当给定一个返回列表的下一个排列的函数时，查找列表的所有排列

Question

In my assignment this week I was asked to write a python script that takes a number n and returns all permutations of [0,1,2,...,n-1]. So far I have written a script that takes a list and returns the next permutation of the list. I am looking for ideas on how I can write the script based on what I've written so far.

def next_permutation(p):
    a = len(p)
    i = a -2 
    while i >= 0 and p[i] >= p[i+1]:
        i = i-1
    if i == -1:
        return []

    j = i+1
    while j < a and p[j] >= p[i]:
        j += 1
    j-=1

    p[i], p[j] = p[j], p[i]

    k = i + 1
    l = a - 1

    while k < l:
        p[k], p[l] = p[l], p[k]
        k += 1
        l -= 1
    return p

EDIT: this is the code that returns the next permutation of a list. I wrote this entirely based on the instruction provided by my instructor.

Answer 1

Since you want to have all the permutations of a list with numbers from 0 to n-1, you already have clear steps that you need to take:

1. Create a list that contains all numbers from 0 to n-1:

This can be easily done with the in-built range() function since it is mostly used for exactly that purpose:

range(stop)

This is a versatile function to create iterables yielding arithmetic progressions.

2. Calculate the amount of permutations that such list would have:

Math tells us that having N elements, there will be N! different permutations of those elements, wher ! means factorial. We can import factorial function from math module which would quickly allow us to calculate the amount of permutations your list will have:

from math import factorial
print(factorial(4)) # 24

3. Call your function next_permutation(p) that you already wrote that many times and yield each and every permutation.

To return something more than once from a function, you can use yield insted.

With these steps in mind, you can create something similar to this:

def all_permutations(n):

    # Constructing a list that contains all numbers from 0 to n-1
    integer_list = list(range(n))

    # Calculating the amount of permutations such list would have
    permutation_count = factorial(n)

    # Output that many permutations
    for _ in range(permutation_count):
        yield integer_list
        integer_list = next_permutation(integer_list)

This generator function will yield all permutations of a list containing numbers from 0 to n-1 which is exactly what you need.

To create a list that would contain all of the permutations you can write something simple like:

n = 4
all_permutations = list(all_permutations(n))