Question

Combinatorics is a branch of mathematics that describes how a set of elements can be arranged or organized. Two common metrics used in combinatorics are combinations, the number of ways items in a set can be arranged, and permutations the number of sequential ways a set can be arranged. Write a function that takes a string as input, and will generate a list of all permutations of the characters used in that string. For example, the input ' AB ' would return ' AB ' and 'BA'. Hint: consider breaking the word into a prefix and a suffix. (40 points)

a) ' ABC '

Answer 1

To generate a list of all permutations of the characters in a given string, you can use the concept of recursion.

Step-by-step explanation:

To generate a list of all permutations of the characters in a given string, you can use the concept of recursion. Here's an example of a Python function that accomplishes this:

def generate_permutations(string):
if len(string) == 1:
return [string]
permutations = []
for i in range(len(string)):
prefix = string[i]
suffix = string[:i] + string[i+1:]
for permutation in generate_permutations(suffix):
permutations.append(prefix + permutation)
return permutations

input_string = 'ABC'
permutations = generate_permutations(input_string)
print(permutations)

In this example, the function generate_permutations takes a string as input. It first checks if the length of the string is 1, in which case it returns the string itself as the only permutation.

If the string has a length greater than 1, it iterates over each character of the string and recursively generates permutations for the remaining characters. It then appends the current character to each of these permutations to obtain the complete list of permutations.