I am trying to make a function that counts the number of cycles within a permutated list.

I do sometimes get the right answer when running the code, but most times I receive an error message - and I am unable to figure out why.

My code is as follows:

def count_cycles(n):

    cycle_count = 0
    copy_list = []
    
    for element in n:
        copy_list.append(element)

    while len(copy_list) != 0:
        ran_num = random.choice(copy_list)

        while True:
            if n[ran_num] == ran_num:
                cycle_count = circle_count   1
                if int(ran_num) in copy_list:
                    copy_list.remove(ran_num)
                    
                break
            
            else:
                n.insert(ran_num, ran_num)
                print(n, ran_num, copy_list)
                ran_num = n[ran_num   1]
                
                print(ran_num)
                copy_list.remove(ran_num)
                    
                n.remove(ran_num)
                continue

    return print(cycle_count, n)

What I use is that I test with this permutated list with 3 cycles [2, 6, 0, 3, 1, 4, 5].

Picture of output from a correct and incorrect run

I used print(n, ran_num, copy_list) to assess the output as per the picture.

CodePudding user response：

Here is one possibility:

p = [2, 6, 0, 3, 1, 4, 5]

cycles = set()
elts = set(range(len(p)))
while elts:
    cycle = []
    x0 = elts.pop()
    cycle.append(x0)
    x = p[x0]
    while x != x0:
        cycle.append(x)
        x = p[x]
    elts -= set(cycle)
    cycles.add(tuple(cycle))
    
print(cycles)

It gives:

{(0, 2), (1, 6, 5, 4), (3,)}

Then to get the number of cycles you can use len(cycles).

CodePudding user response：

In addition to the existing answer, sympy provides some functionality to work with permutations. In this case, you could use the following:

from sympy.combinatorics import Permutation
p = Permutation([2, 6, 0, 3, 1, 4, 5])
num_cycles = p.cycles # 3