Generate all subsequences using backtracking (#961)

* Add all_subsequences to backtracking directory

Author: Erfaniaa

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)