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 |
ソースコード
#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_LOCALconst 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.hpptemplate <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 andidx[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 voiddual(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'; }}