Python Program to find all Palindromic Bitlists in length
Last Updated :
05 Sep, 2024
In this article, we will learn to generate all Palindromic Bitlists of a given length using Backtracking in Python. Backtracking can be defined as a general algorithmic technique that considers searching every possible combination in order to solve a computational problem. Whereas, Bitlists are lists of bits(0 and 1). A bit list that is a palindrome is called Palindromic Bitlists. To generate all Palindromic Bitlists of length N, the best way is to generate all possible bit lists of length N/2 and then form palindromic Bitlist using this list of length N/2. Here we will discuss 2 cases:
Case 1: When the length of the list is odd
Let’s consider the value of N = 3. So, N/2 = 1 (floor value).
All possible bit lists of length 1 are [0], [1]. In this case, we can not do exact same thing which we have done for the even length case because doing that thing will give a bit list of length 2 and not 3. Here we will add [0] or [1] in mid of bit list. Consider [0], its reverse will be [0]. To generate bit lists we have to combine 3 lists that are generated bit lists of length 1, [0], Or [1], the reverse of the generated list. Here every bit list will produce 2-bit lists. For [0] there will be [0] + [0] +[0] and [0] + [1] +[0].
Example: The value of N is 5
Python
# list to store all the possible solutions
fianl_ans = []
# this function generates all possible bitlists
# of length N//2 and then saves the final answer
# in the list
def generate_palindromic(n, is_even, lst=[]):
# n==0 is the base condition and after
# reaching here we don't go forward
if n == 0:
if is_even:
# even case
# final_ans = generated list + reverse
# of generated list
fianl_ans.append((lst + lst
[-1::-1]))
else:
# odd case
# final_ans_1 = generated list +
# [0] + reverse of generated list
fianl_ans.append(lst + [0] +
lst[-1::-1])
# final_ans_1 = generated list
# + [1] + reverse of generated list
fianl_ans.append(lst + [1] +
lst[-1::-1])
return
# store 0 in the list to provide the value of
# this step to the next step
lst.append(0)
# call recursive function and decrease
# the value of n by 1
generate_palindromic(n-1, is_even, lst)
# remove 0 from the list (Backtrack)
lst.pop()
# store 1 in the list to provide the value
# of this step to the next step
lst.append(1)
# call recursive function and decrease
# the value of n by 1
generate_palindromic(n-1, is_even, lst)
# remove 1 from the list (Backtrack)
lst.pop()
def check(n):
if n % 2 == 0:
# if n is even then pass 1 to the
# recursive function
generate_palindromic(n/2, 1)
else:
# if n is odd then pass 0 to the
# recursive function
generate_palindromic(n//2, 0)
if __name__ == "__main__":
# calling function to generate all
# bitlists of length 5
check(5)
# printing final answers
for i in fianl_ans:
print(i)
Output:
Â
Case 2: When the length of the list is even
Let’s consider the value of N = 4. So, N/2 = 2.
All possible bit lists of length 2 are [0,0], [0,1], [1,0], [1,1]. Consider [0,1], its reverse will be [1,0]. Combining both of them we will get [0,1,1,0] which is a Palindromic bit list of length 4. In this way, we can generate all Palindromic Bitlists of length N where N is even.
Example: The value of N is 4
Python
# list to store all the possible solutions
fianl_ans = []
# this function generates all possible bitlists
# of length N//2 and then saves the final answer in the list
def generate_palindromic(n, is_even, lst=[]):
# n==0 is the base condition and after
# reaching here we don't go forward
if n == 0:
if is_even:
# even case
# final_ans = generated list + reverse
# of generated list
fianl_ans.append((lst +
lst[-1::-1]))
else:
# odd case
# final_ans_1 = generated list +
# [0] + reverse of generated list
fianl_ans.append(lst + [0] +
lst[-1::-1])
# final_ans_1 = generated list +
# [1] + reverse of generated list
fianl_ans.append(lst + [1] +
lst[-1::-1])
return
# store 0 in the list to provide the value of
# this step to the next step
lst.append(0)
# call recursive function and decrease the
# value of n by 1
generate_palindromic(n-1, is_even, lst)
# remove 0 from the list (Backtrack)
lst.pop()
# store 1 in the list to provide the
# value of this step to the next step
lst.append(1)
# call recursive function and decrease
# the value of n by 1
generate_palindromic(n-1, is_even, lst)
# remove 1 from the list (Backtrack)
lst.pop()
def check(n):
if n % 2 == 0:
# if n is even then pass 1 to
# the recursive function
generate_palindromic(n/2, 1)
else:
# if n is odd then pass 0 to
# the recursive function
generate_palindromic(n//2, 0)
if __name__ == "__main__":
# calling function to generate all
# bitlists of length 5
check(4)
# printing final answers
for i in fianl_ans:
print(i)
Output:
Â
The time complexity of both Case 1 and Case 2 of the Python program to find all Palindromic Bitlists of a given length using backtracking is O(2^(N/2)), where N is the length of the bitlist.The space complexity of both Case 1 and Case 2 algorithms is O(2^(N/2)), where N is the length of the palindromic bitlist.
