"""
Find all the permutations of a given string
Sample input: 'ABC'
Expected output: ['ABC', 'ACB', 'BAC', 'BCA', 'CAB', 'CBA']
Description: The algorithm is recursive. In each recursion, each element of the string (left) is removed and added to the beginning (head). This process is repeated until left is empty.
Time complexity: (n!)
"""

def permutation(head, left, permutations):
    if len(left) == 0:
        permutations.append(head)
    else:
        for i in range(len(left)):
            permutation(head+left[i], left[:i]+left[i+1:], permutations)

def find_all_permutations(string):
    permutations = []
    permutation('', string, permutations)
    return permutations

if __name__ == "__main__": 
    input = 'ABC'
    output = find_all_permutations(input)

    expected = ['ABC', 'ACB', 'BAC', 'BCA', 'CAB', 'CBA']
    assert len(output) == len(expected), f"Expected 6 permutations, got: {len(expected)}"
    for perm in expected:
        assert perm in output, f"Expected permutation {perm} to be in output, missing"