


'''simple docstring'''


from __future__ import annotations


def 		_lowercase   (SCREAMING_SNAKE_CASE					,				SCREAMING_SNAKE_CASE       ):




     '''simple docstring'''





     __A  :					Dict						     =       0
     __A  :					str						     =       len(SCREAMING_SNAKE_CASE       ) - 1
     while left <= right:
          __A  :					Any						     =       (left + right) // 2
          if left == right:
               if sorted_list[middle] < item:
                    __A  :					Dict						     =       middle + 1
               break
          elif sorted_list[middle] < item:
               __A  :					int						     =       middle + 1
          else:
               __A  :					Optional[int]						     =       middle - 1
     sorted_list.insert(SCREAMING_SNAKE_CASE					,				SCREAMING_SNAKE_CASE       )
     return sorted_list


def 		_lowercase   (SCREAMING_SNAKE_CASE					,				SCREAMING_SNAKE_CASE       ):




     '''simple docstring'''





     __A  :					Any						     =       []
     while left and right:
          if left[0][0] < right[0][0]:
               result.append(left.pop(0       )       )
          else:
               result.append(right.pop(0       )       )
     return result + left + right


def 		_lowercase   (SCREAMING_SNAKE_CASE       ):




     '''simple docstring'''





     __A  :					Tuple						     =       len(SCREAMING_SNAKE_CASE       )
     if length <= 1:
          return list_ad
     __A  :					Optional[Any]						     =       length // 2
     return merge(sortlist_ad(list_ad[:middle]       )					,				sortlist_ad(list_ad[middle:]       )       )


def 		_lowercase   (SCREAMING_SNAKE_CASE       ):




     '''simple docstring'''





     if len(SCREAMING_SNAKE_CASE       ) <= 1:
          return collection
     __A  :					Optional[int]						     =       []
     __A  :					str						     =       False
     for i in range(0					,				len(SCREAMING_SNAKE_CASE       )					,				2       ):
          if i == len(SCREAMING_SNAKE_CASE       ) - 1:
               __A  :					str						     =       True
          else:
               if collection[i] < collection[i + 1]:
                    two_paired_list.append([collection[i], collection[i + 1]]       )
               else:
                    two_paired_list.append([collection[i + 1], collection[i]]       )
     __A  :					Tuple						     =       sortlist_ad(SCREAMING_SNAKE_CASE       )
     __A  :					Optional[Any]						     =       [i[0] for i in sorted_list_ad]
     result.append(sorted_list_ad[-1][1]       )
     if has_last_odd_item:
          __A  :					Optional[Any]						     =       collection[-1]
          __A  :					int						     =       binary_search_insertion(SCREAMING_SNAKE_CASE					,				SCREAMING_SNAKE_CASE       )
     __A  :					int						     =       False
     for i in range(len(SCREAMING_SNAKE_CASE       ) - 1       ):
          if result[i] == collection[-1] and has_last_odd_item:
               __A  :					Union[str, Any]						     =       True
          __A  :					List[str]						     =       sorted_list_ad[i][1]
          # If last_odd_item is inserted before the item's index,
          # you should forward index one more.
          if is_last_odd_item_inserted_before_this_index:
               __A  :					Union[str, Any]						     =       result[: i + 2] + binary_search_insertion(result[i + 2 :]					,				SCREAMING_SNAKE_CASE       )
          else:
               __A  :					int						     =       result[: i + 1] + binary_search_insertion(result[i + 1 :]					,				SCREAMING_SNAKE_CASE       )

     return result


if __name__ == "__main__":
      _UpperCamelCase          =     input("""Enter numbers separated by a comma:\n""").strip()
      _UpperCamelCase          =     [int(item) for item in user_input.split(""",""")]
      print(merge_insertion_sort(unsorted))





'''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
_UpperCamelCase          =     {
    """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 		_lowercase   (SCREAMING_SNAKE_CASE       ):




     '''simple docstring'''





     __A  :					Any						     =       {node: {node} for node in graph}

     __A  :					List[str]						     =       {node: graph[node][:] for node in graph}

     while len(SCREAMING_SNAKE_CASE       ) > 2:
          # Choose a random edge.
          __A  :					Tuple						     =       random.choice(list(graph_copy.keys()       )       )
          __A  :					Any						     =       random.choice(graph_copy[u]       )

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

          __A  :					str						     =       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(SCREAMING_SNAKE_CASE       )
               if v in graph_copy[neighbor]:
                    graph_copy[neighbor].remove(SCREAMING_SNAKE_CASE       )

    # Find cutset.
     __A  :					int						     =       [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))

