Combination

Code

Method 1:

def combine(A):
    return [x for i in range(len(A)) for x in combineHelper(A, 0, i+1)]

def combineHelper(A, p, n):
    if n == 0:
        return [()]
    else:
        return [(A[i],) + x for i in range(p, len(A)) if (i + n - 1) < len(A) for x in combineHelper(A, i+1, n-1)]

def main():
    A = [3, 1, 2]
    print('the combination of A is: ', combine(A))

main()

Method 2:

def combine(A, p, n):
    if n == 1:
        return [(A[p],)]
    else:
        B = combine(A, p+1, n-1)
        return [(A[p],) + x for x in B] + [(A[p],)] + B

def main():
    A = [3, 1, 2]
    print('the combination of A is: ', combine(A, 0, len(A)))

main()

Mathematical formula

![][1]
[1]: http://latex.codecogs.com/gif.latex?2^n=(1+1)n=\sum_{k=0}^n\binom{n}{k}

![][2]
[2]: http://latex.codecogs.com/gif.latex?\binom{n}{m}=\frac{n!}{m!(n-m)!}