How would you remove duplicates in a string?

Focus on outlining a clear algorithm to remove duplicates from a string, considering both time and space complexity. Start by discussing different approaches, such as using a hash set to track seen characters or utilizing a data structure like a list to maintain order. Be prepared to explain the trade-offs of each method, including efficiency and memory usage. If applicable, consider edge cases, such as empty strings or strings with all unique characters, and how your solution would handle them. Finally, if time permits, discuss how you would implement this in a specific programming language, emphasizing syntax and any relevant built-in functions.