Given n and k, Construct a palindrome of size n using a binary number of size k repeating itself to wrap into the palindrome. The palindrome must always begin with 1 and contains maximum number of zeros.
Input : n = 5, k = 3 Output : 11011 Explanation : the 3 sized substring is 110 combined twice and trimming the extra 0 in the end to give 11011. Input : n = 2, k = 8 Output : 11 Explanation : the 8 sized substring is 11...... wrapped to two places to give 11.
The naive approach would be to try every palindrome of size k starting with 1 such that a palindrome of size n is formed. This approach has an exponential complexity.
A better way to do this is to initialize the k sized binary number with the index and connect the palindrome in the way it should be. Like last character of palindrome should match to first, find which indexes will be present at those locations and link them. Set every character linked with 0th index to 1 and the string is ready. This approach will have a linear complexity.
In this approach, first lay the index of the k sized binary to hold into an array, for example if n = 7, k = 3 arr becomes [0, 1, 2, 0, 1, 2, 0]. Following that in the connectchars graph, connect the indices of the k sized binary which should be same by going through the property of palindrome which is kth and (n – k – 1)th variable should be same, such that 0 is linked to 1(and vice versa), 1 is linked to 2(and vice versa) and so on. After that, check what is linked with 0 in connectchars array and make all of the associated indices one (because the first number should be non-zero) by using dfs approach. In the dfs, pass 0, the final answer string and the graph. Begin by making the parent 1 and checking if its children are zero, if they are make them and their children 1. This makes only the required indices of the k sized string one, others are left zero. Finally, the answer contains the 0 to k – 1 indexes and corresponding to arr the digits are printed.
Time Complexity : O(n)
Don’t stop now and take your learning to the next level. Learn all the important concepts of Data Structures and Algorithms with the help of the most trusted course: DSA Self Paced. Become industry ready at a student-friendly price.
- Construct lexicographically smallest palindrome
- Minimum steps to delete a string after repeated deletion of palindrome substrings
- Construct a binary string following the given constraints
- Construct Binary Tree from Ancestor Matrix | Top Down Approach
- Construct Binary Tree from given Parent Array representation | Iterative Approach
- Binary String of given length that without a palindrome of size 3
- Python | Check if binary representation is palindrome
- Check if Inorder traversal of a Binary Tree is palindrome or not
- Check if actual binary representation of a number is palindrome
- Longest sub string of 0's in a binary string which is repeated K times
- Count of root to leaf paths whose permutation is palindrome in a Binary Tree
- Sentence Palindrome (Palindrome after removing spaces, dots, .. etc)
- Count all palindrome which is square of a palindrome
- Find top three repeated in array
- N/3 repeated number in an array with O(1) space
- Smallest element in an array that is repeated exactly 'k' times.
- Largest element in the array that is repeated exactly k times
- Number of subsequences of maximum length K containing no repeated elements
- Maximum subarray sum in an array created after repeated concatenation
- Minimum array size after repeated replacement of even sum pair with sum
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.