



"""simple docstring"""
from __future__ import annotations

from collections.abc import Iterable
class    a		:



  def __init__(  self	:   List[Any]    ,						lowerCAmelCase	:   int    ,						lowerCAmelCase	:   Tuple						)       ->   Optional[Any]:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_     ,						SCREAMING_SNAKE_CASE_:	Optional[int]            =float(lowerCAmelCase						), float(lowerCAmelCase						)



  def __eq__(  self	:   str    ,						lowerCAmelCase	:   List[Any]						)       ->   Optional[Any]:


     '''simple docstring'''




     return self.x == other.x and self.y == other.y



  def __ne__(  self	:   Any    ,						lowerCAmelCase	:   Optional[Any]						)       ->   int:


     '''simple docstring'''




     return not self == other



  def __gt__(  self	:   str    ,						lowerCAmelCase	:   List[str]						)       ->   Union[str, Any]:


     '''simple docstring'''




     if self.x > other.x:
        return True
     elif self.x == other.x:
        return self.y > other.y
     return False



  def __lt__(  self	:   Optional[int]    ,						lowerCAmelCase	:   Tuple						)       ->   Any:


     '''simple docstring'''




     return not self > other



  def __ge__(  self	:   List[str]    ,						lowerCAmelCase	:   Any						)       ->   Union[str, Any]:


     '''simple docstring'''




     if self.x > other.x:
        return True
     elif self.x == other.x:
        return self.y >= other.y
     return False



  def __le__(  self	:   Tuple    ,						lowerCAmelCase	:   Dict						)       ->   Dict:


     '''simple docstring'''




     if self.x < other.x:
        return True
     elif self.x == other.x:
        return self.y <= other.y
     return False



  def __repr__(  self	:   Tuple						)       ->   str:


     '''simple docstring'''




     return f'''({self.x}, {self.y})'''





  def __hash__(  self	:   List[str]						)       ->   int:


     '''simple docstring'''




     return hash(self.x						)







def        __magic_name__			(							lowercase							,     ):
   SCREAMING_SNAKE_CASE_:	list[Point]            =[]
   if list_of_tuples:
      for p in list_of_tuples:
         if isinstance(lowercase							,     lowercase	):
            points.append(lowercase	)
         else:
            try:
               points.append(Point(p[0]							,     p[1]	)	)
            except (IndexError, TypeError):
               print(
                   f'''Ignoring deformed point {p}. All points'''
                   """ must have at least 2 coordinates."""	)
   return points





def        __magic_name__			(							lowercase	):

   if not hasattr(lowercase							,     """__iter__"""	):
      SCREAMING_SNAKE_CASE_:	str            =f'''Expecting an iterable object but got an non-iterable type {points}'''
      raise ValueError(lowercase	)

   if not points:
      SCREAMING_SNAKE_CASE_:	Tuple            =f'''Expecting a list of points but got {points}'''
      raise ValueError(lowercase	)

   return _construct_points(lowercase	)





def        __magic_name__			(							lowercase							,     lowercase							,     lowercase	):
   SCREAMING_SNAKE_CASE_:	List[Any]            =(a.x * b.y + b.x * c.y + c.x * a.y) - (a.y * b.x + b.y * c.x + c.y * a.x)
   return det





def        __magic_name__			(							lowercase	):
   SCREAMING_SNAKE_CASE_:	Optional[Any]            =sorted(_validate_input(lowercase	)	)
   SCREAMING_SNAKE_CASE_:	str            =len(lowercase	)
   SCREAMING_SNAKE_CASE_:	int            =set()

   for i in range(n - 1	):
      for j in range(i + 1							,     lowercase	):
         SCREAMING_SNAKE_CASE_:	Optional[int]            =False
         SCREAMING_SNAKE_CASE_:	Any            =True
         for k in range(lowercase	):
            if k != i and k != j:
               SCREAMING_SNAKE_CASE_:	Tuple            =_det(points[i]							,     points[j]							,     points[k]	)

               if det_k > 0:
                  SCREAMING_SNAKE_CASE_:	List[Any]            =True
               elif det_k < 0:
                  SCREAMING_SNAKE_CASE_:	int            =True
               else:
                  # point[i], point[j], point[k] all lie on a straight line
                  # if point[k] is to the left of point[i] or it's to the
                  # right of point[j], then point[i], point[j] cannot be
                  # part of the convex hull of A
                  if points[k] < points[i] or points[k] > points[j]:
                     SCREAMING_SNAKE_CASE_:	Any            =False
                     break

            if points_left_of_ij and points_right_of_ij:
               SCREAMING_SNAKE_CASE_:	List[str]            =False
               break

         if ij_part_of_convex_hull:
            convex_set.update([points[i], points[j]]	)

   return sorted(lowercase	)





def        __magic_name__			(							lowercase	):
   SCREAMING_SNAKE_CASE_:	List[str]            =sorted(_validate_input(lowercase	)	)
   SCREAMING_SNAKE_CASE_:	Dict            =len(lowercase	)

