backtracking.all_permutations
=============================

.. py:module:: backtracking.all_permutations

.. autoapi-nested-parse::

   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.



Attributes
----------

.. autoapisummary::

   backtracking.all_permutations.sequence
   backtracking.all_permutations.sequence_2


Functions
---------

.. autoapisummary::

   backtracking.all_permutations.create_state_space_tree
   backtracking.all_permutations.generate_all_permutations


Module Contents
---------------

.. py:function:: 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.

   :param sequence: The input sequence for which permutations are generated.
   :param current_sequence: The current permutation being built.
   :param index: The current index in the sequence.
   :param index_used: list to track which elements are used in permutation.

   Example 1:
   >>> sequence = [1, 2, 3]
   >>> current_sequence = []
   >>> index_used = [False, False, False]
   >>> create_state_space_tree(sequence, current_sequence, 0, index_used)
   [1, 2, 3]
   [1, 3, 2]
   [2, 1, 3]
   [2, 3, 1]
   [3, 1, 2]
   [3, 2, 1]

   Example 2:
   >>> sequence = ["A", "B", "C"]
   >>> current_sequence = []
   >>> index_used = [False, False, False]
   >>> create_state_space_tree(sequence, current_sequence, 0, index_used)
   ['A', 'B', 'C']
   ['A', 'C', 'B']
   ['B', 'A', 'C']
   ['B', 'C', 'A']
   ['C', 'A', 'B']
   ['C', 'B', 'A']

   Example 3:
   >>> sequence = [1]
   >>> current_sequence = []
   >>> index_used = [False]
   >>> create_state_space_tree(sequence, current_sequence, 0, index_used)
   [1]


.. py:function:: generate_all_permutations(sequence: list[int | str]) -> None

.. py:data:: sequence
   :type:  list[int | str]
   :value: [3, 1, 2, 4]


.. py:data:: sequence_2
   :type:  list[int | str]
   :value: ['A', 'B', 'C']