[SOLVED] N choose r possibilities as increasing binary numbers

N choose r possibilities as increasing binary numbers

I am looking for a function that inputs (n,r) and outputs the all the ways in which we can pick r objects from a string of n objects. Moreover, I would like this list as an increasing, binary sequence.

For example:

(5,2)

would output: [00011,00101,00110,01001,01010,01100,10001,10010,10100,11000]

I have tried to do this by considering the rightmost 1 and checking whether it can 'move left without bumping into another 1'. If it cannot, then I move to the next 1 and check the same thing. If any of the 1's can be 'moved to the left', every 1 to the right of it gets 'reset'.

Although my code has not been working trying this method.

Solution

Your desired order is simply the lexicographic order emitted by itertools.combinations when choosing n - r positions for 0s from n positions:

from itertools import combinations

def binary_combinations(n, r):
    for c in map(set, combinations(range(n), n - r)):
        yield ''.join('0' if i in c else '1' for i in range(n))

print(*binary_combinations(5, 2), sep='\n')

This outputs:

Demo here