Good morning! Here's our prompt for today.

Write an algorithm that takes an input string like "abc", and prints out all possible permutations of the string. A permutation of a group of elements is defined as one of the n! number possible arrangements the elements can take, where n is the number of elements in the range.

We'd expect the following to hold true, note the permutations printed out:

1str = "abc"
2permutations(str)
3# abc
4# acb
5# bac
6# bca
7# cba
8# cab

A hint here: break the problem down, and think about what steps are going to be repeated. How would we get from "abc" to "acb"?

Constraints

• The string will only consist of lowercase letters
• Length of the string <= 7
• Expected time complexity : O(n*n!)
• Expected space complexity : O(n*n!)

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​

def permutations(string):

    # fill in

    return string

​

​

import unittest

​

​

class Test(unittest.TestCase):

    def test_1(self):

        assert permutations("abc") == ["abc", "acb", "bac", "bca", "cab", "cba"]

        print(

            "PASSED: assert permutations('abc') == ['abc', 'acb', 'bac', 'bca', 'cab', 'cba']"

        )

​

    def test_2(self):

        assert permutations("a") == ["a"]

        print("PASSED: assert permutations('a') == ['a']")

​

    def test_3(self):

        assert permutations("rand") == [

            "rand",

            "radn",

            "rnad",

            "rnda",

            "rdan",

            "rdna",

            "arnd",

            "ardn",

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