Design a data structure to store anagrams

Problem

You are building a small in-memory service that stores words and can return all stored words that are anagrams of a query.

Design and implement a data structure AnagramStore supporting the following operations:

1. add(word: string) -> void : Add a word to the store (duplicates may exist).
2. getAnagrams(query: string) -> list<string> : Return all words previously added that are anagrams of query (including the word itself if it was added). The order of the returned list does not matter.

Two words are anagrams if they contain the same letters with the same frequencies (case-insensitive; assume input is lowercase a-z unless you state otherwise).

Example

• Add: "eat" , "tea" , "tan" , "ate" , "nat" , "bat"
• getAnagrams("ate") can return: ["eat", "tea", "ate"]
• getAnagrams("ant") can return: ["tan", "nat"]
• getAnagrams("tab") can return: ["bat"]

Constraints (you may assume)

• Up to 10^5 total add operations
• Word length up to 100

Requirements

• Explain the time and space complexity of your approach.
• Discuss how you would handle duplicates (e.g., adding the same word multiple times).