Function create_state_space_tree

backtracking/all_permutations.py:16–74

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

(
    sequence: list[int | str],
    current_sequence: list[int | str],
    index: int,
    index_used: list[int],
)

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.

    :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]
    """

    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()