結果

問題 No.2309 [Cherry 5th Tune D] 夏の先取り
ユーザー hitonanode
提出日時 2023-05-19 21:54:04
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 3 ms / 3,000 ms
コード長 13,586 bytes
コンパイル時間 2,952 ms
コンパイル使用メモリ 201,352 KB
実行使用メモリ 6,824 KB
最終ジャッジ日時 2024-12-18 02:37:08
合計ジャッジ時間 4,366 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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ファイルパターン 結果
other AC * 50
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ソースコード

diff # 

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
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##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> 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 <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &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 <algorithm>
#include <chrono>
#include <cmath>
#include <numeric>
#include <random>
#include <vector>

// 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 <typename Float = double, int DEPS = 30, bool Randomize = true> struct Simplex {
    const Float EPS = Float(1.0) / (1LL << DEPS);
    int N, M;
    std::vector<int> shuffle_idx;
    std::vector<int> idx;
    std::vector<std::vector<Float>> mat;
    int i_ch, j_ch;

private:
    void _initialize(const std::vector<std::vector<Float>> &A, const std::vector<Float> &b,
                     const std::vector<Float> &c) {
        N = c.size(), M = A.size();

        mat.assign(M + 2, std::vector<Float>(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<int> 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<std::vector<Float>> A, std::vector<Float> b, std::vector<Float> c) {
        is_infty = infeasible = false;

        if (Randomize) {
            std::mt19937 rng(std::chrono::steady_clock::now().time_since_epoch().count());

            std::vector<std::pair<std::vector<Float>, 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<Float> x;
    Float ans;

    static void
    dual(std::vector<std::vector<Float>> &A, std::vector<Float> &b, std::vector<Float> &c) {
        const int n = b.size(), m = c.size();
        std::vector<std::vector<Float>> At(m, std::vector<Float>(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<lint> XYZW(4);
    cin >> XYZW;

    vector<double> c;
    for (int x : XYZW) c.push_back(x);

    vector<vector<double>> mat(3, vector<double>(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<double> vec;
    vec.push_back(A);
    vec.push_back(B);
    vec.push_back(C);

    Simplex simplex(mat, vec, c);

    lint ret = 0;
    constexpr int D = 4;
    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'; }
}
0