Problem p03004 (C++)

Buggy submission (status: Time Limit Exceeded):
/*** Template Begin ***/

#pragma region template

#define USING_NAMESPACE

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

typedef int64_t i64;
typedef uint64_t u64;

auto init_ = [] {
  std::ios_base::sync_with_stdio(false);
  std::cout << std::fixed;
  return 0;
}();

template <typename T> inline void in(T &x) { std::cin >> x; }

template <typename T, typename... Ts> inline void in(T &t, Ts &...ts) {
  std::cin >> t;
  in(ts...);
}

template <typename T, typename U = std::vector<T>> inline U vin(int n) {
  U v(n);
  for (int i = 0; i < n; ++i) {
    std::cin >> v[i];
  }
  return v;
}

template <typename T, typename U = std::vector<T>, typename V = std::vector<U>>
inline V vin(int h, int w) {
  V vv(h, U(w));
  for (int i = 0; i < h; ++i) {
    for (int j = 0; j < w; ++j) {
      std::cin >> vv[i][j];
    }
  }
  return vv;
}

template <typename T> inline void out(const T &x) {
  std::cout << x << std::endl;
}

template <char delimiter = ' ', typename T, typename... Ts>
inline void out(const T &t, const Ts &...ts) {
  std::cout << t << delimiter;
  out(ts...);
}

template <char delimiter = ' ', typename T>
inline void vout(const T &v, int n) {
  for (int i = 0; i < n; ++i) {
    if (i)
      std::cout << delimiter;
    std::cout << v[i];
  }
  std::cout << std::endl;
}

template <char delimiter = ' ', typename T>
inline void vout(const T &v, int h, int w) {
  for (int i = 0; i < h; ++i) {
    for (int j = 0; j < w; ++j) {
      if (j)
        std::cout << delimiter;
      std::cout << v[i][j];
    }
    std::cout << std::endl;
  }
}

template <typename T, size_t D> struct multi_vector_type {
  using type = std::vector<typename multi_vector_type<T, D - 1>::type>;
};

template <typename T> struct multi_vector_type<T, 1> {
  using type = std::vector<T>;
};

template <typename T> struct multi_vector_type<T, 0> {
  using type = T;
};

template <typename T, size_t D>
using multi_vector = typename multi_vector_type<T, D>::type;

template <typename T, size_t D, class = typename std::enable_if<D == 0>::type>
T make_vector(const T &val = T()) {
  return val;
}

template <typename T, size_t D = 1, typename... Ts,
          class = typename std::enable_if<D != 0>::type>
multi_vector<T, D> make_vector(size_t n, Ts &&...args) {
  return multi_vector<T, D>(n, make_vector<T, D - 1>(args...));
}

namespace detail {

template <typename F> struct Debug {
  const char *delim_ = "\n";
  F fun;

  Debug(F f) : fun(f) {}

  ~Debug() { fun(delim_); }

  Debug &delim(const char *d) {
    delim_ = d;
    return *this;
  }
};

std::deque<std::string> split(const std::string &s, char c) {
  std::deque<std::string> v;
  std::stringstream ss(s);
  std::string x;
  while (std::getline(ss, x, c))
    v.emplace_back(x);
  return v;
}

template <typename T>
void deb(const char *delim, std::deque<std::string> v, T a) {
  std::cerr << v[0].substr(v[0][0] == ' ', v[0].length()) << " = " << a << '\n';
  std::cerr << std::flush;
}

template <typename T, typename... Args>
void deb(const char *delim, std::deque<std::string> v, T a, Args... args) {
  std::cerr << v[0].substr(v[0][0] == ' ', v[0].length()) << " = " << a
            << delim;
  v.pop_front();
  deb(delim, std::move(v), args...);
}

template <typename... Args> auto wrap(std::deque<std::string> v, Args... args) {
  auto f = [=](const char *delim = "\n") { deb(delim, v, args...); };

  return Debug<decltype(f)>(f);
}
} // namespace detail

#define debug(args...) ::detail::wrap(::detail::split(#args, ','), args)

#ifdef USING_BOOST

#include <boost/math/common_factor.hpp>
#include <boost/range.hpp>
#include <boost/range/adaptors.hpp>
#include <boost/range/algorithm.hpp>
#include <boost/range/algorithm_ext.hpp>
#include <boost/range/irange.hpp>
#include <boost/range/numeric.hpp>

inline auto rep(int begin, int end) {
  if (begin > end) {
    return boost::irange(0, 0);
  } else {
    return boost::irange(begin, end);
  }
}

inline auto rep(int begin, int end, int step) {
  if ((step > 0 && begin > end) || (step < 0 && begin < end)) {
    return boost::irange(0, 0, step);
  } else {
    return boost::irange(begin, end, step);
  }
}

