



from __future__ import annotations

from collections import Counter
from random import random

class     _A       :



       def __init__(		self							:     Optional[Any]):


           '''simple docstring'''

           __a						       =				{}



       def 		_lowerCamelCase			(		self							:     List[str]     ,		__SCREAMING_SNAKE_CASE							:     str):


           '''simple docstring'''

           __a						       =				{}



       def 		_lowerCamelCase			(		self							:     Union[str, Any]     ,		__SCREAMING_SNAKE_CASE							:     str     ,		__SCREAMING_SNAKE_CASE							:     str     ,		__SCREAMING_SNAKE_CASE							:     float):


           '''simple docstring'''

           if nodea not in self.connections:
               self.add_node(__SCREAMING_SNAKE_CASE)
           if nodea not in self.connections:
               self.add_node(__SCREAMING_SNAKE_CASE)
           __a						       =				probability



       def 		_lowerCamelCase			(		self							:     Optional[int]):


           '''simple docstring'''

           return list(self.connections)





       def 		_lowerCamelCase			(		self							:     List[str]     ,		__SCREAMING_SNAKE_CASE							:     str):


           '''simple docstring'''

           __a						       =				0
           __a						       =				random()

           for dest in self.connections[node]:
               current_probability += self.connections[node][dest]
               if current_probability > random_value:
                   return dest
           return ""





def      __snake_case	(			_UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase				):
    __a						       =				MarkovChainGraphUndirectedUnweighted()

    for nodea, nodea, probability in transitions:
        graph.add_transition_probability(_UpperCAmelCase   , _UpperCAmelCase   , _UpperCAmelCase				)

    __a						       =				Counter(graph.get_nodes()				)
    __a						       =				start

    for _ in range(_UpperCAmelCase				):
        __a						       =				graph.transition(_UpperCAmelCase				)
        visited[node] += 1

    return visited


if __name__ == "__main__":
 import doctest

 doctest.testmod()













def      lowercase__      (     __snake_case    :							Dict  ):


					'''simple docstring'''


					if not head:
										return True
					# split the list to two parts
					UpperCAmelCase_       ,  UpperCAmelCase_    :      Any            =						head.next, head
					while fast and fast.next:
										UpperCAmelCase_    :      str            =						fast.next.next
										UpperCAmelCase_    :      Union[str, Any]            =						slow.next
					UpperCAmelCase_    :      int            =						slow.next
					UpperCAmelCase_    :      List[Any]            =						None  # Don't forget here! But forget still works!
					# reverse the second part
					UpperCAmelCase_    :      Tuple            =						None
					while second:
										UpperCAmelCase_    :      int            =						second.next
										UpperCAmelCase_    :      Any            =						node
										UpperCAmelCase_    :      Optional[Any]            =						second
										UpperCAmelCase_    :      Tuple            =						nxt
					# compare two parts
					# second part has the same or one less node
					while node:
										if node.val != head.val:
															return False
										UpperCAmelCase_    :      Optional[Any]            =						node.next
										UpperCAmelCase_    :      Dict            =						head.next
					return True




def      lowercase__      (     __snake_case    :							Union[str, Any]  ):


					'''simple docstring'''


					if not head or not head.next:
										return True

					# 1. Get the midpoint (slow)
					UpperCAmelCase_    :      Any            =						head
					while fast and fast.next:
										UpperCAmelCase_       ,  UpperCAmelCase_    :      Tuple            =						fast.next.next, slow.next

					# 2. Push the second half into the stack
					UpperCAmelCase_    :      List[str]            =						[slow.val]
					while slow.next:
										UpperCAmelCase_    :      List[str]            =						slow.next
										stack.append(slow.val  )

					# 3. Comparison
					while stack:
										if stack.pop() != cur.val:
															return False
										UpperCAmelCase_    :      int            =						cur.next

					return True






def      lowercase__      (     __snake_case    :							Dict  ):


					'''simple docstring'''


					if not head or not head.next:
										return True
					UpperCAmelCase_    :      Tuple            =						{}
					UpperCAmelCase_    :      int            =						0
					while head:
										if head.val in d:
															d[head.val].append(__snake_case  )
										else:
															UpperCAmelCase_    :      List[Any]            =						[pos]
										UpperCAmelCase_    :      Any            =						head.next
										pos += 1
					UpperCAmelCase_    :      Dict            =						pos - 1
					UpperCAmelCase_    :      Optional[int]            =						0
					for v in d.values():
										if len(__snake_case  ) % 2 != 0:
															middle += 1
										else:
															UpperCAmelCase_    :      int            =						0
															for i in range(0     ,       len(__snake_case  )  ):
																				if v[i] + v[len(__snake_case  ) - 1 - step] != checksum:
																									return False
																				step += 1
										if middle > 1:
															return False
					return True