   # divide all the points into an upper hull and a lower hull
   # the left most point and the right most point are definitely
   # members of the convex hull by definition.
   # use these two anchors to divide all the points into two hulls,
   # an upper hull and a lower hull.

   # all points to the left (above) the line joining the extreme points belong to the
   # upper hull
   # all points to the right (below) the line joining the extreme points below to the
   # lower hull
   # ignore all points on the line joining the extreme points since they cannot be
   # part of the convex hull

   SCREAMING_SNAKE_CASE_:	List[str]            =points[0]
   SCREAMING_SNAKE_CASE_:	int            =points[n - 1]

   SCREAMING_SNAKE_CASE_:	Union[str, Any]            ={left_most_point, right_most_point}
   SCREAMING_SNAKE_CASE_:	Optional[Any]            =[]
   SCREAMING_SNAKE_CASE_:	List[Any]            =[]

   for i in range(1							,     n - 1	):
      SCREAMING_SNAKE_CASE_:	List[Any]            =_det(lowercase							,     lowercase							,     points[i]	)

      if det > 0:
         upper_hull.append(points[i]	)
      elif det < 0:
         lower_hull.append(points[i]	)

   _construct_hull(lowercase							,     lowercase							,     lowercase							,     lowercase	)
   _construct_hull(lowercase							,     lowercase							,     lowercase							,     lowercase	)

   return sorted(lowercase	)





def        __magic_name__			(							lowercase							,     lowercase							,     lowercase							,     lowercase	):
   if points:
      SCREAMING_SNAKE_CASE_:	List[str]            =None
      SCREAMING_SNAKE_CASE_:	List[Any]            =float("""-inf"""	)
      SCREAMING_SNAKE_CASE_:	Dict            =[]

      for p in points:
         SCREAMING_SNAKE_CASE_:	Dict            =_det(lowercase							,     lowercase							,     lowercase	)

         if det > 0:
            candidate_points.append(lowercase	)

            if det > extreme_point_distance:
               SCREAMING_SNAKE_CASE_:	List[str]            =det
               SCREAMING_SNAKE_CASE_:	List[Any]            =p

      if extreme_point:
         _construct_hull(lowercase							,     lowercase							,     lowercase							,     lowercase	)
         convex_set.add(lowercase	)
         _construct_hull(lowercase							,     lowercase							,     lowercase							,     lowercase	)





def        __magic_name__			(							lowercase	):
   SCREAMING_SNAKE_CASE_:	Optional[int]            =sorted(_validate_input(lowercase	)	)
   SCREAMING_SNAKE_CASE_:	str            =len(lowercase	)

   SCREAMING_SNAKE_CASE_:	List[str]            =points[:2]
   for i in range(2							,     lowercase	):
      SCREAMING_SNAKE_CASE_:	List[str]            =_det(convex_hull[1]							,     convex_hull[0]							,     points[i]	)
      if det > 0:
         convex_hull.insert(0							,     points[i]	)
         break
      elif det < 0:
         convex_hull.append(points[i]	)
         break
      else:
         SCREAMING_SNAKE_CASE_:	int            =points[i]
   i += 1

   for j in range(lowercase							,     lowercase	):
      if (
          _det(convex_hull[0]							,     convex_hull[-1]							,     points[j]	) > 0
          and _det(convex_hull[-1]							,     convex_hull[0]							,     points[1]	) < 0
      ):
         # The point lies within the convex hull
         continue

      convex_hull.insert(0							,     points[j]	)
      convex_hull.append(points[j]	)
      while _det(convex_hull[0]							,     convex_hull[1]							,     convex_hull[2]	) >= 0:
         del convex_hull[1]
      while _det(convex_hull[-1]							,     convex_hull[-2]							,     convex_hull[-3]	) <= 0:
         del convex_hull[-2]

