p209

p209.py

def find_next(curr):
    #Helper function to find cycles
    t = bin(curr)[2:][::-1]
    b = [int(x) for x in t + '0'*(6 - len(t))]
    nb = b[1:] + [b[0] ^ (b[1] & b[2])]
    snb = ''.join([str(x) for x in nb])
    curr = int(snb[::-1], 2)
    return curr

def lucas(n):
    #Finds n-th Lucas number using my Fibonacci number generator
    f2, f1, f0 = 1, 1, 0
    for bit in bin(n)[3:]:
        v = f1*f1
        f2, f1, f0 = f2 * f2 + v, (f2 + f0) * f1, v + f0 * f0
        if bit == '1':
            f2, f1, f0 = f2 + f1, f2, f1   
    return f2 + f0

def compute():
    pointer = [None] * 64
    total = 1
    while None in pointer:
        for start, x in enumerate(pointer):
            if x == None:
                break
            
        curr = find_next(start)
        pointer[start] = curr
        cycle = (start, curr)
        while curr != start:
            t = find_next(curr)
            cycle += (t, )
            pointer[curr] = t
            curr = t
        
        total *= lucas(len(cycle) - 1)
    
    return total