How can I find all the subsets of a set with exactly n elements

Question

I am writing a program in Python  and I realized that a problem I need to solve requires me  given a set S with n elements   S  n   to test a function on all possible subsets of a certain order m  i e  with m number of elements   To use the answer to produce a partial solution  and then try again with the next order m m 1  until m n   I am on my way to write a solution of the form   def findsubsets S  m       subsets   set                 return subsets   But knowing Python I expected a solution to be already there   What is the best way to accomplish this

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Another solution using recursion  def subsets nums  List int   - gt  List List int        n   len nums      output                 for num in nums          output     curr    num  for curr in output           return output  Starting from empty subset in output list  At each step we take a new integer into consideration and generates new subsets from the existing ones

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Using the canonical function to get the powerset from the the itertools recipe page   from itertools import chain  combinations  def powerset iterable               powerset  1 2 3   -- gt      1    2    3    1 2   1 3   2 3   1 2 3              xs   list iterable        note we return an iterator rather than a list     return chain from iterable combinations xs n  for n in range len xs  1     Used like    gt  gt  gt  list powerset  abc           a       b       c       a    b      a    c      b    c      a    b    c      gt  gt  gt  list powerset set  1 2 3           1     2     3     1  2    1  3    2  3    1  2  3     map to sets if you want so you can use union  intersection  etc       gt  gt  gt  map set  powerset set  1 2 3      set      set  1    set  2    set  3    set  1  2    set  1  3    set  2  3    set  1  2  3      gt  gt  gt  reduce lambda x y  x union y   map set  powerset set  1 2 3      set  1  2  3

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python -c  import itertools  a  2 3 5 7 11   print sum  list itertools combinations a  i   for i in range len a  1               2     3     5     7     11     2  3    2  5    2  7    2  11    3  5    3  7    3  11    5  7    5  11    7  11    2  3  5    2  3  7    2  3  11    2  5  7    2  5  11    2  7  11    3  5  7    3  5  11    3  7  11    5  7  11    2  3  5  7    2  3  5  11    2  3  7  11    2  5  7  11    3  5  7  11    2  3  5  7  11

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itertools combinations is your friend if you have Python 2 6 or greater   Otherwise  check the link for an implementation of an equivalent function   import itertools def findsubsets S m       return set itertools combinations S  m     S  The set for which you want to find subsets m  The number of elements in the subset

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Here s a function that gives you all subsets of the integers  0  n   not just the subsets of a given length  from itertools import combinations  chain  def allsubsets n       return list chain   combinations range n   ni  for ni in range n 1      so e g   gt  gt  gt  allsubsets 3        0     1     2     0  1    0  2    1  2    0  1  2

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Without using itertools   In Python 3 you can use yield from to add a subset generator method to buit-in set class   class SetWithSubset set       def subsets self           s1              s2   list self           def recfunc i 0                           if i    len s2                   yield frozenset s1              else                                  yield from recfunc i   1                  s1 append s2  i                    yield from recfunc i   1                  s1 pop            yield from recfunc     For example below snippet works as expected   x   SetWithSubset  1 2 3 5 6    2 3  in x subsets                True set   in x subsets                True x in x subsets                    True x  7  in x subsets                False set  5 3   in x subsets           True - better alternative  set  5 3    lt  x len x subsets                     32

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Here s some pseudocode - you can cut same recursive calls by storing the values for each call as you go and before recursive call checking if the call value is already present   The following algorithm will have all the subsets excluding the empty set   list   subsets string s  list   v         if s length      1            list add s               return v            else               list   temp   subsets s 1 to length-1   v           int length   temp- gt size             for int i 0 i lt length i                  temp add s 0  temp i                       list add s 0            return temp            So  for example if s    123  then output is   1 2 3 12 13 23 123

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Without using itertools   In Python 3 you can use yield from to add a subset generator method to buit-in set class   class SetWithSubset set       def subsets self           s1              s2   list self           def recfunc i 0                           if i    len s2                   yield frozenset s1              else                                  yield from recfunc i   1                  s1 append s2  i                    yield from recfunc i   1                  s1 pop            yield from recfunc     For example below snippet works as expected   x   SetWithSubset  1 2 3 5 6    2 3  in x subsets                True set   in x subsets                True x in x subsets                    True x  7  in x subsets                False set  5 3   in x subsets           True - better alternative  set  5 3    lt  x len x subsets                     32

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Another solution using recursion  def subsets nums  List int   - gt  List List int        n   len nums      output                 for num in nums          output     curr    num  for curr in output           return output  Starting from empty subset in output list  At each step we take a new integer into consideration and generates new subsets from the existing ones