This is because the algorithms generate all possible palindromic bitlists of length N, which is equal to generating all possible bitlists of length N/2 and then combining them in a palindromic manner. Therefore, the space required to store all possible bitlists of length N/2 is O(2^(N/2)), which is the maximum space required by both the algorithms.
In both cases, the bitlists are generated recursively and stored in a list, which is then appended to the final_ans list. The maximum size of this list would be O(2^(N/2)), as there are 2^(N/2) possible bitlists of length N/2. Hence, the space complexity of both algorithms is O(2^(N/2)).
Similar Reads
Python Program to Remove Palindromic Elements from a List
Given a list, the task here is to write Python programs that can remove all the elements which have palindromic equivalent element present in the list. Examples: Input : test_list = [54, 67, 12, 45, 98, 76, 9] Output : [12, 98] Explanation : 67 has 76 as palindromic element, both are omitted. Input
2 min read
Python program to check if number is palindrome (one-liner)
In this article, we are given a number and we have to check whether the number is palindrome or not in one-liner code. The output will be True if it's a Palindrome number otherwise it would be False. Let's discuss how to find whether a number is palindrome or not in this article. Input1: test_number
3 min read
Python Program To Check If A Singly Linked List Is Palindrome
Given a singly linked list of characters, write a function that returns true if the given list is a palindrome, else false. Recommended: Please solve it on "PRACTICE" first, before moving on to the solution. METHOD 1 (Use a Stack): A simple solution is to use a stack of list nodes. This mainly invol
6 min read
Python Program For Checking Linked List With A Loop Is Palindrome Or Not
Given a linked list with a loop, the task is to find whether it is palindrome or not. You are not allowed to remove the loop. Examples: Input: 1 -> 2 -> 3 -> 2 /| |/ ------- 1 Output: Palindrome Linked list is 1 2 3 2 1 which is a palindrome. Input: 1 -> 2 -> 3 -> 4 /| |/ ------- 1
4 min read
Python Program for Longest Palindromic Subsequence | DP-12
Given a sequence, find the length of the longest palindromic subsequence in it. As another example, if the given sequence is "BBABCBCAB", then the output should be 7 as "BABCBAB" is the longest palindromic subsequence in it. "BBBBB" and "BBCBB" are also palindromic subsequences of the given sequence
2 min read
Print all palindrome numbers in a list - Python
A palindrome number is a number that remains the same when its digits are reversed. In this article, we will check How to print all palindrome numbers in a list in Python. Using String ReversalIn this method, we convert the number into a string and check if it is the same when reversed. This approac
2 min read
Python Program To Check If A Linked List Of Strings Forms A Palindrome
Given a linked list handling string data, check to see whether data is palindrome or not? Examples: Input: a -> bc -> d -> dcb -> a -> NULL Output: True String "abcddcba" is palindrome. Input: a -> bc -> d -> ba -> NULL Output: False String "abcdba" is not palindrome. Reco
2 min read
Python program to check if given string is vowel Palindrome
Given a string (may contain both vowel and consonant letters), remove all consonants, then check if the resulting string is palindrome or not. Examples: Input : abcuhuvmnba Output : YES Explanation : The consonants in the string "abcuhuvmnba" are removed. Now the string becomes "auua". Input : xayzu
5 min read
Test if List is Palindrome - Python
We are given a list we need to find that given list is a palindrome. For example a = [1, 2, 3, 2, 1] we need to check whether it is a palindrome or not so that the output should be 'True'. Using SlicingWe can check if a list is a palindrome by comparing it with its reverse using slicing ([::-1]). If
2 min read
Python Program to Find the Longest Bitonic Subsequence
Given an array arr[0 ... n-1] containing n positive integers, a subsequence of arr[] is called Bitonic if it is first increasing, then decreasing. Write a function that takes an array as argument and returns the length of the longest bitonic subsequence. A sequence, sorted in increasing order is con
3 min read