# 1. Introduction

The "Palindrome Permutation" problem combines concepts of string manipulation, palindromes, and permutation theory. It explores whether the letters of a given string can be rearranged to form a palindrome. This problem is prevalent in computer science, particularly in areas focusing on algorithms for string processing and combinatorics.

## Problem

Given a string, determine if a permutation of the string could form a palindrome. A palindrome is a word or phrase that reads the same backward as forward. The solution should identify whether the characters of the string can be rearranged to achieve this property.

# 2. Solution Steps

1. Use a hash set to store characters.

2. Iterate through each character in the string.

3. For each character, if it's not in the set, add it; if it's already in the set, remove it.

4. By the end of the iteration, check the size of the set.

5. If the size is 0 or 1, the string can form a palindrome (since the middle character in a palindrome can be unique).

6. If the size is greater than 1, it cannot form a palindrome.

# 3. Code Program

``````def canPermutePalindrome(s):
charSet = set()
for char in s:
if char in charSet:
charSet.remove(char)
else:
return len(charSet) <= 1

# Example Usage
print(canPermutePalindrome("code"))  # Output: False
print(canPermutePalindrome("aab"))   # Output: True
print(canPermutePalindrome("carerac"))  # Output: True
``````

```False
True
True
```

### Explanation:

1. HashSet for Character Tracking: Efficiently tracks the occurrence of each character.

2. Character Addition and Removal: Adds/removes characters to/from the set based on their occurrence.

3. Final Check: If the set has 0 or 1 characters, a palindrome permutation is possible.

4. Odd Characters: Allows for one unique character, which can be the center of a palindrome.

5. Time Complexity: Achieves O(n) time complexity, where n is the length of the string.

6. Practical Use Case: Useful in text analysis and cryptography where palindrome properties are of interest.