Question 1: Problem Definition & Naive Approach Analysis (25 points)

• Explain the core problem an autocomplete feature aims to solve in a search bar.
• Describe a 'naive' approach to implementing autocomplete by iterating through a simple list of all possible words. Analyze the time complexity (Big O notation) of this naive approach for a typical search query (e.g., finding all words starting with a given prefix 'P' in a dictionary of 'N' words, where the maximum word length is 'L'). Discuss its scalability issues with a very large dictionary.

Question 2: Introduction to Trie (25 points)

• Define what a Trie (Prefix Tree) is and explain its fundamental principle of operation.
• Describe how words are typically stored within a Trie, including the role of nodes, edges, and how the end of a complete word is usually indicated.

Question 3: Efficiency Comparison (25 points)

• Compare the efficiency of a Trie-based autocomplete system with the naive list-iteration approach discussed in Question 1.
• Specifically, analyze and compare the time complexity (Big O notation) for the following operations, assuming a dictionary of 'N' words, a maximum word length of 'L', and a prefix length of 'P':
  • Searching for all words with a given prefix.
  • Inserting a new word into the data structure.
• Elaborate on why the Trie is considered 'far more efficient' for prefix-based searches, especially in scenarios with large dictionaries and frequent queries.

Question 4: Trie Structure Description (25 points)

• Using a textual description (e.g., node representations, indentation, or ASCII art if suitable), clearly describe the structure of a Trie that would store the following three words: "cat", "catch", and "car".
• Explicitly show the root node, all intermediate nodes, edges (transitions), and how you would mark the end of each complete word within your description.