Given a string str, we need to find the no. of positions where a letter(lowercase) can be inserted so that string becomes a palindrome.
Input : str = "abca" Output : possible palindromic strings: 1) acbca (at position 2) 2) abcba (at position 4) Hence, the output is 2. Input : str = "aaa" Output : possible palindromic strings: 1) aaaa 2) aaaa 3) aaaa 4) aaaa Hence, the output is 4.
Naive Approach:This approach is to insert all 26 alphabets at every position possible i.e., N+1 positions and check at every position if this insertion makes it a palindrome and increase the count.
First you have to observe that we have to make insertion only at the point when the character at that point violates the palindrome condition i.e., . Now, there will be two cases based on the above fact:
Case I: What if the given string is already a palindrome
Then we can only insert at the position such that the insertion does not violate the palindrome.
1) If the length is even then we can always insert any letter in the middle.
2) If the length is odd then we can insert the letter which is in middle, to the left or right to it.
3) In both the cases we can insert the letter which is in middle(let it be ‘CH’), at positions equals to:
(no.of consecutive CH’s to the left of middle letter)*2.
Case II:If it is not a palindrome
As mentioned above we should start inserting at position where , So we increase the count and check for the cases if insertion at any other position makes it a palindrome.
1) If is a palindrome, then we can insert* at any position before until , K in range .(*letter = S[N-i-1])
2.)If is a palindrome, then we can insert* at any position after until , K in range .(*letter = S[i])
In all the cases we keep increasing the count.
This article is contributed by Harsha Mogali. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
- Number of Positions to partition the string such that atleast m characters with same frequency are present in each substring
- Print the arranged positions of characters to make palindrome
- String containing first letter of every word in a given string with spaces
- Minimum number of deletions to make a string palindrome | Set 2
- Number of Counterclockwise shifts to make a string palindrome
- Minimum number of deletions to make a string palindrome
- Minimum number of characters to be replaced to make a given string Palindrome
- Minimum number of Appends needed to make a string palindrome
- Count of words whose i-th letter is either (i-1)-th, i-th, or (i+1)-th letter of given word
- First uppercase letter in a string (Iterative and Recursive)
- Get the first letter of each word in a string using regex in Java
- Check if the string contains consecutive letters and each letter occurs exactly once
- Get K-th letter of the decoded string formed by repeating substrings
- Reverse a string preserving space positions
- Find numbers of balancing positions in string