generate all partitions of a set [closed]

Answer 1

You can try the recursive answer if your set is not to big (or else use stack) :

The principle is the following, you have a function that give back :

rec_func(SET) = List of List of Set

And work as follow :

rec_func(SET) =
  if SET = {empty}:
    // if no element, easy to give the answer
    return([[]])
  else:
    // 1. Remove one element from the set : 'a' to this set
    a = SET.pop()
    // 2. Call rec_func :
    list_of_list_of_set = rec_func(SET\'a')  
    response = []
    // 3. For every possibilities given by the function add the element 'a' :
    For every list_of_set in list_of_list_of_set  :
       // Case 1, you add 'a' to list_of_set
       response.push( [{'a'} + list_of_set] )
       // Case 2, for every set, you create a copy where you add 'a'
       for every set in list_of_set:
           response.push( [{set,'a'} + list_of_set\set] )

    // The function return the list of list of set created.        
    return(response)