backtracking.all_subsequences
=============================

.. py:module:: backtracking.all_subsequences

.. autoapi-nested-parse::

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

   Time complexity: O(2^n),
   where n denotes the length of the given sequence.



Attributes
----------

.. autoapisummary::

   backtracking.all_subsequences.seq


Functions
---------

.. autoapisummary::

   backtracking.all_subsequences.create_state_space_tree
   backtracking.all_subsequences.generate_all_subsequences


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

.. py:function:: create_state_space_tree(sequence: list[Any], current_subsequence: list[Any], index: int) -> None

   Creates a state space tree to iterate through each branch using DFS.
   We know that each state has exactly two children.
   It terminates when it reaches the end of the given sequence.

   :param sequence: The input sequence for which subsequences are generated.
   :param current_subsequence: The current subsequence being built.
   :param index: The current index in the sequence.

   Example:
   >>> sequence = [3, 2, 1]
   >>> current_subsequence = []
   >>> create_state_space_tree(sequence, current_subsequence, 0)
   []
   [1]
   [2]
   [2, 1]
   [3]
   [3, 1]
   [3, 2]
   [3, 2, 1]

   >>> sequence = ["A", "B"]
   >>> current_subsequence = []
   >>> create_state_space_tree(sequence, current_subsequence, 0)
   []
   ['B']
   ['A']
   ['A', 'B']

   >>> sequence = []
   >>> current_subsequence = []
   >>> create_state_space_tree(sequence, current_subsequence, 0)
   []

   >>> sequence = [1, 2, 3, 4]
   >>> current_subsequence = []
   >>> create_state_space_tree(sequence, current_subsequence, 0)
   []
   [4]
   [3]
   [3, 4]
   [2]
   [2, 4]
   [2, 3]
   [2, 3, 4]
   [1]
   [1, 4]
   [1, 3]
   [1, 3, 4]
   [1, 2]
   [1, 2, 4]
   [1, 2, 3]
   [1, 2, 3, 4]


.. py:function:: generate_all_subsequences(sequence: list[Any]) -> None

.. py:data:: seq
   :type:  list[Any]
   :value: [1, 2, 3]