__author__ = "Maryam Bahrani"

""" Permutation statistics 
    Computes the exact ratio of permuations of a fixed length
    with no singleton or doubleton cycles. Note that a brute
    force method is used, so the code is too slow for n >> 10.
    
    sample usage:
    $ python perm.py
    Number of elements to permute: 10
"""

import click
import numpy
from itertools import permutations

""" accepts a permutation that has no singleton or doubleton cycle """
def isValid(a):
    for i in range(len(a)):
        if a[i] == i or a[a[i]]==i:
            return False
    return True

""" Returns the number of permutations of length n with no singleton
    or doubleton cycles """
def countPerms(n):
    num = 0
    for a in permutations(range(n)):
        if isValid(a):
            num += 1
    return num

@click.command()
@click.option('--n', prompt = 'Number of elements to permute',
              default = "10",
              help = 'The number of elements to permute.')
def run(n):
    numValid = countPerms(int(n))
    click.echo("Number of permutations of length %s with no singleton or doubleton cycles: %s."
               % (n, numValid))
    numAll = numpy.math.factorial(int(n))
    click.echo("Number of permutations of length %s with no constraints: %s."
               % (n, numAll))
    click.echo("The ratio: %f." % ((numValid+.0)/numAll,))

if __name__ == '__main__':
  run()