Given a string, find out if the string is K-Palindrome or not. A K-palindrome string transforms into a palindrome on removing at most k characters from it.
Input : String - abcdecba, k = 1 Output : Yes String can become palindrome by removing 1 character i.e. either d or e Input : String - abcdeca, K = 2 Output : Yes Can become palindrome by removing 2 characters b and e (or b and d). Input : String - acdcb, K = 1 Output : No String can not become palindrome by removing only one character.
The idea is to find the longest palindromic subsequence of the given string. If the difference between longest palindromic subsequence and the original string is less than equal to k, then the string is k-palindrome else it is not k-palindrome.
For example, longest palindromic subsequence of string abcdeca is acdca(or aceca). The characters which do not contribute to longest palindromic subsequence of the string should be removed in order to make the string palindrome. So on removing b and d (or e) from abcdeca, string will transform into a palindrome.
Longest palindromic subsequence of a string can easily be found using LCS. Following is the two step solution for finding longest palindromic subsequence that uses LCS.
- Reverse the given sequence and store the reverse in another array say rev[0..n-1]
- LCS of the given sequence and rev will be the longest palindromic sequence.
Below is C++ implementation of above idea –
Time complexity of above solution is O(n2).
Auxiliary space used by the program is O(n2). It can further be reduced to O(n) by using Space Optimized Solution of LCS.
Thanks to Ravi Teja Kaveti for suggesting above solution.
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