#955691 (C++23) No.5020 Averaging

• 問題: No.5020 Averaging
• ユーザー: risujiroh
• 提出日時: 2024-02-25 16:43:22
• 言語: C++23 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 767 ms / 1,000 ms
• コード長: 6,661 bytes
• コンパイル時間: 3,602 ms
• コンパイル使用メモリ: 274,376 KB
• 実行使用メモリ: 6,676 KB
• スコア: 81,581,001
• 最終ジャッジ日時: 2024-02-25 16:45:41
• 合計ジャッジ時間: 43,115 ms
• ジャッジサーバーID （参考情報）: judge13 / judge14

ファイルパターン	結果
other	AC * 50

ソースコード

#if __INCLUDE_LEVEL__ == 0

#include __BASE_FILE__

namespace {

void solve() {
  int n;
  scan(n);
  std::vector<i64> a(n), b(n);
  for (const int i : rep(n)) {
    scan(a[i], b[i]);
  }

  std::vector<std::pair<int, int>> ans_pre;
  {
    const auto var = [n](auto a, auto b, int i, int j) -> double {
      const i64 na = (a[i] + a[j]) / 2;
      const i64 nb = (b[i] + b[j]) / 2;
      a[i] = a[j] = na;
      b[i] = b[j] = nb;
      double mu = 0;
      double mu2 = 0;
      for (const i64 e : a) {
        const double d = static_cast<double>(e);
        mu += d;
        mu2 += d * d;
      }
      for (const i64 e : b) {
        const double d = static_cast<double>(e);
        mu += d;
        mu2 += d * d;
      }
      mu /= n * 2;
      mu2 /= n * 2;
      return mu2 - mu * mu;
    };
    for (int _ = 6; _--;) {
      const auto [i, j] = [&] {
        double min = inf<double>();
        std::pair<int, int> ret;
        for (const int j : rep(n)) {
          for (const int i : rep(j)) {
            if (chmin(min, var(a, b, i, j))) {
              ret = {i, j};
            }
          }
        }
        return ret;
      }();
      const i64 na = (a[i] + a[j]) / 2;
      const i64 nb = (b[i] + b[j]) / 2;
      a[i] = a[j] = na;
      b[i] = b[j] = nb;
      ans_pre.emplace_back(i, j);
    }
  }

  std::vector<int> p(n);
  std::iota(p.begin(), p.end(), 0);

  const auto evaluate = [&] {
    constexpr i64 H = 500'000'000'000'000'000;
    i64 x = a[p.back()];
    i64 y = b[p.back()];
    for (const int i : p | views::reverse | views::drop(1)) {
      x = (x + a[i]) / 2;
      y = (y + b[i]) / 2;
    }
    return std::max(std::abs(x - H), std::abs(y - H));
  };

  i64 cur = evaluate();
  i64 best = cur;
  auto ans = p;
  for (const auto& sa : Sa<256>(7 << 20, 1e17, 0.01)) {
    int i, j;
    do {
      i = randint(0, len(p) - 1);
      j = randint(0, len(p) - 1);
    } while (i == j);
    std::swap(p[i], p[j]);
    const i64 nxt = evaluate();
    if (cur + static_cast<i64>(sa.tol) < nxt) {
      std::swap(p[i], p[j]);
    } else {
      cur = nxt;
      if (chmin(best, cur)) {
        ans = p;
      }
    }
  }

  print(len(ans_pre) + (len(ans) - 1));
  for (const auto& [i, j] : ans_pre) {
    print(i + 1, j + 1);
  }
  int min_i = ans.back();
  for (const int i : ans | views::reverse | views::drop(1)) {
    print(min_i + 1, i + 1);
    chmin(min_i, i);
  }
}

}  // namespace

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  std::cout << std::setprecision(DBL_DECIMAL_DIG);

  solve();
}

#else  // __INCLUDE_LEVEL__

#include <bits/stdc++.h>

namespace xorshift {

using u64 = std::uint64_t;
using u128 = ::__uint128_t;

inline u64 x = std::chrono::steady_clock::now().time_since_epoch().count();

inline u64 next() {
  x ^= x << 7;
  x ^= x >> 9;
  return x;
}

int randint(int a, int b) {
  const u64 m = static_cast<u64>(b) - static_cast<u64>(a) + 1;
  return a + static_cast<int>(u128{next()} * m >> 64);
}

template <std::ranges::random_access_range R>
void shuffle(R&& r) {
  const int n = static_cast<int>(std::ranges::size(r));
  if (n < 2) {
    return;
  }
  for (const int i : std::views::iota(1, n)) {
    if (const int j = randint(0, i); j < i) {
      std::ranges::swap(r[i], r[j]);
    }
  }
}

double uniform() { return static_cast<double>(next()) / static_cast<double>(UINT64_MAX); }
double uniform(double a, double b) { return a + (b - a) * uniform(); }