#endif

#ifdef USING_NAMESPACE
using namespace std;

#ifdef USING_BOOST
using namespace boost;
using namespace boost::adaptors;
#endif
#endif

#pragma endregion

/*** Template End ***/

pair<long double, long double> move(long double x, long double y, char d,
                                    long double t) {
  if (d == 'R') {
    return {x + t, y};
  } else if (d == 'L') {
    return {x - t, y};
  } else if (d == 'U') {
    return {x, y + t};
  } else {
    return {x, y - t};
  }
}

long double area(vector<long double> &x, vector<long double> &y,
                 vector<char> &d, long double t) {
  int n = x.size();

  long double xmax, xmin, ymax, ymin;

  auto p = move(x[0], y[0], d[0], t);

  xmax = xmin = p.first;
  ymax = ymin = p.second;

  for (int i = 1; i < n; i++) {
    auto p = move(x[i], y[i], d[i], t);

    xmax = max(xmax, p.first);
    xmin = min(xmin, p.first);

    ymax = max(ymax, p.second);
    ymin = min(ymin, p.second);
  }

  return (xmax - xmin) * (ymax - ymin);
}

int main() {
  int n;
  in(n);

  vector<long double> x(n), y(n);
  vector<char> d(n);

  for (int i = 0; i < n; i++) {
    in(x[i], y[i], d[i]);
  }

  long double l = 0, r = 1e12;

  auto ans = min(area(x, y, d, 0), area(x, y, d, r));

  for (int i = 0; i < 2000; i++) {
    long double m1 = (r - l) / 3 + l;
    long double m2 = (r - l) * 2 / 3 + l;

    long double f1 = area(x, y, d, m1);
    long double f2 = area(x, y, d, m2);

    if (f1 < f2) {
      r = m2;
    } else {
      l = m1;
    }

    ans = min(ans, f1);
    ans = min(ans, f2);
  }

  out(ans);
}

Fixed submission:
/*** Template Begin ***/

#pragma region template

#define USING_NAMESPACE

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

typedef int64_t i64;
typedef uint64_t u64;

auto init_ = [] {
  std::ios_base::sync_with_stdio(false);
  std::cout << std::fixed;
  return 0;
}();

template <typename T> inline void in(T &x) { std::cin >> x; }

template <typename T, typename... Ts> inline void in(T &t, Ts &...ts) {
  std::cin >> t;
  in(ts...);
}

template <typename T, typename U = std::vector<T>> inline U vin(int n) {
  U v(n);
  for (int i = 0; i < n; ++i) {
    std::cin >> v[i];
  }
  return v;
}

template <typename T, typename U = std::vector<T>, typename V = std::vector<U>>
inline V vin(int h, int w) {
  V vv(h, U(w));
  for (int i = 0; i < h; ++i) {
    for (int j = 0; j < w; ++j) {
      std::cin >> vv[i][j];
    }
  }
  return vv;
}

template <typename T> inline void out(const T &x) {
  std::cout << x << std::endl;
}

template <char delimiter = ' ', typename T, typename... Ts>
inline void out(const T &t, const Ts &...ts) {
  std::cout << t << delimiter;
  out(ts...);
}

template <char delimiter = ' ', typename T>
inline void vout(const T &v, int n) {
  for (int i = 0; i < n; ++i) {
    if (i)
      std::cout << delimiter;
    std::cout << v[i];
  }
  std::cout << std::endl;
}

template <char delimiter = ' ', typename T>
inline void vout(const T &v, int h, int w) {
  for (int i = 0; i < h; ++i) {
    for (int j = 0; j < w; ++j) {
      if (j)
        std::cout << delimiter;
      std::cout << v[i][j];
    }
    std::cout << std::endl;
  }
}

template <typename T, size_t D> struct multi_vector_type {
  using type = std::vector<typename multi_vector_type<T, D - 1>::type>;
};

template <typename T> struct multi_vector_type<T, 1> {
  using type = std::vector<T>;
};

template <typename T> struct multi_vector_type<T, 0> {
  using type = T;
};

template <typename T, size_t D>
using multi_vector = typename multi_vector_type<T, D>::type;

template <typename T, size_t D, class = typename std::enable_if<D == 0>::type>
T make_vector(const T &val = T()) {
  return val;
}

template <typename T, size_t D = 1, typename... Ts,
          class = typename std::enable_if<D != 0>::type>
multi_vector<T, D> make_vector(size_t n, Ts &&...args) {
  return multi_vector<T, D>(n, make_vector<T, D - 1>(args...));
}

namespace detail {

template <typename F> struct Debug {
  const char *delim_ = "\n";
  F fun;

