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The Algorithms

All Permutations

        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.
from __future__ import annotations

def generate_all_permutations(sequence: list[int | str]) -> None:
    create_state_space_tree(sequence, [], 0, [0 for i in range(len(sequence))])

def create_state_space_tree(
    sequence: list[int | str],
    current_sequence: list[int | str],
    index: int,
    index_used: list[int],
) -> None:
    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):

    for i in range(len(sequence)):
        if not index_used[i]:
            index_used[i] = True
            create_state_space_tree(sequence, current_sequence, index + 1, index_used)
            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: list[int | str] = [3, 1, 2, 4]

sequence_2: list[int | str] = ["A", "B", "C"]