





"""simple docstring"""


# using dfs for finding eulerian path traversal




def        lowercase__     (       lowercase_		,lowercase_		,lowercase_		,lowercase_=None      )       ->		str:




      """simple docstring"""

      _UpperCamelCase   :						Union[str, Any]    =							(path or []) + [u]
      for v in graph[u]:
            if visited_edge[u][v] is False:
                  _UpperCamelCase,	_UpperCamelCase   :						Optional[int]    =							True, True
                  _UpperCamelCase   :						List[str]    =							dfs(lowercase_		,lowercase_		,lowercase_		,lowercase_      )
      return path




def        lowercase__     (       lowercase_		,lowercase_      )       ->		Dict:




      """simple docstring"""

      _UpperCamelCase   :						Optional[Any]    =							0
      _UpperCamelCase   :						Any    =							-1
      for i in range(lowercase_      ):
            if i not in graph.keys():
                  continue
            if len(graph[i]      ) % 2 == 1:
                  odd_degree_nodes += 1
                  _UpperCamelCase   :						Any    =							i
      if odd_degree_nodes == 0:
            return 1, odd_node
      if odd_degree_nodes == 2:
            return 2, odd_node
      return 3, odd_node




def        lowercase__     (       lowercase_		,lowercase_      )       ->		int:




      """simple docstring"""

      _UpperCamelCase   :						Optional[Any]    =							[[False for _ in range(max_node + 1      )] for _ in range(max_node + 1      )]
      _UpperCamelCase,	_UpperCamelCase   :						List[str]    =							check_circuit_or_path(lowercase_		,lowercase_      )
      if check == 3:
            print("graph is not Eulerian"      )
            print("no path"      )
            return
      _UpperCamelCase   :						Dict    =							1
      if check == 2:
            _UpperCamelCase   :						str    =							odd_node
            print("graph has a Euler path"      )
      if check == 1:
            print("graph has a Euler cycle"      )
      _UpperCamelCase   :						Optional[Any]    =							dfs(lowercase_		,lowercase_		,lowercase_      )
      print(lowercase_      )




def        lowercase__     (       )       ->		Any:




      """simple docstring"""

      _UpperCamelCase   :						Dict    =							{1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
      _UpperCamelCase   :						List[Any]    =							{1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
      _UpperCamelCase   :						str    =							{1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
      _UpperCamelCase   :						int    =							{1: [2, 3], 2: [1, 3], 3: [1, 2]}
      _UpperCamelCase   :						Tuple    =							{
          1: [],
          2: []
          # all degree is zero
      }
      _UpperCamelCase   :						Optional[int]    =							10
      check_euler(lowercase_		,lowercase_      )
      check_euler(lowercase_		,lowercase_      )
      check_euler(lowercase_		,lowercase_      )
      check_euler(lowercase_		,lowercase_      )
      check_euler(lowercase_		,lowercase_      )


if __name__ == "__main__":
  main()







"""simple docstring"""


import random
from typing import Any




def        lowercase__     (       lowercase_      )       ->		list[Any]:




      """simple docstring"""

      for _ in range(len(lowercase_      )      ):
            _UpperCamelCase   :						Dict    =							random.randint(0		,len(lowercase_      ) - 1      )
            _UpperCamelCase   :						str    =							random.randint(0		,len(lowercase_      ) - 1      )
            _UpperCamelCase,	_UpperCamelCase   :						Optional[Any]    =							data[b], data[a]
      return data


if __name__ == "__main__":
  lowerCamelCase__						= [0, 1, 2, 3, 4, 5, 6, 7]
  lowerCamelCase__						= ["python", "says", "hello", "!"]
  print("Fisher-Yates Shuffle:")
  print("List", integers, strings)
  print("FY Shuffle", fisher_yates_shuffle(integers), fisher_yates_shuffle(strings))
