Twiddle algorithm by Phillip J Chase, `Algorithm 382: Combinations of M out of N Objects [G6]', Communications of the Association for Computing Machinery 13:6:368 (1970). Code based on Matthew Belmonte [http://www.netlib.no/netlib/toms/382].

Twiddle.py

import numpy as np

def twiddle(p, x=None, y=None, z=None):

    j = np.argmax(p[1:]>0)+1
    
    if p[j-1] == 0:
        i = j-1
        while i != 1:
            p[i] = -1
            i -= 1
        p[j], p[1] = 0, 1
        return (0,j-1,0,False)

    if j>1:
        p[j-1] = 0
    j+=1
    while p[j] > 0:
        j+=1

    i, k = j, j-1
    while p[i] == 0:
        p[i] = -1
        i+=1

    if p[i] == -1:
        p[i] = p[k]
        z = p[k]-1
        p[k] = -1
        return (i-1,k-1,z,False)
    elif i != p[0]:
        p[j] = p[i]
        z = p[i]-1
        p[i] = 0
        return (j-1,i-1,z,False)
    
    return (x,y,z,True)
    

def init_twiddle(m, n):
        
    p = np.zeros((n+2),dtype=int)
        
    p[0] = n+1
    p[n-m+1:n+1] = np.arange(1,m+1)
    p[n+1] = -2
    if m == 0:
        p[1] = 1            
    return p

N = 5
M = 2

b = np.zeros((N),dtype=int)
b[N-M:] = 1

i = 0
print i, b
p = init_twiddle(M, N)
x, y, z, done = twiddle(p)
while not done:
    i +=1
    b[x], b[y] = 1, 0
    print(i, b)
    x, y, z, done = twiddle(p, x, y, z)