Implement Prefix Match Filter

Design a data structure that stores a collection of prefix strings. Then, given a list of input strings, return every string that begins with at least one stored prefix. Requirements: - Support `addPrefix(prefix)` to store a prefix. - Support checking whether a given string matches any stored prefix. - Given a list of strings, output each matching string exactly once, even if multiple prefixes match it. Example: - Stored prefixes: `["ab", "cat", "pre"]` - Input strings: `["abc", "dog", "prefix", "cater", "zoo"]` - Output: `["abc", "prefix", "cater"]` Follow-up: 1. First discuss or implement a straightforward hash-based approach. 2. Then optimize the solution using a trie (prefix tree). 3. Compare the time and space complexity of both approaches.