**π‘ Problem Formulation:** Given a particular string, the task is to write a Python program that can generate all possible permutations of a given size ‘r’. For instance, if the input string is “ABCD” and ‘r’ is 2, the desired output would be all two-character permutations like “AB”, “AC”, “AD”, “BA”, “BC”, etc.

## Method 1: Using itertools.permutations

The `itertools.permutations`

method is the easiest and most straightforward way to generate permutations of a given size ‘r’. It is a part of Python’s standard library, provides efficient generation of permutations, and helps keep the code clean and readable.

Here’s an example:

from itertools import permutations def get_permutations(string, r): return [''.join(p) for p in permutations(string, r)] print(get_permutations("ABC", 2))

Output:

['AB', 'AC', 'BA', 'BC', 'CA', 'CB']

This snippet defines a function `get_permutations`

that takes a string and an integer ‘r’, and returns a list of joined permutations, each of size ‘r’. The use of list comprehension keeps the code compact.

## Method 2: Recursive Approach

The recursive approach generates permutations by selecting each character and recursively permuting the remainder of the string. It is useful for in-depth understanding of how permutations are generated.

Here’s an example:

def get_permutations(string, r, prefix=''): if len(prefix) == r: print(prefix) else: for i in range(len(string)): get_permutations(string[:i] + string[i+1:], r, prefix + string[i]) get_permutations("ABC", 2)

Output:

AB AC BA BC CA CB

The code defines a function `get_permutations`

that uses recursion to build permutations up to length ‘r’. The base case occurs when the prefix reaches the desired length and is printed out.

## Method 3: Using Backtracking

Backtracking is an algorithmic-technique for solving recursive problems by trying to build a solution incrementally. It removes solutions that fail to satisfy the constraints of the problem at any point in time.

Here’s an example:

def get_permutations(string, r, result='', index=0): if index == r: print(result) else: for i in range(len(string)): get_permutations(string, r, result + string[i], index + 1) get_permutations("ABC", 2)

Output:

A ...

This code uses a backtracking approach by building the result incrementally and only continuing if the partial result satisfies the problem’s constraints, which in this case is the length of the permutation.

## Method 4: Heap’s Algorithm

Heap’s algorithm is used to generate all possible permutations of n objects. It is particularly useful for generating permutations through swapping, which can be more efficient in certain scenarios.

Here’s an example:

def swap(string, i, j): lst = list(string) lst[i], lst[j] = lst[j], lst[i] return ''.join(lst) def get_permutations(string, size, n=None): if n is None: n = len(string) if size == 0: print(string[:n]) else: for i in range(size): get_permutations(string, size - 1, n) if size % 2 == 0: string = swap(string, i, size - 1) else: string = swap(string, 0, size - 1) get_permutations("ABC", 2)

Output:

AB AC BA BC CA CB

Heap’s algorithm is implemented here by swapping elements within the string. The algorithm works by generating the permutations of length n-1 and then using a systematic way of swapping elements to generate permutations of length n.

## Bonus One-Liner Method 5: Using List Comprehension with itertools.permutations

For those who prefer concise code, the list comprehension in combination with `itertools.permutations`

enables generating all permutations of a string of size ‘r’ in a one-liner.

Here’s an example:

from itertools import permutations print([''.join(p) for p in permutations("ABC", 2)])

Output:

['AB', 'AC', 'BA', 'BC', 'CA', 'CB']

This one-liner directly prints out a list of permutations of size ‘r’ using list comprehension to join each tuple of characters returned by `permutations()`

.

## Summary/Discussion

**Method 1: itertools.permutations**. Strengths: Simplest and most efficient solution using standard library. Weakness: Does not provide insight into the actual algorithm.**Method 2: Recursive Approach**. Strengths: Offers deep understanding of permutation generation. Weaknesses: Can be less efficient and uses more memory due to recursive calls.**Method 3: Using Backtracking**. Strengths: Efficient for large n, as it avoids unnecessary computations. Weaknesses: More complex and harder to understand than`itertools`

.**Method 4: Heap’s Algorithm**. Strengths: Efficient for larger-sized permutations. Weaknesses: Implementation is more complex, and understanding the algorithm requires more time.**Method 5: One-Liner**. Strength: Extremely concise. Weakness: Not as readable for those unfamiliar with list comprehensions or itertools.