Generate all permutations of a sequence, using backtracking (#962)

* Fix typo

* Add all_permutations algorithm to backtracking directory

Author: Erfaniaa

backtracking/all_permutations.py

@@ -0,0 +1,45 @@
+'''
+	In this problem, we want to determine all possible permutations
+	of the given sequence. We use backtracking to solve this problem.
+
+	Time complexity: O(n!),
+	where n denotes the length of the given sequence.
+'''
+
+
+def generate_all_permutations(sequence):
+	create_state_space_tree(sequence, [], 0, [0 for i in range(len(sequence))])
+
+
+def create_state_space_tree(sequence, current_sequence, index, index_used):
+	'''
+	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.
+	'''
+
+	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()
+			index_used[i] = False
+
+
+'''
+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_permutations(sequence)
+
+sequence = ["A", "B", "C"]
+generate_all_permutations(sequence)