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Print All the Subsets of a Given Set (Power Set)

Objec­tive: Given a set of num­bers, print all the poss­si­ble sub­sets of it includ­ing empty set.

Power Set: In math­e­mat­ics, Pow­er­Set of any given set S, PS(S) is set of all sub­sets of S includ­ing empty set.

 S ={1,2,3}

PS(S): {{ᵩ}, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}.


Solu­tion to this prob­lem is sim­i­lar to — Print All Com­bi­na­tions of sub­set of size K from Given Array

  • Cre­ate an binary array of the same size as the given array.
  • Now for every inte­ger we have two options, whether to select it or ignore it.
  • Now if we select it, we will put 1 in the boolean array at the cor­re­spond­ing index or if we ignore it, put 0 at that index.
  • Say you have a vari­able called x, which rep­re­sents the cur­rent index at the given array.
  • Make x = 0 ( ignor­ing xth index) and x = 1( select­ing xth index) and make recur­sive



{Empty} {3}  {2}  {23}  {1}  {13}  {12}  {123}  

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