}  // namespace xorshift

using xorshift::randint;
using xorshift::shuffle;
using xorshift::uniform;

template <int UpdateInterval = 1>
class Sa {
 public:
  explicit Sa(std::int64_t n_iters, double start_temp = 0, double end_temp = 0)
      : n_iters_(n_iters),
        start_temp_(start_temp),
        cooling_rate_(start_temp ? end_temp / start_temp : 1),
        iter_(0),
        elapsed_(0),
        temp_(start_temp) {
    assert(0 <= end_temp && end_temp <= start_temp);
  }

  Sa begin() const { return *this; }
  int end() const { return 0; }

  bool operator!=(int) const { return iter_ < n_iters_; }

  void operator++() {
    if (++iter_ % UpdateInterval == 0) {
      elapsed_ = static_cast<double>(iter_) / static_cast<double>(n_iters_);
      temp_ = start_temp_ * std::pow(cooling_rate_, elapsed_);
    }
  }

  auto operator*() const {
    struct {
      std::int64_t iter;
      double elapsed;
      double temp;
      double tol;
    } sa{iter_, elapsed_, temp_, temp_ * -std::log(uniform())};
    return sa;
  }

 private:
  std::int64_t n_iters_;
  double start_temp_;
  double cooling_rate_;
  std::int64_t iter_;
  double elapsed_;
  double temp_;
};

template <class T, class U = T>
bool chmin(T& x, U&& y) {
  return y < x && (x = std::forward<U>(y), true);
}

template <class T, class U = T>
bool chmax(T& x, U&& y) {
  return x < y && (x = std::forward<U>(y), true);
}

template <std::signed_integral T = int>
T inf() {
  T ret;
  std::memset(&ret, 0x3f, sizeof(ret));
  return ret;
}

template <std::floating_point T>
T inf() {
  return std::numeric_limits<T>::infinity();
}

template <class T>
concept Range = std::ranges::range<T> && !std::convertible_to<T, std::string_view>;

template <class T>
concept Tuple = std::__is_tuple_like<T>::value && !Range<T>;

namespace std {

istream& operator>>(istream& is, Range auto&& r) {
  for (auto&& e : r) {
    is >> e;
  }
  return is;
}

istream& operator>>(istream& is, Tuple auto&& t) {
  return apply([&](auto&... xs) -> istream& { return (is >> ... >> xs); }, t);
}

ostream& operator<<(ostream& os, Range auto&& r) {
  for (string_view sep = ""; auto&& e : r) {
    os << exchange(sep, " ") << e;
  }
  return os;
}

ostream& operator<<(ostream& os, Tuple auto&& t) {
  const auto f = [&](auto&... xs) -> ostream& {
    [[maybe_unused]] string_view sep = "";
    ((os << exchange(sep, " ") << xs), ...);
    return os;
  };
  return apply(f, t);
}

}  // namespace std

void scan(auto&&... xs) { std::cin >> std::tie(xs...); }
void print(auto&&... xs) { std::cout << std::tie(xs...) << '\n'; }

template <class F>
class fix {
 public:
  explicit fix(F f) : f_(std::move(f)) {}

  decltype(auto) operator()(auto&&... xs) const {
    return f_(std::ref(*this), std::forward<decltype(xs)>(xs)...);
  }

 private:
  F f_;
};

inline auto rep(int l, int r) { return std::views::iota(std::min(l, r), r); }
inline auto rep(int n) { return rep(0, n); }
inline auto rep1(int l, int r) { return rep(l, r + 1); }
inline auto rep1(int n) { return rep(1, n + 1); }

namespace ranges = std::ranges;
namespace views = std::views;

using i64 = std::int64_t;

#define len(...) static_cast<int>(ranges::size(__VA_ARGS__))

#endif  // __INCLUDE_LEVEL__