How can I maximally partition a set?

Question

I\'m trying to solve one of the Project Euler problems. As a consequence, I need an algorithm that will help me find all possible partitions of a set, in any order.

Answer 1

Here is the code you need for this part of your problem:

def memoize(f):
    memo={}
    def helper(x):
        if x not in memo:
            memo[x]=f(x)
        return memo[x]
    return helper

@memoize
def A000041(n):
    if n == 0: return 1
    S = 0
    J = n-1
    k = 2
    while 0 <= J:
        T = A000041(J)
        S = S+T if k//2%2!=0 else S-T
        J -= k if k%2!=0 else k//2
        k += 1
    return S

print A000041(100) #the 100's number in this series, as an example