Sign of a permutation

sgn.py

def find_a_cycle(x, start):
    cycle = [start]
    s = start
    while x[s] != start:
        cycle.append(x[s])
        s = x[s]
        
    return cycle 

def find_cycles(x):
    """find cycles in a permutation of [0, 1, ..., len(x) - 1]"""
    cycles = []
    remaining = set(range(len(x)))
    
    while remaining != set():
        start = next(iter(remaining))
        cycle = find_a_cycle(x, start)
        cycles.append(cycle)
        remaining = remaining.difference(cycle)
    
    return cycles

def sgn(x):
    cycles = find_cycles(x)
    num_transpositions = sum(len(cycle) - 1 for cycle in cycles)
    return 1 if num_transpositions % 2 == 0 else -1

if __name__ == "__main__":
    assert sgn([1, 0, 2]) == -1
    assert sgn([2, 1, 0, 3]) == -1
    assert sgn([1, 2, 0, 3]) == 1