
"""simple docstring"""
def 					a__ ( a :					str							,  a :					str							,  a :					int							,  a :					int							,  a :					int							,  a :					int							,  ):

  """simple docstring"""







  _snake_case  :    Union[str, Any]            = list(a		)
  _snake_case  :    List[str]            = list(a		)
  _snake_case  :    Dict            = len(a		)
  _snake_case  :    List[str]            = len(a		)

  _snake_case  :    Union[str, Any]            = [
      [0 for _ in range(len_destination_seq + 1		)] for _ in range(len_source_seq + 1		)
  ]
  _snake_case  :    Union[str, Any]            = [
      ["0" for _ in range(len_destination_seq + 1		)] for _ in range(len_source_seq + 1		)
  ]

  for i in range(1							,  len_source_seq + 1		):
    _snake_case  :    Dict            = i * delete_cost
    _snake_case  :    Any            = f'D{source_seq[i - 1]:c}'

  for i in range(1							,  len_destination_seq + 1		):
    _snake_case  :    Optional[Any]            = i * insert_cost
    _snake_case  :    str            = f'I{destination_seq[i - 1]:c}'

  for i in range(1							,  len_source_seq + 1		):
    for j in range(1							,  len_destination_seq + 1		):
      if source_seq[i - 1] == destination_seq[j - 1]:
        _snake_case  :    List[str]            = costs[i - 1][j - 1] + copy_cost
        _snake_case  :    List[Any]            = f'C{source_seq[i - 1]:c}'
      else:
        _snake_case  :    str            = costs[i - 1][j - 1] + replace_cost
        _snake_case  :    Any            = f'R{source_seq[i - 1]:c}' + str(destination_seq[j - 1]		)

      if costs[i - 1][j] + delete_cost < costs[i][j]:
        _snake_case  :    List[Any]            = costs[i - 1][j] + delete_cost
        _snake_case  :    str            = f'D{source_seq[i - 1]:c}'

      if costs[i][j - 1] + insert_cost < costs[i][j]:
        _snake_case  :    List[str]            = costs[i][j - 1] + insert_cost
        _snake_case  :    int            = f'I{destination_seq[j - 1]:c}'

  return costs, ops
def 					a__ ( a :					list[list[str]]							,  a :					int							,  a :					int		):

  """simple docstring"""







  if i == 0 and j == 0:
    return []
  else:
    if ops[i][j][0] == "C" or ops[i][j][0] == "R":
      _snake_case  :    int            = assemble_transformation(a							,  i - 1							,  j - 1		)
      seq.append(ops[i][j]		)
      return seq
    elif ops[i][j][0] == "D":
      _snake_case  :    Dict            = assemble_transformation(a							,  i - 1							,  a		)
      seq.append(ops[i][j]		)
      return seq
    else:
      _snake_case  :    Any            = assemble_transformation(a							,  a							,  j - 1		)
      seq.append(ops[i][j]		)
      return seq


if __name__ == "__main__":
    _a,      _a   :      List[str]       =				compute_transform_tables("""Python""", """Algorithms""", -1, 1, 2, 2)

    _a   :      str       =				len(operations)
    _a   :      str       =				len(operations[0])
    _a   :      Dict       =				assemble_transformation(operations, m - 1, n - 1)

    _a   :      List[str]       =				list("""Python""")
    _a   :      Optional[int]       =				0
    _a   :      Union[str, Any]       =				0

    with open("""min_cost.txt""", """w""") as file:
        for op in sequence:
            print("""""".join(string))

            if op[0] == "C":
                file.write("""%-16s""" % """Copy %c""" % op[1])
                file.write("""\t\t\t""" + """""".join(string))
                file.write("""\r\n""")

                cost -= 1
            elif op[0] == "R":
                _a   :      Dict       =				op[2]

                file.write("""%-16s""" % ("""Replace %c""" % op[1] + """ with """ + str(op[2])))
                file.write("""\t\t""" + """""".join(string))
                file.write("""\r\n""")

                cost += 1
            elif op[0] == "D":
                string.pop(i)

                file.write("""%-16s""" % """Delete %c""" % op[1])
                file.write("""\t\t\t""" + """""".join(string))
                file.write("""\r\n""")

                cost += 2
            else:
                string.insert(i, op[1])

                file.write("""%-16s""" % """Insert %c""" % op[1])
                file.write("""\t\t\t""" + """""".join(string))
                file.write("""\r\n""")

                cost += 2

            i += 1

        print("""""".join(string))
        print("""Cost: """, cost)

        file.write("""\r\nMinimum cost: """ + str(cost))



"""simple docstring"""
from __future__ import annotations

import random

# Adjacency list representation of this graph:
# https://en.wikipedia.org/wiki/File:Single_run_of_Karger%E2%80%99s_Mincut_algorithm.svg
_a   :      List[str]       =				{
    """1""": ["""2""", """3""", """4""", """5"""],
    """2""": ["""1""", """3""", """4""", """5"""],
    """3""": ["""1""", """2""", """4""", """5""", """10"""],
    """4""": ["""1""", """2""", """3""", """5""", """6"""],
    """5""": ["""1""", """2""", """3""", """4""", """7"""],
    """6""": ["""7""", """8""", """9""", """10""", """4"""],
    """7""": ["""6""", """8""", """9""", """10""", """5"""],
    """8""": ["""6""", """7""", """9""", """10"""],
    """9""": ["""6""", """7""", """8""", """10"""],
    """10""": ["""6""", """7""", """8""", """9""", """3"""],
}
def 					a__ ( a :					dict[str, list[str]]		):

  """simple docstring"""







  _snake_case  :    List[Any]            = {node: {node} for node in graph}

  _snake_case  :    str            = {node: graph[node][:] for node in graph}

  while len(a		) > 2:
    # Choose a random edge.
    _snake_case  :    str            = random.choice(list(graph_copy.keys()		)		)
    _snake_case  :    Union[str, Any]            = random.choice(graph_copy[u]		)

    # Contract edge (u, v) to new node uv
    _snake_case  :    Union[str, Any]            = u + v
    _snake_case  :    Union[str, Any]            = list(set(graph_copy[u] + graph_copy[v]		)		)
    uv_neighbors.remove(a		)
    uv_neighbors.remove(a		)
    _snake_case  :    Union[str, Any]            = uv_neighbors
    for neighbor in uv_neighbors:
      graph_copy[neighbor].append(a		)

    _snake_case  :    Dict            = set(contracted_nodes[u].union(contracted_nodes[v]		)		)

    # Remove nodes u and v.
    del graph_copy[u]
    del graph_copy[v]
    for neighbor in uv_neighbors:
      if u in graph_copy[neighbor]:
        graph_copy[neighbor].remove(a		)
      if v in graph_copy[neighbor]:
        graph_copy[neighbor].remove(a		)

    # Find cutset.
  _snake_case  :    List[Any]            = [contracted_nodes[node] for node in graph_copy]
  return {
      (node, neighbor)
      for node in groups[0]
      for neighbor in graph[node]
      if neighbor in groups[1]
  }


if __name__ == "__main__":
    print(partition_graph(TEST_GRAPH))