  Debug(F f) : fun(f) {}

  ~Debug() { fun(delim_); }

  Debug &delim(const char *d) {
    delim_ = d;
    return *this;
  }
};

std::deque<std::string> split(const std::string &s, char c) {
  std::deque<std::string> v;
  std::stringstream ss(s);
  std::string x;
  while (std::getline(ss, x, c))
    v.emplace_back(x);
  return v;
}

template <typename T>
void deb(const char *delim, std::deque<std::string> v, T a) {
  std::cerr << v[0].substr(v[0][0] == ' ', v[0].length()) << " = " << a << '\n';
  std::cerr << std::flush;
}

template <typename T, typename... Args>
void deb(const char *delim, std::deque<std::string> v, T a, Args... args) {
  std::cerr << v[0].substr(v[0][0] == ' ', v[0].length()) << " = " << a
            << delim;
  v.pop_front();
  deb(delim, std::move(v), args...);
}

template <typename... Args> auto wrap(std::deque<std::string> v, Args... args) {
  auto f = [=](const char *delim = "\n") { deb(delim, v, args...); };

  return Debug<decltype(f)>(f);
}
} // namespace detail

#define debug(args...) ::detail::wrap(::detail::split(#args, ','), args)

#ifdef USING_BOOST

#include <boost/math/common_factor.hpp>
#include <boost/range.hpp>
#include <boost/range/adaptors.hpp>
#include <boost/range/algorithm.hpp>
#include <boost/range/algorithm_ext.hpp>
#include <boost/range/irange.hpp>
#include <boost/range/numeric.hpp>

inline auto rep(int begin, int end) {
  if (begin > end) {
    return boost::irange(0, 0);
  } else {
    return boost::irange(begin, end);
  }
}

inline auto rep(int begin, int end, int step) {
  if ((step > 0 && begin > end) || (step < 0 && begin < end)) {
    return boost::irange(0, 0, step);
  } else {
    return boost::irange(begin, end, step);
  }
}

#endif

#ifdef USING_NAMESPACE
using namespace std;

#ifdef USING_BOOST
using namespace boost;
using namespace boost::adaptors;
#endif
#endif

#pragma endregion

/*** Template End ***/

pair<long double, long double> move(long double x, long double y, char d,
                                    long double t) {
  if (d == 'R') {
    return {x + t, y};
  } else if (d == 'L') {
    return {x - t, y};
  } else if (d == 'U') {
    return {x, y + t};
  } else {
    return {x, y - t};
  }
}

long double area(vector<long double> &x, vector<long double> &y,
                 vector<char> &d, long double t) {
  int n = x.size();

  long double xmax, xmin, ymax, ymin;

  auto p = move(x[0], y[0], d[0], t);

  xmax = xmin = p.first;
  ymax = ymin = p.second;

  for (int i = 1; i < n; i++) {
    auto p = move(x[i], y[i], d[i], t);

    xmax = max(xmax, p.first);
    xmin = min(xmin, p.first);

    ymax = max(ymax, p.second);
    ymin = min(ymin, p.second);
  }

  return (xmax - xmin) * (ymax - ymin);
}

int main() {
  int n;
  in(n);

  vector<long double> x(n), y(n);
  vector<char> d(n);

  for (int i = 0; i < n; i++) {
    in(x[i], y[i], d[i]);
  }
  long double l = 0, r = 1e14;

  long double ans = min(area(x, y, d, l), area(x, y, d, r));

  for (int i = 0; i < 1000; i++) {
    long double m1 = (r - l) / 3 + l;
    long double m2 = (r - l) * 2 / 3 + l;

    long double f1 = area(x, y, d, m1);
    long double f2 = area(x, y, d, m2);

    if (f1 < f2) {
      r = m2;
    } else {
      l = m1;
    }

    ans = min(ans, f1);
    ans = min(ans, f2);
  }

  out(ans);
}