All possible combinations of elements

Question

Hi,

I'd like to know a possible algorithm to calculate all possible combinations, without repetitions, starting from length=1 until lenght=N of N elements.

Example:

Elements: 1, 2, 3.

Output:

1 2 3 12 13 23 123

Answer 1

Look at the binary presentation of the numbers 0 to 2^n - 1.

n = 3

i  Binary  Combination

   CBA

0  000
1  001     A
2  010       B
3  011     A B
4  100         C
5  101     A   C
6  110       B C
7  111     A B C

So you just have to enumerate the numbers 1 to 2^n - 1 and look at the binary representation to know with elements to include. If you want to have them ordered by the number of elements, post sort them or generate the numbers in order (there are several example codes on SO).