


# using dfs for finding eulerian path traversal






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE=None )->  Dict:




      """simple docstring"""

      snake_case_	=				(path or []) + [u]
      for v in graph[u]:
            if visited_edge[u][v] is False:
                  snake_case_	,   snake_case_	=				True, True
                  snake_case_	=				dfs(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )
      return path






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )->  Dict:




      """simple docstring"""

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






def 	__lowerCAmelCase   (SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )->  List[Any]:




      """simple docstring"""

      snake_case_	=				[[False for _ in range(max_node + 1 )] for _ in range(max_node + 1 )]
      snake_case_	,   snake_case_	=				check_circuit_or_path(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )
      if check == 3:
            print('''graph is not Eulerian''' )
            print('''no path''' )
            return
      snake_case_	=				1
      if check == 2:
            snake_case_	=				odd_node
            print('''graph has a Euler path''' )
      if check == 1:
            print('''graph has a Euler cycle''' )
      snake_case_	=				dfs(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )
      print(SCREAMING_SNAKE_CASE )






def 	__lowerCAmelCase   ()->  List[Any]:




      """simple docstring"""

      snake_case_	=				{1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
      snake_case_	=				{1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
      snake_case_	=				{1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
      snake_case_	=				{1: [2, 3], 2: [1, 3], 3: [1, 2]}
      snake_case_	=				{
          1: [],
          2: []
          # all degree is zero
      }
      snake_case_	=				10
      check_euler(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )
      check_euler(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )
      check_euler(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )
      check_euler(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )
      check_euler(SCREAMING_SNAKE_CASE , SCREAMING_SNAKE_CASE )


if __name__ == "__main__":
   main()



from __future__ import annotations

import time

UpperCAmelCase      =   list[tuple[int, int]]

UpperCAmelCase      =   [
    [0, 0, 0, 0, 0, 0, 0],
    [0, 1, 0, 0, 0, 0, 0],  # 0 are free path whereas 1's are obstacles
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 1, 0, 0, 0, 0],
    [1, 0, 1, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 1, 0, 0],
]

UpperCAmelCase      =   [[-1, 0], [0, -1], [1, 0], [0, 1]]  # up, left, down, right







class lowerCAmelCase_						:

 '''simple docstring'''

 def __init__(     self		,				_UpperCAmelCase		,				_UpperCAmelCase		,				_UpperCAmelCase		,				_UpperCAmelCase		,				_UpperCAmelCase ):
       snake_case_	=				pos_x
       snake_case_	=				pos_y
       snake_case_	=				(pos_y, pos_x)
       snake_case_	=				goal_x
       snake_case_	=				goal_y
       snake_case_	=				parent







class lowerCAmelCase_						:

 '''simple docstring'''

 def __init__(     self		,				_UpperCAmelCase		,				_UpperCAmelCase ):
       snake_case_	=				Node(start[1]		,				start[0]		,				goal[1]		,				goal[0]		,				_UpperCAmelCase )
       snake_case_	=				Node(goal[1]		,				goal[0]		,				goal[1]		,				goal[0]		,				_UpperCAmelCase )

       snake_case_	=				[self.start]
       snake_case_	=				False



 def 						UpperCamelCase__					(     self ):
       while self.node_queue:
             snake_case_	=				self.node_queue.pop(0 )

             if current_node.pos == self.target.pos:
                   snake_case_	=				True
                   return self.retrace_path(_UpperCAmelCase )

             snake_case_	=				self.get_successors(_UpperCAmelCase )

             for node in successors:
                   self.node_queue.append(_UpperCAmelCase )

       if not self.reached:
             return [self.start.pos]
       return None



 def 						UpperCamelCase__					(     self		,				_UpperCAmelCase ):
       snake_case_	=				[]
       for action in delta:
             snake_case_	=				parent.pos_x + action[1]
             snake_case_	=				parent.pos_y + action[0]
             if not (0 <= pos_x <= len(grid[0] ) - 1 and 0 <= pos_y <= len(_UpperCAmelCase ) - 1):
                   continue

             if grid[pos_y][pos_x] != 0:
                   continue

             successors.append(
                 Node(_UpperCAmelCase		,				_UpperCAmelCase		,				self.target.pos_y		,				self.target.pos_x		,				_UpperCAmelCase ) )
       return successors





 def 						UpperCamelCase__					(     self		,				_UpperCAmelCase ):
       snake_case_	=				node
       snake_case_	=				[]
       while current_node is not None:
             path.append((current_node.pos_y, current_node.pos_x) )
             snake_case_	=				current_node.parent
       path.reverse()
       return path







class lowerCAmelCase_						:

 '''simple docstring'''

 def __init__(     self		,				_UpperCAmelCase		,				_UpperCAmelCase ):
       snake_case_	=				BreadthFirstSearch(_UpperCAmelCase		,				_UpperCAmelCase )
       snake_case_	=				BreadthFirstSearch(_UpperCAmelCase		,				_UpperCAmelCase )
       snake_case_	=				False



 def 						UpperCamelCase__					(     self ):
       while self.fwd_bfs.node_queue or self.bwd_bfs.node_queue:
             snake_case_	=				self.fwd_bfs.node_queue.pop(0 )
             snake_case_	=				self.bwd_bfs.node_queue.pop(0 )

             if current_bwd_node.pos == current_fwd_node.pos:
                   snake_case_	=				True
                   return self.retrace_bidirectional_path(
                       _UpperCAmelCase		,				_UpperCAmelCase )

             snake_case_	=				current_bwd_node
             snake_case_	=				current_fwd_node

             snake_case_	=				{
                 self.fwd_bfs: self.fwd_bfs.get_successors(_UpperCAmelCase ),
                 self.bwd_bfs: self.bwd_bfs.get_successors(_UpperCAmelCase ),
             }

             for bfs in [self.fwd_bfs, self.bwd_bfs]:
                   for node in successors[bfs]:
                         bfs.node_queue.append(_UpperCAmelCase )

       if not self.reached:
             return [self.fwd_bfs.start.pos]
       return None





 def 						UpperCamelCase__					(     self		,				_UpperCAmelCase		,				_UpperCAmelCase ):
       snake_case_	=				self.fwd_bfs.retrace_path(_UpperCAmelCase )
       snake_case_	=				self.bwd_bfs.retrace_path(_UpperCAmelCase )
       bwd_path.pop()
       bwd_path.reverse()
       snake_case_	=				fwd_path + bwd_path
       return path


if __name__ == "__main__":
   # all coordinates are given in format [y,x]
   import doctest

   doctest.testmod()
   UpperCAmelCase      =   (0, 0)
   UpperCAmelCase      =   (len(grid) - 1, len(grid[0]) - 1)
   for elem in grid:
      print(elem)

   UpperCAmelCase      =   time.time()
   UpperCAmelCase      =   BreadthFirstSearch(init, goal)
   UpperCAmelCase      =   bfs.search()
   UpperCAmelCase      =   time.time() - start_bfs_time

   print("""Unidirectional BFS computation time : """, bfs_time)

   UpperCAmelCase      =   time.time()
   UpperCAmelCase      =   BidirectionalBreadthFirstSearch(init, goal)
   UpperCAmelCase      =   bd_bfs.search()
   UpperCAmelCase      =   time.time() - start_bd_bfs_time

   print("""Bidirectional BFS computation time : """, bd_bfs_time)