AB Equality Create a recursive function in a file called ab_equality.py: def ab equalín

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AB Equality Create a recursive function in a file called ab_equality.py: def ab equalín, k, current) Print out all of the strings of a’s and b’s of length n so that the number of a’s and b’s are equal. For n = 2, there’s ab and ba. For n = 3 there are no strings since they’d have to have 2 a’s and lb, or 2 b’s a la so not equal. For n = 4, there

Problem 3 – AB Equality Create a recursive function in a file called ab_equality.py: def ab equalín, k, current) Print out all of the strings of a’s and b’s of length n so that the number of a’s and b’s are equal. For n = 2, there’s ab and ba. For n = 3 there are no strings since they’d have to have 2 a’s and lb, or 2 b’s a la so not equal. For n = 4, there will be 6 of these strings, and for n = 5, zero again. Hint: use k to track the difference between a’s and b’s. So for instance if your current is aaabb then k should be equal to either 1 or -1 (your choice depending). When you call the function, you should call it from your main or testing function with the length in the n parameter, O should be put into the k parameter, and then an empty string will be passed in for current. What length do you want to run? 4 aabb abab abba baab baba bbaa linux5[110] % python3 ab_equality.py What length do you want to run? 6 aaabbb aababb aabbab aabbba abaabb ababab ababba abbaab abbaba abbbaa baaabb baabab baabba babaab bababa babbaa bbaaab bbaaba bbabaa bbbaaa

The Correct Answer and Explanation is :

To generate all strings of ‘a’s and ‘b’s of length n where the number of ‘a’s equals the number of ‘b’s, we can utilize a recursive approach. This method systematically builds strings by adding ‘a’s and ‘b’s while ensuring that at any point, the number of ‘a’s does not exceed the number of ‘b’s, maintaining balance.

Here’s how you can implement this in Python:

def ab_equality(n, k, current):
    if len(current) == n:
        print(current)
        return
    if k < n // 2:
        ab_equality(n, k + 1, current + 'a')
    if k > len(current) - k:
        ab_equality(n, k, current + 'b')

if __name__ == "__main__":
    n = int(input("What length do you want to run? "))
    ab_equality(n, 0, "")

Explanation:

  1. Function Definition:
  • ab_equality(n, k, current): A recursive function that generates and prints all balanced strings of length n. Here:
    • n: Total length of the string.
    • k: Tracks the number of ‘a’s added so far.
    • current: The current string being built.
  1. Base Case:
  • if len(current) == n:: When the length of current equals n, the string is complete and balanced. It is then printed.
  1. Recursive Cases:
  • if k < n // 2:: If the number of ‘a’s added is less than half of n, add an ‘a’ and recurse.
  • if k > len(current) - k:: If the number of ‘b’s added is less than the number of ‘a’s, add a ‘b’ and recurse.
  1. Main Block:
  • Prompts the user to input the desired length n and initiates the recursive function with k = 0 and an empty current string.

Example Output:

For n = 4, the output will be:

aabb
abab
abba
baab
baba
bbaa

Explanation of the Approach:

  • Recursive Backtracking: The function explores all possible combinations of ‘a’s and ‘b’s by adding one character at a time and recursing. The conditions ensure that at any point, the number of ‘a’s does not exceed half of n, and the number of ‘b’s does not exceed the number of ‘a’s, maintaining balance.
  • Efficiency: This approach efficiently generates only the valid balanced strings, avoiding the need to generate all possible strings and then filter them.
  • User Interaction: The program prompts the user for the desired length n and displays the corresponding balanced strings.

This method leverages the power of recursion to elegantly solve the problem, ensuring that all generated strings are balanced and of the specified length.

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