User · Answer

itertools combinations is your friend if you have Python 2 6 or greater   Otherwise  check the link for an implementation of an equivalent function   import itertools def findsubsets S m       return set itertools combinations S  m     S  The set for which you want to find subsets m  The number of elements in the subset

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Here is one neat way with easy to understand algorithm   import copy  nums    2 3 4 5  subsets         for n in nums      prev   copy deepcopy subsets       k append n  for k in subsets      subsets extend prev   print subsets   print len subsets        2  3  4  5    3  4  5    2  4  5    4  5    2  3  5    3  5    2  5    5       2  3  4    3  4    2  4    4    2  3    3    2          16  2 len nums

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gt  gt  gt Set     A    B   C   D    gt  gt  gt n   2  gt  gt  gt Subsets   i for i s in zip Set  status  if int s     for status in   format bit  b   zfill len Set    for bit in range 2  len Set    if sum map int status      n   gt  gt  gt Subsets    C    D      B    D      B    C      A    D      A    C      A    B

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Here s a function that gives you all subsets of the integers  0  n   not just the subsets of a given length  from itertools import combinations  chain  def allsubsets n       return list chain   combinations range n   ni  for ni in range n 1      so e g   gt  gt  gt  allsubsets 3        0     1     2     0  1    0  2    1  2    0  1  2

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itertools combinations is your friend if you have Python 2 6 or greater   Otherwise  check the link for an implementation of an equivalent function   import itertools def findsubsets S m       return set itertools combinations S  m     S  The set for which you want to find subsets m  The number of elements in the subset

User · Answer

Using the canonical function to get the powerset from the the itertools recipe page   from itertools import chain  combinations  def powerset iterable               powerset  1 2 3   -- gt      1    2    3    1 2   1 3   2 3   1 2 3              xs   list iterable        note we return an iterator rather than a list     return chain from iterable combinations xs n  for n in range len xs  1     Used like    gt  gt  gt  list powerset  abc           a       b       c       a    b      a    c      b    c      a    b    c      gt  gt  gt  list powerset set  1 2 3           1     2     3     1  2    1  3    2  3    1  2  3     map to sets if you want so you can use union  intersection  etc       gt  gt  gt  map set  powerset set  1 2 3      set      set  1    set  2    set  3    set  1  2    set  1  3    set  2  3    set  1  2  3      gt  gt  gt  reduce lambda x y  x union y   map set  powerset set  1 2 3      set  1  2  3

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Here is one neat way with easy to understand algorithm   import copy  nums    2 3 4 5  subsets         for n in nums      prev   copy deepcopy subsets       k append n  for k in subsets      subsets extend prev   print subsets   print len subsets        2  3  4  5    3  4  5    2  4  5    4  5    2  3  5    3  5    2  5    5       2  3  4    3  4    2  4    4    2  3    3    2          16  2 len nums

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Here s some pseudocode - you can cut same recursive calls by storing the values for each call as you go and before recursive call checking if the call value is already present   The following algorithm will have all the subsets excluding the empty set   list   subsets string s  list   v         if s length      1            list add s               return v            else               list   temp   subsets s 1 to length-1   v           int length   temp- gt size             for int i 0 i lt length i                  temp add s 0  temp i                       list add s 0            return temp            So  for example if s    123  then output is   1 2 3 12 13 23 123

User · Answer

python -c  import itertools  a  2 3 5 7 11   print sum  list itertools combinations a  i   for i in range len a  1               2     3     5     7     11     2  3    2  5    2  7    2  11    3  5    3  7    3  11    5  7    5  11    7  11    2  3  5    2  3  7    2  3  11    2  5  7    2  5  11    2  7  11    3  5  7    3  5  11    3  7  11    5  7  11    2  3  5  7    2  3  5  11    2  3  7  11    2  5  7  11    3  5  7  11    2  3  5  7  11

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gt  gt  gt Set     A    B   C   D    gt  gt  gt n   2  gt  gt  gt Subsets   i for i s in zip Set  status  if int s     for status in   format bit  b   zfill len Set    for bit in range 2  len Set    if sum map int status      n   gt  gt  gt Subsets    C    D      B    D      B    C      A    D      A    C      A    B

User · Answer

itertools combinations is your friend if you have Python 2 6 or greater   Otherwise  check the link for an implementation of an equivalent function   import itertools def findsubsets S m       return set itertools combinations S  m     S  The set for which you want to find subsets m  The number of elements in the subset

[python] How can I find all the subsets of a set, with exactly n elements?

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