Language: C++

#include <bits/stdc++.h>
#define PB push_back
#define MP make_pair
#define F first
#define S second
#define SZ(x) ((int)(x).size())
#define ALL(x) (x).begin(),(x).end()
#ifdef _DEBUG_
  #define debug(...) printf(__VA_ARGS__)
#else
  #define debug(...) (void)0
#endif
using namespace std;
typedef long long ll;
typedef pair<int,int> PII;
typedef vector<int> VI;


const double EPS = 1e-10;
const double PI = acos(-1.0);

struct PT {
  ll x, y;
  int id;
  PT() {}
  PT(ll x_, ll y_): x(x_), y(y_), id(-1) {}
  ll len2() const {
    return x * x + y * y;
  }
  double len() const {
    return sqrt(len2());
  }
  PT operator - (const PT &b) const {
    return PT(x - b.x, y - b.y);
  }
  ll operator * (const PT &b) const {
    return x * b.x + y * b.y;
  }
  ll operator % (const PT &b) const {
    return x * b.y - y * b.x;
  }
  bool operator < (const PT &b) const {
    return tie(x, y) < tie(b.x, b.y);
  }
};

const int MAXN = 123;
PT in[MAXN];
double ans[MAXN];

int main() {
  int N;
  scanf("%d", &N);
  for (int i = 0; i < N; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    in[i].x = x;
    in[i].y = y;
    in[i].id = i;
  }
  sort(in, in + N);
  vector<PT> st, st2;;
  for (int i = 0; i < N; i++) {
    while (SZ(st) >= 2 && (st[SZ(st) - 1] - st[SZ(st) - 2]) % (in[i] - st[SZ(st) - 1]) <= 0)
      st.pop_back();
    st.PB(in[i]);
  }
  for (int i = N - 1; i >= 0; i--) {
    while (SZ(st2) >= 2 && (st2[SZ(st2) - 1] - st2[SZ(st2) - 2]) % (in[i] - st2[SZ(st2) - 1]) <= 0)
      st2.pop_back();
    st2.PB(in[i]);
  }
  st.pop_back();
  for (const auto &p : st2)
    st.PB(p);
  for (int i = 0; i < N; i++)
    ans[i] = 0;
  debug("SZ %d\n", SZ(st));
  st.PB(st[1]);
  debug("!\n");
  assert(SZ(st) == 4);
  assert(st[0] == st[2]);
  assert(st[1] == st[3]);
  for (int i = 1; i < SZ(st) - 1; i++) {
    debug("i = %d\n", i);
    PT A = st[i - 1] - st[i];
    PT B = st[i + 1] - st[i];
    debug("%f %f\n", A.len(), B.len());
    assert(B.len() > 0.5);
    double tmp = A * B / (A.len() * B.len());
    debug("! %d %f\n", i, tmp);
    double ang = PI - acos(tmp);
    ans[st[i].id] = ang / (2 * PI);
    double ori = ang / (2 * PI);
//    assert(fabs(ori - 0.5) < 1e-2);
    ans[st[i].id] = 0.5;
  }
  finish:
  for (int i = 0; i < N; i++)
    printf("%.10f\n", ans[i]);
//  double sum = 0;
//  for (int i = 0; i < N; i++)
//    sum += ans[i];
//  assert(fabs(sum - 1.0) < EPS);
  return 0;
}


