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ffaa976f6c
* added doctest for all_permutations.py * added doctest for all_subsequences.py * added doctest for all_subsequences.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * doctest added * updated * Update backtracking/all_subsequences.py --------- Co-authored-by: Harsh Buddhdev <harshbuddhdev5@.com> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
94 lines
2.2 KiB
Python
94 lines
2.2 KiB
Python
"""
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In this problem, we want to determine all possible subsequences
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of the given sequence. We use backtracking to solve this problem.
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Time complexity: O(2^n),
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where n denotes the length of the given sequence.
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"""
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from __future__ import annotations
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from typing import Any
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def generate_all_subsequences(sequence: list[Any]) -> None:
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create_state_space_tree(sequence, [], 0)
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def create_state_space_tree(
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sequence: list[Any], current_subsequence: list[Any], index: int
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) -> None:
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"""
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Creates a state space tree to iterate through each branch using DFS.
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We know that each state has exactly two children.
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It terminates when it reaches the end of the given sequence.
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:param sequence: The input sequence for which subsequences are generated.
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:param current_subsequence: The current subsequence being built.
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:param index: The current index in the sequence.
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Example:
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>>> sequence = [3, 2, 1]
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>>> current_subsequence = []
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>>> create_state_space_tree(sequence, current_subsequence, 0)
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[]
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[1]
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[2]
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[2, 1]
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[3]
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[3, 1]
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[3, 2]
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[3, 2, 1]
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>>> sequence = ["A", "B"]
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>>> current_subsequence = []
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>>> create_state_space_tree(sequence, current_subsequence, 0)
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[]
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['B']
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['A']
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['A', 'B']
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>>> sequence = []
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>>> current_subsequence = []
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>>> create_state_space_tree(sequence, current_subsequence, 0)
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[]
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>>> sequence = [1, 2, 3, 4]
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>>> current_subsequence = []
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>>> create_state_space_tree(sequence, current_subsequence, 0)
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[]
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[4]
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[3]
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[3, 4]
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[2]
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[2, 4]
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[2, 3]
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[2, 3, 4]
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[1]
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[1, 4]
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[1, 3]
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[1, 3, 4]
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[1, 2]
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[1, 2, 4]
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[1, 2, 3]
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[1, 2, 3, 4]
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"""
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if index == len(sequence):
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print(current_subsequence)
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return
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create_state_space_tree(sequence, current_subsequence, index + 1)
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current_subsequence.append(sequence[index])
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create_state_space_tree(sequence, current_subsequence, index + 1)
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current_subsequence.pop()
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if __name__ == "__main__":
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seq: list[Any] = [1, 2, 3]
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generate_all_subsequences(seq)
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seq.clear()
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seq.extend(["A", "B", "C"])
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generate_all_subsequences(seq)
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