Python/backtracking/all_permutations.py

"""
        In this problem, we want to determine all possible permutations
        of the given sequence. We use backtracking to solve this problem.

        Time complexity: O(n! * n),
        where n denotes the length of the given sequence.
"""


def generate_all_permutations(sequence):
    create_state_space_tree(sequence, [], 0, [0 for i in range(len(sequence))])


def create_state_space_tree(sequence, current_sequence, index, index_used):
    """
    Creates a state space tree to iterate through each branch using DFS.
    We know that each state has exactly len(sequence) - index children.
    It terminates when it reaches the end of the given sequence.
    """

    if index == len(sequence):
        print(current_sequence)
        return

    for i in range(len(sequence)):
        if not index_used[i]:
            current_sequence.append(sequence[i])
            index_used[i] = True
            create_state_space_tree(sequence, current_sequence, index + 1, index_used)
            current_sequence.pop()
            index_used[i] = False


"""
remove the comment to take an input from the user

print("Enter the elements")
sequence = list(map(int, input().split()))
"""

sequence = [3, 1, 2, 4]
generate_all_permutations(sequence)

sequence = ["A", "B", "C"]
generate_all_permutations(sequence)