Generating Power Set Algorithm?

Question

This is the algorithm to print PowerSet From a Set

Input: Set[], set_size

1. Get the size of power set
   powet_set_size = pow(2, set_size)

2  Loop for counter from 0 to pow_set_size
     (a) Loop for i = 0 to set_size

          (i) If ith bit in counter is set
              Print ith element from set for this subset
     (b) Print seperator for subsets i.e., newline

Can anyone explain me what it means by If the ith bit in counter is set.

Thanks :)

A digit in binary is called a bit. Bits are numbered right to left, so if the i'th bit is set, that means that the i'th digit (right-to-left) is equal to one. — willeM_ Van Onsem
– willeM_ Van Onsem, Commented Feb 25, 2015 at 9:02

willeM_ Van Onsem · Accepted Answer · 2015-02-25 07:59:48Z

1

A number is in a computer represented in binary notation. For instance 5 is represented as:

00000000101

Because the zero'th bit is one and so is the second. Thus 2^0+2^2=5.

You can for instance test whether the i-th bit is "set" (meaning it is equal to one), using the following test:

(n&(1<<i)) != 0

You first shift 1 i places to the left. Such that it creates a number where only the i-th bit is set.
Next you perform a bitwise and such that the result differs from zero if and only if that bit is set for n as well.
Finally you perform that check.

If you count in binary, eventually all possible combinations of zero's and one's will be enumerated:

answered Feb 25, 2015 at 7:59

willeM_ Van Onsem

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