1) + D + 1) { FOR(i2, simplex.x.at(2) - D, simplex.x.at(2) + D + 1) { FOR(i3, simplex.x.at(3) - D, simplex.x.at(3) + D + 1) { if (i0 < 0 or i1 < 0 or i2 < 0 or i3 < 0) continue; if (i0 + i2 + i3 > A) continue; if (i0 + i1 + i3 > B) continue; if (i3 + i1 + i2 > C) continue; dbg(make_tuple(i0, i1, i2, i3)); chmax(ret, i0 * XYZW.at(0) + i1 * XYZW.at(1) + i2 * XYZW.at(2) + i3 * XYZW.at(3)); } } } } return ret; } int main() { int T; cin >> T; while (T--) { cout << solve() << '\n'; } }