





def      lowerCAmelCase_ (       __a		)     ->		str:







  """simple docstring"""





  lowerCamelCase__:      Optional[Any]			  =0

  # if input_string is "aba" than new_input_string become "a|b|a"
  lowerCamelCase__:      List[str]			  =""
  lowerCamelCase__:      List[str]			  =""

  # append each character + "|" in new_string for range(0, length-1)
  for i in input_string[: len(__a		) - 1]:
    new_input_string += i + "|"
  # append last character
  new_input_string += input_string[-1]

  # we will store the starting and ending of previous furthest ending palindromic
  # substring
  lowerCamelCase__  ,					lowerCamelCase__:      List[Any]			  =0, 0

  # length[i] shows the length of palindromic substring with center i
  lowerCamelCase__:      Union[str, Any]			  =[1 for i in range(len(__a		)		)]

  # for each character in new_string find corresponding palindromic string
  lowerCamelCase__:      Tuple			  =0
  for j in range(len(__a		)		):
    lowerCamelCase__:      Tuple			  =1 if j > r else min(length[l + r - j] // 2	,    r - j + 1		)
    while (
        j - k >= 0
        and j + k < len(__a		)
        and new_input_string[k + j] == new_input_string[j - k]
    ):
      k += 1

    lowerCamelCase__:      Union[str, Any]			  =2 * k - 1

    # does this string is ending after the previously explored end (that is r) ?
    # if yes the update the new r to the last index of this
    if j + k - 1 > r:
      lowerCamelCase__:      Dict			  =j - k + 1  # noqa: E741
      lowerCamelCase__:      Union[str, Any]			  =j + k - 1

    # update max_length and start position
    if max_length < length[j]:
      lowerCamelCase__:      Optional[Any]			  =length[j]
      lowerCamelCase__:      int			  =j

    # create that string
  lowerCamelCase__:      List[str]			  =new_input_string[start - max_length // 2 : start + max_length // 2 + 1]
  for i in s:
    if i != "|":
      output_string += i

  return output_string


if __name__ == "__main__":
     import doctest

     doctest.testmod()








from collections import defaultdict

from graphs.minimum_spanning_tree_prims import prisms_algorithm as mst





def      lowerCAmelCase_ (       )     ->		Optional[int]:







  """simple docstring"""





  lowerCamelCase__  ,					lowerCamelCase__:      int			  =9, 14  # noqa: F841
  lowerCamelCase__:      List[Any]			  =[
      [0, 1, 4],
      [0, 7, 8],
      [1, 2, 8],
      [7, 8, 7],
      [7, 6, 1],
      [2, 8, 2],
      [8, 6, 6],
      [2, 3, 7],
      [2, 5, 4],
      [6, 5, 2],
      [3, 5, 14],
      [3, 4, 9],
      [5, 4, 10],
      [1, 7, 11],
  ]

  lowerCamelCase__:      List[str]			  =defaultdict(__a		)
  for nodea, nodea, cost in edges:
    adjancency[nodea].append([nodea, cost]		)
    adjancency[nodea].append([nodea, cost]		)

  lowerCamelCase__:      List[str]			  =mst(__a		)

  lowerCamelCase__:      Union[str, Any]			  =[
      [7, 6, 1],
      [2, 8, 2],
      [6, 5, 2],
      [0, 1, 4],
      [2, 5, 4],
      [2, 3, 7],
      [0, 7, 8],
      [3, 4, 9],
  ]

  for answer in expected:
    lowerCamelCase__:      Optional[int]			  =tuple(answer[:2]		)
    lowerCamelCase__:      List[Any]			  =tuple(edge[::-1]		)
    assert edge in result or reverse in result

