






def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase      )			->     str:
     return (pointa[0] - pointa[0]) ** 2 + (pointa[1] - pointa[1]) ** 2







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase=0      )			->     Optional[Any]:
     return sorted(__lowerCAmelCase ,   key=lambda __lowerCAmelCase      : x[column]      )







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase=float("inf"      )      )			->     Union[str, Any]:

     for i in range(points_counts - 1      ):
          for j in range(i + 1 ,   __lowerCAmelCase      ):
               UpperCamelCase__      :       List[str]	    =  euclidean_distance_sqr(points[i] ,   points[j]      )
               if current_dis < min_dis:
                    UpperCamelCase__      :       List[Any]	    =  current_dis
     return min_dis







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase=float("inf"      )      )			->     Any:

     for i in range(min(6 ,   points_counts - 1      ) ,   __lowerCAmelCase      ):
          for j in range(max(0 ,   i - 6      ) ,   __lowerCAmelCase      ):
               UpperCamelCase__      :       Union[str, Any]	    =  euclidean_distance_sqr(points[i] ,   points[j]      )
               if current_dis < min_dis:
                    UpperCamelCase__      :       Optional[Any]	    =  current_dis
     return min_dis







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase      )			->     Optional[int]:

     # base case
     if points_counts <= 3:
          return dis_between_closest_pair(__lowerCAmelCase ,   __lowerCAmelCase      )

     # recursion
     UpperCamelCase__      :       Union[str, Any]	    =  points_counts // 2
     UpperCamelCase__      :       Tuple	    =  closest_pair_of_points_sqr(
         __lowerCAmelCase ,   points_sorted_on_y[:mid] ,   __lowerCAmelCase      )
     UpperCamelCase__      :       List[str]	    =  closest_pair_of_points_sqr(
         __lowerCAmelCase ,   points_sorted_on_y[mid:] ,   points_counts - mid      )
     UpperCamelCase__      :       Any	    =  min(__lowerCAmelCase ,   __lowerCAmelCase      )
     UpperCamelCase__      :       int	    =  []
     for point in points_sorted_on_x:
          if abs(point[0] - points_sorted_on_x[mid][0]      ) < closest_pair_dis:
               cross_strip.append(__lowerCAmelCase      )

     UpperCamelCase__      :       Dict	    =  dis_between_closest_in_strip(
         __lowerCAmelCase ,   len(__lowerCAmelCase      ) ,   __lowerCAmelCase      )
     return min(__lowerCAmelCase ,   __lowerCAmelCase      )







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase      )			->     str:
     UpperCamelCase__      :       Optional[int]	    =  column_based_sort(__lowerCAmelCase ,   column=0      )
     UpperCamelCase__      :       Optional[int]	    =  column_based_sort(__lowerCAmelCase ,   column=1      )
     return (
         closest_pair_of_points_sqr(
             __lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase      )
     ) ** 0.5


if __name__ == "__main__":
 lowerCamelCase     :							List[Any]    =[(2, 3), (12, 30), (40, 50), (5, 1), (12, 10), (3, 4)]
 print('''Distance:''', closest_pair_of_points(points, len(points)))







lowerCamelCase     :							Optional[int]    ={
    '''A''': ['''B''', '''C''', '''E'''],
    '''B''': ['''A''', '''D''', '''E'''],
    '''C''': ['''A''', '''F''', '''G'''],
    '''D''': ['''B'''],
    '''E''': ['''A''', '''B''', '''D'''],
    '''F''': ['''C'''],
    '''G''': ['''C'''],
}







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase      )			->     list[str]:
     UpperCamelCase__      :       Optional[Any]	    =  set()
     # keep track of all the paths to be checked
     UpperCamelCase__      :       Optional[Any]	    =  [[start]]

     # return path if start is goal
     if start == goal:
          return [start]

     # keeps looping until all possible paths have been checked
     while queue:
          # pop the first path from the queue
          UpperCamelCase__      :       int	    =  queue.pop(0      )
          # get the last node from the path
          UpperCamelCase__      :       Dict	    =  path[-1]
          if node not in explored:
               UpperCamelCase__      :       Tuple	    =  graph[node]
               # go through all neighbour nodes, construct a new path and
               # push it into the queue
               for neighbour in neighbours:
                    UpperCamelCase__      :       List[str]	    =  list(__lowerCAmelCase      )
                    new_path.append(__lowerCAmelCase      )
                    queue.append(__lowerCAmelCase      )
                    # return path if neighbour is goal
                    if neighbour == goal:
                         return new_path

            # mark node as explored
               explored.add(__lowerCAmelCase      )

    # in case there's no path between the 2 nodes
     return []







def 		SCREAMING_SNAKE_CASE							( __lowerCAmelCase ,   __lowerCAmelCase ,   __lowerCAmelCase      )			->     int:
     if not graph or start not in graph or target not in graph:
          return -1
     if start == target:
          return 0
     UpperCamelCase__      :       Tuple	    =  [start]
     UpperCamelCase__      :       Optional[int]	    =  set(__lowerCAmelCase      )
     # Keep tab on distances from `start` node.
     UpperCamelCase__      :       str	    =  {start: 0, target: -1}
     while queue:
          UpperCamelCase__      :       Any	    =  queue.pop(0      )
          if node == target:
               UpperCamelCase__      :       Union[str, Any]	    =  (
                   dist[node] if dist[target] == -1 else min(dist[target] ,   dist[node]      )
               )
          for adjacent in graph[node]:
               if adjacent not in visited:
                    visited.add(__lowerCAmelCase      )
                    queue.append(__lowerCAmelCase      )
                    UpperCamelCase__      :       List[Any]	    =  dist[node] + 1
     return dist[target]


if __name__ == "__main__":
 print(bfs_shortest_path(demo_graph, '''G''', '''D'''))  # returns ['G', 'C', 'A', 'B', 'D']
 print(bfs_shortest_path_distance(demo_graph, '''G''', '''D'''))  # returns 4