Compiler output:
In file included from /usr/include/c++/14/cassert:44,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:106,
                 from a.cc:1:
a.cc: In function 'int main()':
a.cc:82:16: error: no match for 'operator==' (operand types are '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'} and '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'})
   82 |   assert(st[0] == st[2]);
In file included from /usr/include/c++/14/regex:68,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:181:
/usr/include/c++/14/bits/regex.h:1103:5: note: candidate: 'template<class _BiIter> bool std::__cxx11::operator==(const sub_match<_BiIter>&, const sub_match<_BiIter>&)'
 1103 |     operator==(const sub_match<_BiIter>& __lhs, const sub_match<_BiIter>& __rhs)
      |     ^~~~~~~~
/usr/include/c++/14/bits/regex.h:1103:5: note:   template argument deduction/substitution failed:
a.cc:82:23: note:   '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'} is not derived from 'const std::__cxx11::sub_match<_BiIter>'
   82 |   assert(st[0] == st[2]);
      |                       ^
/usr/include/c++/14/bits/regex.h:1199:5: note: candidate: 'template<class _Bi_iter, class _Ch_traits, class _Ch_alloc> bool std::__cxx11::operator==(__sub_match_string<_Bi_iter, _Ch_traits, _Ch_alloc>&, const sub_match<_BiIter>&)'
 1199 |     operator==(const __sub_match_string<_Bi_iter, _Ch_traits, _Ch_alloc>& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/regex.h:1199:5: note:   template argument deduction/substitution failed:
a.cc:82:23: note:   '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'} is not derived from 'std::__cxx11::__sub_match_string<_Bi_iter, _Ch_traits, _Ch_alloc>'
   82 |   assert(st[0] == st[2]);
      |                       ^
/usr/include/c++/14/bits/regex.h:1274:5: note: candidate: 'template<class _Bi_iter, class _Ch_traits, class _Ch_alloc> bool std::__cxx11::operator==(const sub_match<_BiIter>&, __sub_match_string<_Bi_iter, _Ch_traits, _Ch_alloc>&)'
 1274 |     operator==(const sub_match<_Bi_iter>& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/regex.h:1274:5: note:   template argument deduction/substitution failed:
a.cc:82:23: note:   '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'} is not derived from 'const std::__cxx11::sub_match<_BiIter>'
   82 |   assert(st[0] == st[2]);
      |                       ^
/usr/include/c++/14/bits/regex.h:1366:5: note: candidate: 'template<class _Bi_iter> bool std::__cxx11::operator==(const typename std::iterator_traits<_Iter>::value_type*, const sub_match<_BiIter>&)'
 1366 |     operator==(typename iterator_traits<_Bi_iter>::value_type const* __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/regex.h:1366:5: note:   template argument deduction/substitution failed:
a.cc:82:23: note:   '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'} is not derived from 'const std::__cxx11::sub_match<_BiIter>'
   82 |   assert(st[0] == st[2]);
      |                       ^
/usr/include/c++/14/bits/regex.h:1441:5: note: candidate: 'template<class _Bi_iter> bool std::__cxx11::operator==(const sub_match<_BiIter>&, const typename std::iterator_traits<_Iter>::value_type*)'
 1441 |     operator==(const sub_match<_Bi_iter>& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/regex.h:1441:5: note:   template argument deduction/substitution failed:
a.cc:82:23: note:   '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'} is not derived from 'const std::__cxx11::sub_match<_BiIter>'
   82 |   assert(st[0] == st[2]);
      |                       ^
/usr/include/c++/14/bits/regex.h:1534:5: note: candidate: 'template<class _Bi_iter> bool std::__cxx11::operator==(const typename std::iterator_traits<_Iter>::value_type&, const sub_match<_BiIter>&)'
 1534 |     operator==(typename iterator_traits<_Bi_iter>::value_type const& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/regex.h:1534:5: note:   template argument deduction/substitution failed:
a.cc:82:23: note:   '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'} is not derived from 'const std::__cxx11::sub_match<_BiIter>'
   82 |   assert(st[0] == st[2]);
      |                       ^
/usr/include/c++/14/bits/regex.h:1613:5: note: candidate: 'template<class _Bi_iter> bool std::__cxx11::operator==(const sub_match<_BiIter>&, const typename std::iterator_traits<_Iter>::value_type&)'
 1613 |     operator==(const sub_match<_Bi_iter>& __lhs,
      |     ^~~~~~~~
/usr/include/c++/14/bits/regex.h:1613:5: note:   template argument deduction/substitution failed:
a.cc:82:23: note:   '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'} is not derived from 'const std::__cxx11::sub_match<_BiIter>'
   82 |   assert(st[0] == st[2]);
      |                       ^
/usr/include/c++/14/bits/regex.h:2186:5: note: candidate: 'template<class _Bi_iter, class _Alloc> bool std::__cxx11::operator==(const match_results<_BiIter, _Alloc>&, const match_results<_BiIter, _Alloc>&)'
