**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.

**Example**:

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

**Approach:**

**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
, which represents the current index at the given array.*x* - Make
and*x = 0 ( ignoring xth index)*and make*x = 1( selecting xth index)**recursive*

**Code:**

public class AllCombinations { | |

static int[] B = { 1, 2, 3 }; | |

public void combinations(int[] A, int x) { | |

if (x == A.length – 1) { | |

A[x] = 0; // last digit, don't select it | |

printArray(A); // print the set | |

A[x] = 1; //// last digit, select it | |

printArray(A); | |

return; | |

} | |

A[x] = 0; //either you will not select this digit | |

combinations(A, x + 1); | |

A[x] = 1; //either you will select this digit | |

combinations(A, x + 1); | |

} | |

public void printArray(int[] A) { | |

boolean isNULL = true; | |

System.out.print("{"); | |

for (int i = 0; i < B.length; i++) { | |

if (A[i] == 1) { | |

System.out.print(B[i] + ""); | |

isNULL = false; | |

} | |

} | |

if (isNULL == false) { | |

System.out.print("}"); | |

System.out.print(" "); | |

} | |

if (isNULL) { | |

System.out.print("Empty"); | |

System.out.print("} "); | |

} | |

} | |

public static void main(String[] args) { | |

AllCombinations a = new AllCombinations(); | |

int[] A = new int[B.length]; | |

a.combinations(A, 0); | |

} | |

} |

**Output**:

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

this post has very good explanation http://javabypatel.blogspot.in/2015/10/all-subsets-of-set-powerset.html