Given a string of length n. Find the minimum number of possible cuts after rearranging the string (if required), such that each cut is a palindrome and length of every cut is equal. That is, find the minimum number of palindromes of equal lengths that can be obtained by partitioning the given string if rearrangement of string is allowed before partitioning.
Input : string = "aabaac" Output : 2 Explanation : Rearrange the string as "abaaca" and cut into "aba" and "aca" Input : string = "aabbccdd" Output : 1 Explanation : Rearrange the string as "abcddcba" This is a palindrome and cannot be cut further.
If we observe carefully, our problem reduces to calculating characters with odds and even counts. Below are the possible cases,
- If the characters present in the string have only even counts then the answer will be 1 as we can rearrange the entire string to form a palindrome.
If there is only one character with odd count, then also the answer will be 1 as we can
rearrange the entire string to form a palindrome.
- If there is more than one character with odd count, then we will create two separate list of characters – one for odd characters and one for even characters. Now, if we notice that if a character has odd count then if we subtract 1 from it, the count will become even. So we will insert the element with odd counts only once in the odd list. We will insert the elements with even counts (evenCount/2) times, i.e. half of their count in the even list. Now our problem is to uniformly distribute the even count elements among odd count elements to form palindromes of equal length. Suppose the list of even count characters is even and odd count characters is odd. If even.size() is divisible by odd.size() our answer will be odd.size() otherwise we will transfer elements from even list to odd list until even.size() is divisible by odd.size().
Below is the implementation of above idea:
- Minimum cuts required to convert a palindromic string to a different palindromic string
- Minimum insertions to form a palindrome with permutations allowed
- Minimum number of palindromic subsequences to be removed to empty a binary string
- Make palindromic string non-palindromic by rearranging its letters
- Longest Palindromic Substring using Palindromic Tree | Set 3
- Minimum operations to make frequency of all characters equal K
- Minimum operation to make all elements equal in array
- Minimum move to end operations to make all strings equal
- Minimum length String with Sum of the alphabetical values of the characters equal to N
- Minimum number of swaps to make two binary string equal
- Minimum number of given operations required to make two strings equal
- Minimum Bitwise XOR operations to make any two array elements equal
- Minimum Bitwise AND operations to make any two array elements equal
- Form lexicographically smallest string with minimum replacements having equal number of 0s, 1s and 2s
- Find the minimum number of preprocess moves required to make two strings equal
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