 2186 |     operator==(const match_results<_Bi_iter, _Alloc>& __m1,
      |     ^~~~~~~~
/usr/include/c++/14/bits/regex.h:2186:5: note:   template argument deduction/substitution failed:
a.cc:82:23: note:   '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'} is not derived from 'const std::__cxx11::match_results<_BiIter, _Alloc>'
   82 |   assert(st[0] == st[2]);
      |                       ^
In file included from /usr/include/c++/14/bits/stl_algobase.h:64,
                 from /usr/include/c++/14/algorithm:60,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:51:
/usr/include/c++/14/bits/stl_pair.h:1033:5: note: candidate: 'template<class _T1, class _T2> constexpr bool std::operator==(const pair<_T1, _T2>&, const pair<_T1, _T2>&)'
 1033 |     operator==(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_pair.h:1033:5: note:   template argument deduction/substitution failed:
a.cc:82:23: note:   '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'} is not derived from 'const std::pair<_T1, _T2>'
   82 |   assert(st[0] == st[2]);
      |                       ^
In file included from /usr/include/c++/14/bits/stl_algobase.h:67:
/usr/include/c++/14/bits/stl_iterator.h:441:5: note: candidate: 'template<class _Iterator> constexpr bool std::operator==(const reverse_iterator<_Iterator>&, const reverse_iterator<_Iterator>&)'
  441 |     operator==(const reverse_iterator<_Iterator>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:441:5: note:   template argument deduction/substitution failed:
a.cc:82:23: note:   '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'} is not derived from 'const std::reverse_iterator<_Iterator>'
   82 |   assert(st[0] == st[2]);
      |                       ^
/usr/include/c++/14/bits/stl_iterator.h:486:5: note: candidate: 'template<class _IteratorL, class _IteratorR> constexpr bool std::operator==(const reverse_iterator<_Iterator>&, const reverse_iterator<_IteratorR>&)'
  486 |     operator==(const reverse_iterator<_IteratorL>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:486:5: note:   template argument deduction/substitution failed:
a.cc:82:23: note:   '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'} is not derived from 'const std::reverse_iterator<_Iterator>'
   82 |   assert(st[0] == st[2]);
      |                       ^
/usr/include/c++/14/bits/stl_iterator.h:1667:5: note: candidate: 'template<class _IteratorL, class _IteratorR> constexpr bool std::operator==(const move_iterator<_IteratorL>&, const move_iterator<_IteratorR>&)'
 1667 |     operator==(const move_iterator<_IteratorL>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1667:5: note:   template argument deduction/substitution failed:
a.cc:82:23: note:   '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'} is not derived from 'const std::move_iterator<_IteratorL>'
   82 |   assert(st[0] == st[2]);
      |                       ^
/usr/include/c++/14/bits/stl_iterator.h:1737:5: note: candidate: 'template<class _Iterator> constexpr bool std::operator==(const move_iterator<_IteratorL>&, const move_iterator<_IteratorL>&)'
 1737 |     operator==(const move_iterator<_Iterator>& __x,
      |     ^~~~~~~~
/usr/include/c++/14/bits/stl_iterator.h:1737:5: note:   template argument deduction/substitution failed:
a.cc:82:23: note:   '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'} is not derived from 'const std::move_iterator<_IteratorL>'
   82 |   assert(st[0] == st[2]);
      |                       ^
In file included from /usr/include/c++/14/bits/char_traits.h:42,
                 from /usr/include/c++/14/string:42,
                 from /usr/include/c++/14/bitset:52,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:52:
/usr/include/c++/14/bits/postypes.h:192:5: note: candidate: 'template<class _StateT> bool std::operator==(const fpos<_StateT>&, const fpos<_StateT>&)'
  192 |     operator==(const fpos<_StateT>& __lhs, const fpos<_StateT>& __rhs)
      |     ^~~~~~~~
/usr/include/c++/14/bits/postypes.h:192:5: note:   template argument deduction/substitution failed:
a.cc:82:23: note:   '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'} is not derived from 'const std::fpos<_StateT>'
   82 |   assert(st[0] == st[2]);
      |                       ^
In file included from /usr/include/c++/14/string:43:
/usr/include/c++/14/bits/allocator.h:235:5: note: candidate: 'template<class _T1, class _T2> bool std::operator==(const allocator<_CharT>&, const allocator<_T2>&)'
  235 |     operator==(const allocator<_T1>&, const allocator<_T2>&)
      |     ^~~~~~~~
/usr/include/c++/14/bits/allocator.h:235:5: note:   template argument deduction/substitution failed:
a.cc:82:23: note:   '__gnu_cxx::__alloc_traits<std::allocator<PT>, PT>::value_type' {aka 'PT'} is not derived from 'const std::allocator<_CharT>'
   82 |   assert(st[0] == s