ABA Pattern Recognition in Strings

The ABA problem involves determining if a given string conforms to the ABA pattern. This means the string can be divided into three parts (A, B, and A) such that the first and third parts are identical. This challenge tests your ability to manipulate strings and implement conditional logic in Rust, a common task in text processing and pattern matching.

Problem Description

You are tasked with writing a Rust function that takes a string as input and returns true if the string follows the ABA pattern, and false otherwise. The "A" parts can be empty strings, and the "B" part can also be an empty string. The function should handle various edge cases, including empty strings and strings with lengths that are not divisible by a meaningful "A" and "B" segment.

Key Requirements:

• The function must accept a &str (string slice) as input.
• The function must return a bool indicating whether the input string matches the ABA pattern.
• The function should be efficient and avoid unnecessary string allocations.
• The function must correctly handle empty strings and strings of various lengths.

Expected Behavior:

The function should analyze the input string and determine if it can be split into three parts (A, B, A) where the first and third parts are equal. If such a split exists, the function should return true. Otherwise, it should return false.

Edge Cases to Consider:

• Empty String: An empty string should be considered an ABA pattern (A="", B="", A="").
• Single Character String: A single character string should not be considered an ABA pattern.
• Strings with Even Lengths: The "A" parts must be equal in length.
• Strings with Odd Lengths: The "A" parts must be equal in length.
• Strings with only one character repeated: e.g., "aaa" should return true (A="a", B="", A="a").
• Strings with only the same character: e.g., "bbbb" should return false.

Examples

Example 1:

Input: "abab"
Output: true
Explanation: A = "a", B = "b", A = "a". The first and third parts ("a") are equal.

Example 2:

Input: "abcabc"
Output: true
Explanation: A = "ab", B = "c", A = "ab". The first and third parts ("ab") are equal.

Example 3:

Input: "a"
Output: false
Explanation: A single character cannot be split into ABA.

Example 4:

Input: ""
Output: true
Explanation: Empty string is considered an ABA pattern.

Example 5:

Input: "aaa"
Output: true
Explanation: A = "a", B = "", A = "a".

Example 6:

Input: "bbbb"
Output: false
Explanation: No valid split into ABA where A and A are equal.

Constraints

• The input string will contain only ASCII characters.
• The length of the input string will be between 0 and 1000 characters, inclusive.
• The function should execute in O(n) time complexity, where n is the length of the input string. Avoid nested loops that would result in O(n^2) complexity.

Notes

Consider using string slicing to efficiently extract the "A" and "B" parts of the string. Think about how to determine the appropriate length of the "A" part based on the total string length. The key is to avoid unnecessary copying of string data. A good approach involves calculating the potential length of the "A" part and then comparing the substrings.