    # `convex_hull` is contains the convex hull in circular order
   return sorted(convex_hull[1:] if len(lowercase	) > 3 else convex_hull	)





def        __magic_name__			(							):
   SCREAMING_SNAKE_CASE_:	str            =[
       (0, 3),
       (2, 2),
       (1, 1),
       (2, 1),
       (3, 0),
       (0, 0),
       (3, 3),
       (2, -1),
       (2, -4),
       (1, -3),
   ]
   # the convex set of points is
   # [(0, 0), (0, 3), (1, -3), (2, -4), (3, 0), (3, 3)]
   SCREAMING_SNAKE_CASE_:	Tuple            =convex_hull_bf(lowercase	)

   SCREAMING_SNAKE_CASE_:	Any            =convex_hull_recursive(lowercase	)
   assert results_bf == results_recursive

   SCREAMING_SNAKE_CASE_:	Optional[int]            =convex_hull_melkman(lowercase	)
   assert results_bf == results_melkman

   print(lowercase	)


if __name__ == "__main__":
   main()








"""simple docstring"""
from __future__ import annotations

import sys
class    a		:



  def __init__(  self	:   Optional[Any]    ,						lowerCAmelCase	:   str    ,						lowerCAmelCase	:   int						)       ->   List[str]:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_:	str            =letter
     SCREAMING_SNAKE_CASE_:	int            =freq
     SCREAMING_SNAKE_CASE_:	dict[str, str]            ={}





  def __repr__(  self	:   Optional[Any]						)       ->   str:


     '''simple docstring'''




     return f'''{self.letter}:{self.freq}'''







class    a		:



  def __init__(  self	:   Optional[Any]    ,						lowerCAmelCase	:   int    ,						lowerCAmelCase	:   Letter | TreeNode    ,						lowerCAmelCase	:   Letter | TreeNode						)       ->   List[Any]:


     '''simple docstring'''




     SCREAMING_SNAKE_CASE_:	int            =freq
     SCREAMING_SNAKE_CASE_:	Letter | TreeNode            =left
     SCREAMING_SNAKE_CASE_:	Letter | TreeNode            =right







def        __magic_name__			(							lowercase	):
   SCREAMING_SNAKE_CASE_:	dict[str, int]            ={}
   with open(lowercase	) as f:
      while True:
         SCREAMING_SNAKE_CASE_:	List[Any]            =f.read(1	)
         if not c:
            break
         SCREAMING_SNAKE_CASE_:	Any            =chars[c] + 1 if c in chars else 1
   return sorted((Letter(lowercase							,     lowercase	) for c, f in chars.items())							,     key=lambda lowercase	: x.freq	)





def        __magic_name__			(							lowercase	):
   SCREAMING_SNAKE_CASE_:	list[Letter | TreeNode]            =letters  # type: ignore
   while len(lowercase	) > 1:
      SCREAMING_SNAKE_CASE_:	Any            =response.pop(0	)
      SCREAMING_SNAKE_CASE_:	List[Any]            =response.pop(0	)
      SCREAMING_SNAKE_CASE_:	List[Any]            =left.freq + right.freq
      SCREAMING_SNAKE_CASE_:	Any            =TreeNode(lowercase							,     lowercase							,     lowercase	)
      response.append(lowercase	)
      response.sort(key=lambda lowercase	: x.freq	)
   return response[0]





def        __magic_name__			(							lowercase							,     lowercase	):
   if isinstance(lowercase							,     lowercase	):
      SCREAMING_SNAKE_CASE_:	Optional[Any]            =bitstring
      return [root]
   SCREAMING_SNAKE_CASE_:	TreeNode            =root  # type: ignore
   SCREAMING_SNAKE_CASE_:	Union[str, Any]            =[]
   letters += traverse_tree(treenode.left							,     bitstring + """0"""	)
   letters += traverse_tree(treenode.right							,     bitstring + """1"""	)
   return letters





def        __magic_name__			(							lowercase	):
   SCREAMING_SNAKE_CASE_:	Union[str, Any]            =parse_file(lowercase	)
   SCREAMING_SNAKE_CASE_:	str            =build_tree(lowercase	)
   SCREAMING_SNAKE_CASE_:	List[Any]            ={
       k: v for letter in traverse_tree(lowercase							,     """"""	) for k, v in letter.bitstring.items()
   }
   print(f'''Huffman Coding  of {file_path}: '''	)
   with open(lowercase	) as f:
      while True:
         SCREAMING_SNAKE_CASE_:	Any            =f.read(1	)
         if not c:
            break
         print(letters[c]							,     end=""" """	)
   print()


if __name__ == "__main__":
   # pass the file path to the huffman function
   huffman(sys.argv[1])



