#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; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } 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; } #if __cplusplus >= 201703L 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 << ')'; } #endif 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) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) 0 #define dbgif(cond, x) 0 #endif #ifdef BENCHMARK #define bench(x) (cout << (x) << endl) #define dump_onlinejudge(x) 0 #else #define dump_onlinejudge(x) (cout << (x) << endl) #define bench(x) 0 #endif uint32_t rand_int() // XorShift random integer generator { static uint32_t x = 123456789, y = 362436069, z = 521288629, w = 88675123; uint32_t t = x ^ (x << 11); x = y; y = z; z = w; return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)); } double rand_double() { return (double)rand_int() / UINT32_MAX; } struct Pendulum { int b; // 初期振幅 int m; // 最小振幅 int e; // 減衰振幅 std::vector init; Pendulum() = default; Pendulum(int b_, int m_, int e_) : b(b_), m(m_), e(e_) { assert(1 <= m and m <= b); assert(1 <= e); init.push_back(0); for (int dir = 1, a = b_; a > m or dir < 0; dir = -dir, a = max(m, a - e)) { for (int t = 1; t <= a; ++t) init.push_back(dir * t); for (int t = a - 1; t >= 0; --t) init.push_back(dir * t); } } int get(int t) const { assert(t >= 0); if (t < int(init.size())) return init.at(t); int md = (t - init.size() + 1) % (m * 4); if (md < m) return md; if (md < m * 3) return m * 2 - md; return md - m * 4; } }; constexpr int maxb = 13; vector, vector>>>> txs_uxs(maxb + 1); const pair, vector> &get_txs_uxs(const tuple &bme) { return txs_uxs.at(std::get<0>(bme)).at(std::get<1>(bme)).at(std::get<2>(bme)); } struct Input { int n; vector T; vector U; Input() = default; template Input(OStream &os) { int k; os >> n >> k; T.resize(k), U.resize(k); os >> T >> U; } static Input randgen() { int n = 50, k = 50, delta = 200; vector gs; while (gs.size() < k * 2 + 1) { vector fs(k * 2); for (auto &f : fs) f = rand_double(); gs = {0}; REP(i, fs.size()) { lint gj = roundl(gs.back() + delta / fs[i]); if (gj < gs.back() + delta or gj > 1e9) { gs.clear(); break; } else { gs.push_back(gj); } } } vector T, U; FOR(i, 1, k * 2 + 1) { (i % 2 ? T : U).push_back(gs.at(i)); } assert(T.size() == 50); assert(U.size() == 50); if (rand_int() % 2) swap(T, U); Input ret; ret.n = 50; ret.T = T; ret.U = U; return ret; } }; struct State { vector> sol; vector t_mat; double tsum; double Coeff = 1e7 / (25 * 49 * 50); double teval() const { return tsum * Coeff; } double ueval; inline int f(int k, int i, int j) const noexcept { return (k * 50 + i) * 50 + j; } inline int g(int k, int i) const noexcept { return k * 50 + i; } State(const vector> &sol_) : sol(sol_), t_mat(50 * 50 * 50), tsum(0), // uxs(50 * 50), ueval(0) { REP(k, 50) { REP(i, 50) REP(j, i) { int xi = get_txs_uxs(sol[i]).first.at(k), bi = std::get<0>(sol[i]); int xj = get_txs_uxs(sol[j]).first.at(k), bj = std::get<0>(sol[j]); double v = double(abs(xi - xj)) / (bi + bj); t_mat.at(f(k, i, j)) = t_mat.at(f(k, j, i)) = v; tsum += v; } } REP(k, 50) { constexpr int INF = 1 << 30; int xlo = INF, xhi = -INF; REP(i, 50) { int x = get_txs_uxs(sol[i]).second.at(k); chmin(xlo, x); chmax(xhi, x); } ueval += roundl(1e7 / sqrt((xhi - xlo) * 0.05 + 1)) * 0.02; } } double eval() const { return teval() * ueval; } pair calc_improve(int i, tuple bme_i) const { double tsum_diff = 0; REP(k, 50) { REP(j, 50) { if (i == j) continue; int xi = get_txs_uxs(bme_i).first.at(k), bi = std::get<0>(bme_i); int xj = get_txs_uxs(sol[j]).first.at(k), bj = std::get<0>(sol[j]); double v = double(abs(xi - xj)) / (bi + bj); tsum_diff += v - t_mat.at(f(k, i, j)); } } double uev = 0; REP(k, 50) { int xlo = get_txs_uxs(bme_i).second.at(k), xhi = xlo; REP(j, 50) { if (i == j) continue; int x = get_txs_uxs(sol[j]).second.at(k); chmin(xlo, x); chmax(xhi, x); } uev += roundl(1e7 / sqrt((xhi - xlo) * 0.05 + 1)) * 0.02; } return make_pair((tsum + tsum_diff) * Coeff * uev - eval(), uev); } void set(int i, tuple bme_i, double new_uev) { sol[i] = bme_i; REP(k, 50) { REP(j, 50) { if (i == j) continue; int xi = get_txs_uxs(bme_i).first.at(k), bi = std::get<0>(bme_i); int xj = get_txs_uxs(sol[j]).first.at(k), bj = std::get<0>(sol[j]); double v = double(abs(xi - xj)) / (bi + bj); tsum += v - t_mat.at(f(k, i, j)); t_mat.at(f(k, i, j)) = t_mat.at(f(k, j, i)) = v; } } ueval = new_uev; } }; void dump(const vector> &bmes) { for (auto [b, m, e] : bmes) { string s; s += to_string(b) + " " + to_string(m) + " " + to_string(e); dump_onlinejudge(s); bench(s); } } pair>, double> optimize(const Input &instance) { vector> bmes; FOR(b, 1, maxb + 1) { txs_uxs.at(b).resize(b + 1); FOR(m, 1, b + 1) { if (m < b - 2) continue; txs_uxs.at(b).at(m).resize(max(2, b - m + 1)); FOR(e, 1, max(1, b - m) + 1) { if (e > 3) continue; Pendulum pen(b, m, e); for (int t : instance.T) txs_uxs.at(b).at(m).at(e).first.push_back(pen.get(t)); for (int t : instance.U) txs_uxs.at(b).at(m).at(e).second.push_back(pen.get(t)); bmes.emplace_back(b, m, e); } } } dbg(bmes); vector> solinit; REP(t, 50) solinit.emplace_back(bmes.at(rand_int() % bmes.size())); // REP(t, 50) solinit.emplace_back(t % 2 + 1, 1, 1); State state(solinit); vector> bestsol = state.sol; double besteval = state.eval(); double start_temp = 1e11, end_temp = 1e-10; const int max_iter = 10000; REP(iter, max_iter) { double rate = 1.0 * iter / max_iter; double temp = pow(start_temp, 1 - rate) * pow(end_temp, rate); double pre_score = state.eval(); int i = rand_int() % 50; auto bme = bmes.at(rand_int() % bmes.size()); // FIXME auto imp = state.calc_improve(i, bme); double new_score = pre_score + imp.first; double prob = exp((new_score - pre_score) / temp); // double prob = exp(log(new_score / pre_score) / temp); // if (imp.first > 1) { if (prob > rand_double()) { state.set(i, bme, imp.second); dbg(make_pair(iter, imp.first)); if (chmax(besteval, state.eval())) bestsol = state.sol; } } dbg(besteval); return {bestsol, besteval}; } int main(int argc, char *argv[]) { if (argc >= 2) { // X = std::stoi(argv[1]); } Input instance(cin); auto [sol, f] = optimize(instance); // bench(f); auto [sol2, f2] = optimize(instance); auto [sol3, f3] = optimize(instance); bench(max({f, f2, f3})); dump(sol); }