Problem Statement:

Given a string, determine the length of the longest palindrome that can be constructed using the characters from the string. Return the maximum possible length of the palindromic string.

Examples:

1. • Input: "applepie"
   • Expected Output: 5
   • Justification: The longest palindrome that can be constructed from the string is "pepep", which has a length of 5. There are are other palindromes too but they all will be of length 5.
2. • Input: "aabbcc"
   • Expected Output: 6
   • Justification: We can form the palindrome "abccba" using the characters from the string, which has a length of 6.
3. • Input: "bananas"
   • Expected Output: 5
   • Justification: The longest palindrome that can be constructed from the string is "anana", which has a length of 5.

Constraints:

• 1 <= s.length <= 2000
• s consists of lowercase and/or uppercase English letters only.

Solution

To solve this problem, we can use a hashmap to keep track of the frequency of each character in the string. The idea is to use pairs of characters to form the palindrome. For example, if a character appears an even number of times, we can use all of them in the palindrome. If a character appears an odd number of times, we can use all except one of them in the palindrome. Additionally, if there's any character that appears an odd number of times, we can use one of them as the center of the palindrome.

1. Initialization: Start by initializing a hashmap to keep track of the characters and their frequencies.

2. Character Counting: Iterate through the string and populate the hashmap with the frequency of each character.

3. Palindrome Length Calculation: For each character in the hashmap, if it appears an even number of times, add its count to the palindrome length. If it appears an odd number of times, add its count minus one to the palindrome length. Also, set a flag indicating that there's a character available for the center of the palindrome.

4. Final Adjustment: If the center flag is set, add one to the palindrome length.

Algorithm Walkthrough:

1. Initialize a HashMap:

   • We'll use a hashmap to store the frequency of each character in the string.

2. Populate the HashMap:

   • For the string "bananas", our hashmap will look like this:
     • b: 1
     • a: 3
     • n: 2
     • s: 1

3. Determine Palindrome Length:

   • We'll iterate through the hashmap to determine the length of the palindrome we can form.

4. Even Frequencies:

   • For characters with even frequencies, we can use all of them in the palindrome. For our string, the character 'n' has an even frequency.
     • 'n' can contribute 2 characters.
   • So far, we have a contribution of 2 characters to the palindrome.

5. Odd Frequencies:

   • For characters with odd frequencies, we can use all but one of them in the palindrome. The central character of the palindrome can be any character with an odd frequency.
   • For our string, characters 'b', 'a', and 's' have odd frequencies.
     • 'b' can contribute 0 characters (leaving out 1).
     • 'a' can contribute 2 characters (leaving out 1).
     • 's' can contribute 0 characters (leaving out 1).
   • Additionally, one of the characters left out from the odd frequencies can be used as the central character of the palindrome. Let's use 'a' for this purpose.
   • So, from the odd frequencies, we have a contribution of 2 characters to the palindrome, plus 1 for the central character.

6. Total Length:

   • Combining the contributions from even and odd frequencies, we get a total palindrome length of 2 (from even frequencies) + 3 (from odd frequencies) = 5.

The longest palindrome that can be constructed from "bananas" is of length 5.

Here is the visual representation of the algorithm: