How do I compute all possibilities for an array of numbers/bits (in python, or any language for that matter)

Question

I have been wracking my brains out for 3 hours straight, but I still don\'t get it, so I am asking here. (I wrote Python in the title, but this could be for pretty much any

Answer 1

In Python, use itertools for stuff like this

from itertools import product
for i in product([0,1], repeat=5): 
    print i

Yields:

(0, 0, 0, 0, 0)
(0, 0, 0, 0, 1)
(0, 0, 0, 1, 0)
(0, 0, 0, 1, 1)
(0, 0, 1, 0, 0)
etc...

Answer 2

import numpy as np
def all_combinations(width, vals):
    return np.array(np.meshgrid(*[vals]*width,
                    indexing='ij')).reshape((width,-1)).transpose()

print(all_combinations(width=3, vals=[0,1]))
print(all_combinations(width=2, vals=['a','b','c']))

Output:

[[0 0 0]
 [0 0 1]
 [0 1 0]
 [0 1 1]
 [1 0 0]
 [1 0 1]
 [1 1 0]
 [1 1 1]]
[['a' 'a']
 ['a' 'b']
 ['a' 'c']
 ['b' 'a']
 ['b' 'b']
 ['b' 'c']
 ['c' 'a']
 ['c' 'b']
 ['c' 'c']]

Answer 3

Here is a generalized recursive pseudocode to do what you seek.

array_combination is function (length, elements)
  if length < 1 
  then abort
  end if

  declare arrays as new array
  if length is 1 
  then
    loop for element in elements
      declare element_array as new array
      set element_array[0] to element
      append element_array to arrays
    end loop
  else
    loop for array in array_combination(length - 1, elements)
      loop for element in elements
        declare element_array as new array
        set element_array[0] to element
        append array to element_array
        append element_array to arrays
      end loop
      append array to arrays
    end loop
  end if
  return arrays
end function

You would call this function as "array_combination(5, [1,0])" for your given example. There are better ways to build it but a) I am too old to do homework, b) I don't know the constraints of your assignment, and c) I don't want to make it too obvious that you cheated.

Note repeated code and opportunities for common subexpression elimination along with extremely wasteful memory allocation and cache abuse. However, I'm assuming this is a first quarter computer science assignment, so they probably won't hold it against you.

Answer 4

I would approach this problem by just looping from 0 to 31 (0b11111) and turning the binary representation into an array of fixed length.

You didn't tag this with a language, so I'm not sure how to give you example code, but that approach should work.

1: 00001
2: 00010
3: 00011
...
30:11110
31:11111

Edit: Just saw you tagged this question with Python. Sample python code implementing the above algorithm:

listLength=5
for x in range(0,2**listlength):
    print(list(bin(x)[2:].zfill(listlength)))

prints out:

['0', '0', '0', '0', '0']
['0', '0', '0', '0', '1']
['0', '0', '0', '1', '0']
['0', '0', '0', '1', '1']
['0', '0', '1', '0', '0']
['0', '0', '1', '0', '1']
['0', '0', '1', '1', '0']
['0', '0', '1', '1', '1']
['0', '1', '0', '0', '0']
['0', '1', '0', '0', '1']
['0', '1', '0', '1', '0']
['0', '1', '0', '1', '1']
['0', '1', '1', '0', '0']
['0', '1', '1', '0', '1']
['0', '1', '1', '1', '0']
['0', '1', '1', '1', '1']
['1', '0', '0', '0', '0']
['1', '0', '0', '0', '1']
['1', '0', '0', '1', '0']
['1', '0', '0', '1', '1']
['1', '0', '1', '0', '0']
['1', '0', '1', '0', '1']
['1', '0', '1', '1', '0']
['1', '0', '1', '1', '1']
['1', '1', '0', '0', '0']
['1', '1', '0', '0', '1']
['1', '1', '0', '1', '0']
['1', '1', '0', '1', '1']
['1', '1', '1', '0', '0']
['1', '1', '1', '0', '1']
['1', '1', '1', '1', '0']