Generalized Abbreviation

Given a string, generate all possible "generalized abbreviations". A generalized abbreviation can replace any contiguous substring of characters with its length. This is useful in scenarios where concise representations of strings are needed, such as displaying file paths, long variable names, or search result snippets where space is limited.

Problem Description

The goal is to create a function that takes a string as input and returns a list of all possible generalized abbreviations for that string.

A generalized abbreviation can be formed by:

1. Keeping characters as they are.
2. Replacing any contiguous sequence of one or more characters with their count.

The function should generate all valid combinations of these two rules.

Key Requirements:

• The output should be a list of strings.
• Each output string must be a valid abbreviation of the input string.
• All possible valid abbreviations must be generated.

Important Edge Cases:

• Empty input string.
• Input string with a single character.
• Cases where the entire string is abbreviated.
• Cases where no part of the string is abbreviated (i.e., the original string itself).

Examples

Example 1:

Input: "word"
Output: ["word", "wor1", "wo1d", "wo2", "w1rd", "w1r1", "w2d", "w3", "1ord", "1or1", "1o1d", "1o2", "2rd", "2r1", "3d", "4"]
Explanation:
- "word": No abbreviation.
- "wor1": 'd' is replaced by '1'.
- "wo1d": 'r' is replaced by '1'.
- "wo2": 'rd' is replaced by '2'.
- "w1rd": 'o' is replaced by '1'.
- "w1r1": 'o' replaced by '1', 'd' replaced by '1'.
- "w2d": 'or' replaced by '2'.
- "w3": 'ord' replaced by '3'.
- "1ord": 'w' replaced by '1'.
- "1or1": 'w' replaced by '1', 'd' replaced by '1'.
- "1o1d": 'w' replaced by '1', 'r' replaced by '1'.
- "1o2": 'w' replaced by '1', 'rd' replaced by '2'.
- "2rd": 'wo' replaced by '2'.
- "2r1": 'wo' replaced by '2', 'd' replaced by '1'.
- "3d": 'wor' replaced by '3'.
- "4": 'word' replaced by '4'.

Example 2:

Input: "a"
Output: ["a", "1"]
Explanation:
- "a": No abbreviation.
- "1": 'a' is replaced by '1'.

Example 3:

Input: ""
Output: [""]
Explanation: The only abbreviation for an empty string is an empty string.

Constraints

• The input string will contain only lowercase English letters.
• The length of the input string will be between 0 and 12, inclusive.
• The number of possible abbreviations can grow exponentially, so the solution should be efficient enough for the given constraints.

Notes

This problem can be approached using recursion or backtracking. Consider how to build the abbreviations character by character. At each character, you have two choices: either keep the character as it is, or start/continue an abbreviation. If you decide to abbreviate, you need to keep track of the current count of consecutive characters being abbreviated. Be mindful of consecutive numbers in your output; they should be avoided (e.g., "w21d" is invalid, it should be "w3d").