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# EPI 5.5 - Generating power sets

## Problem

The power set of an alphabet set, S is the list of all strings (of any lengths) that can be formed from the symbols in S. There can be no repetitions however with respect to character swaps within the string.

For instance, for S = “ABC”, one possible power set is:

“”, “A”, “B”, “C”, “AB”, “AC”, “BC”, “ABC”

## Solution

The simplest way to think about this as iterating through the numbers 0 to 2^|S|, where each bit in the integer represents whether the alphabet at that index in the set, S is present in the output. So a solution for this is:

```
import Data.Bits
lowest_set_bit :: Int -> Int
lowest_set_bit x = x .&. complement (x - 1)
lowest_set_bit_index :: Int -> Int
lowest_set_bit_index x = floor (logBase (fromIntegral 2) (fromIntegral (lowest_set_bit x)))
set_bit_positions :: Int -> [Int]
set_bit_positions 0 = []
set_bit_positions x = (lowest_set_bit_index x) : (set_bit_positions (clear_lowest_set_bit x))
power_set :: [Char] -> [[Char]]
power_set [] = []
power_set alphabet = [str_from_int x | x <- [0 .. ((1::Int) `shiftL` numAlpha) - 1]]
where
numAlpha = length alphabet
str_from_int x = [alphabet !! i | i <- set_bit_positions x]
```