How to check if permutations have equal parity?

Question

I am looking for a way to check if 2 permutations (represented by lists) are of the same parity. Note that I am not interested if they are even or odd parity, just the equality.

I am new to Python and my naive solution is given below as a reply. I am looking forward to Python gurus showing me some cool tricks to achieve the same in lesser, more elegant Python code.

Answer 1

Here's slightly refactored Weeble's answer:

def arePermsEqualParity(perm0, perm1):
    """Whether permutations are of equal parity."""
    return parity(combine(perm0, perm1))

def combine(perm0, perm1):
    """Combine two permutations into one."""
    return map(perm0.__getitem__, perm1)

def parity(permutation):
    """Return even parity for the `permutation`."""
    return (len(permutation) - ncycles(permutation)) % 2 == 0

def ncycles(permutation):
    """Return number of cycles in the `permutation`."""
    ncycles = 0
    seen = [False] * len(permutation)
    for i, already_seen in enumerate(seen):
        if not already_seen:
            ncycles += 1
            # mark indices that belongs to the cycle
            j = i 
            while not seen[j]: 
                seen[j] = True
                j = permutation[j]
    return ncycles