From cc4cf3ece7e10f15435365ee331c3530f6c777f5 Mon Sep 17 00:00:00 2001 From: Erfan Alimohammadi Date: Sat, 6 Jul 2019 17:43:50 +0430 Subject: [PATCH] Generate all subsequences using backtracking (#961) * Add all_subsequences to backtracking directory --- backtracking/all_subsequences.py | 42 ++++++++++++++++++++++++++++++++ 1 file changed, 42 insertions(+) create mode 100644 backtracking/all_subsequences.py diff --git a/backtracking/all_subsequences.py b/backtracking/all_subsequences.py new file mode 100644 index 000000000..d86837723 --- /dev/null +++ b/backtracking/all_subsequences.py @@ -0,0 +1,42 @@ +''' + 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. +''' + + +def generate_all_subsequences(sequence): + create_state_space_tree(sequence, [], 0) + + +def create_state_space_tree(sequence, current_subsequence, index): + ''' + 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. + ''' + + if index == len(sequence): + print(current_subsequence) + return + + create_state_space_tree(sequence, current_subsequence, index + 1) + current_subsequence.append(sequence[index]) + create_state_space_tree(sequence, current_subsequence, index + 1) + current_subsequence.pop() + + +''' +remove the comment to take an input from the user + +print("Enter the elements") +sequence = list(map(int, input().split())) +''' + +sequence = [3, 1, 2, 4] +generate_all_subsequences(sequence) + +sequence = ["A", "B", "C"] +generate_all_subsequences(sequence)