





from __future__ import annotations

from collections import deque
class        SCREAMING_SNAKE_CASE     :


   def __init__(					self    :       int    ,  a    :       Tuple )->     Tuple:





     """simple docstring"""







     lowercase__			    =						[]
     self.adlist.append(
         {'value': '', 'next_states': [], 'fail_state': 0, 'output': []} )

     for keyword in keywords:
       self.add_keyword(a )
     self.set_fail_transitions()


   def  SCREAMING_SNAKE_CASE_							(					self    :       List[Any]    ,  a    :       int    ,  a    :       List[str] )->     Union[str, Any]:





     """simple docstring"""







     for state in self.adlist[current_state]["next_states"]:
       if char == self.adlist[state]["value"]:
         return state
     return None


   def  SCREAMING_SNAKE_CASE_							(					self    :       str    ,  a    :       Union[str, Any] )->     Union[str, Any]:





     """simple docstring"""







     lowercase__			    =						0
     for character in keyword:
       lowercase__			    =						self.find_next_state(a    ,  a )
       if next_state is None:
         self.adlist.append(
             {
                 'value': character,
                 'next_states': [],
                 'fail_state': 0,
                 'output': [],
             } )
         self.adlist[current_state]["next_states"].append(len(self.adlist ) - 1 )
         lowercase__			    =						len(self.adlist ) - 1
       else:
         lowercase__			    =						next_state
     self.adlist[current_state]["output"].append(a )


   def  SCREAMING_SNAKE_CASE_							(					self    :       Optional[int] )->     int:





     """simple docstring"""







     lowercase__			    =						deque()
     for node in self.adlist[0]["next_states"]:
       q.append(a )
       lowercase__			    =						0
     while q:
       lowercase__			    =						q.popleft()
       for child in self.adlist[r]["next_states"]:
         q.append(a )
         lowercase__			    =						self.adlist[r]["""fail_state"""]
         while (
             self.find_next_state(a    ,  self.adlist[child]['value'] ) is None
             and state != 0
         ):
           lowercase__			    =						self.adlist[state]["""fail_state"""]
         lowercase__			    =						self.find_next_state(
             a    ,  self.adlist[child]['value'] )
         if self.adlist[child]["fail_state"] is None:
           lowercase__			    =						0
         lowercase__			    =						(
             self.adlist[child]["""output"""]
             + self.adlist[self.adlist[child]["""fail_state"""]]["""output"""]
         )


   def  SCREAMING_SNAKE_CASE_							(					self    :       List[str]    ,  a    :       Dict )->     Optional[Any]:





     """simple docstring"""







     lowercase__			    =						{}  # returns a dict with keywords and list of its occurrences
     lowercase__			    =						0
     for i in range(len(a ) ):
       while (
           self.find_next_state(a    ,  string[i] ) is None
           and current_state != 0
       ):
         lowercase__			    =						self.adlist[current_state]["""fail_state"""]
       lowercase__			    =						self.find_next_state(a    ,  string[i] )
       if next_state is None:
         lowercase__			    =						0
       else:
         lowercase__			    =						next_state
         for key in self.adlist[current_state]["output"]:
           if key not in result:
             lowercase__			    =						[]
           result[key].append(i - len(a ) + 1 )
     return result


if __name__ == "__main__":
      import doctest

      doctest.testmod()










from __future__ import annotations

import math
from collections.abc import Callable




def     __UpperCamelCase						(_SCREAMING_SNAKE_CASE	,		_SCREAMING_SNAKE_CASE	,		_SCREAMING_SNAKE_CASE	,		_SCREAMING_SNAKE_CASE = 100	,		)       ->     float:
  lowercase__			    =						x_start
  lowercase__			    =						fnc(_SCREAMING_SNAKE_CASE	)
  lowercase__			    =						0.0

  for _ in range(_SCREAMING_SNAKE_CASE	):
    # Approximates curve as a sequence of linear lines and sums their length
    lowercase__			    =						(x_end - x_start) / steps + xa
    lowercase__			    =						fnc(_SCREAMING_SNAKE_CASE	)
    length += math.hypot(xa - xa	,		fxa - fxa	)

    # Increment step
    lowercase__			    =						xa
    lowercase__			    =						fxa

  return length


if __name__ == "__main__":




      def     __UpperCamelCase						(_SCREAMING_SNAKE_CASE	)       ->     str:
        return math.sin(10 * x	)

      print("""f(x) = sin(10 * x)""")
      print("""The length of the curve from x = -10 to x = 10 is:""")
      lowercase_					     =	10
      while i <= 100_000:
            print(f'''With {i} steps: {line_length(f, -10, 10, i)}''')
            i *= 10


