The base problem isn't the hard part, writing the trie class cleanly from scratch under time pressure is.
Start by clarifying requirements and edge cases, then design the trie node structure and insertion algorithm. Explain the prefix search traversal and how to collect all words under the prefix node, ensuring lexicographic order by sorting the results or using an ordered traversal.
Pro tip: Mention that you can optimize memory by using a hash map for children instead of an array if the alphabet is large, and discuss trade-offs between sorting at query time versus maintaining sorted order during insertion.
Ask about input constraints, expected output format, and whether the dictionary is static or dynamic. Confirm if case sensitivity and non-alphabetic characters need handling.
Define a TrieNode class with a children map (or array) and a boolean flag indicating end of word. Explain how this supports efficient prefix operations.
Describe inserting each word character by character, creating nodes as needed, and marking the final node as a word end. Discuss time complexity O(L) per word.
Traverse the trie according to the prefix. If the path exists, perform a DFS from that node to collect all complete words. Sort the collected words lexicographically if not already ordered.
State time complexity: O(P + K) for traversal and collection, plus O(K log K) for sorting, where P is prefix length and K is number of results. Discuss potential optimizations like storing words in sorted order during insertion.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the requirements: top-K suggestions ranked by frequency, and whether the data is static or dynamic. Then propose a data structure like a trie with frequency counts at each node, and use a min-heap of size K to efficiently retrieve the top-K suggestions. Discuss trade-offs between preprocessing and query-time computation, and consider scalability for large datasets.
Pro tip: Mention that you can precompute and cache the top-K suggestions at each trie node to achieve O(1) query time after an initial O(N) preprocessing, which is crucial for low-latency systems like Google Search.
Ask if the top-K is based on global frequency or frequency within the prefix, and whether the dataset is static or dynamic. Also confirm if K is fixed or variable.
Propose a trie where each node stores a frequency count and possibly a list of top-K suggestions for the prefix ending at that node. Alternatively, use a hash map for prefix-to-suggestions if memory is not a concern.
For query-time computation, traverse the trie to the prefix node, then perform a DFS to collect all suggestions and use a min-heap of size K to keep the top-K by frequency. For precomputation, update top-K lists during insertion.
Discuss trade-offs: precomputation reduces query time but increases update cost and memory. For dynamic data, consider using a combination of trie and heap, or approximate algorithms like count-min sketch for frequency estimation.
Address cases where fewer than K suggestions exist, ties in frequency, and how to handle updates (e.g., new queries) efficiently, possibly using a batch update or lazy propagation.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Explain that deletion involves recursively traversing the trie to the end of the word, then unwinding the recursion to remove nodes that are no longer needed. Emphasize that you must only delete nodes that are not part of any other word and have no other children, and that you should handle edge cases like deleting a non-existent word or a prefix of another word.
Pro tip: Mention that you can optimize by tracking the number of words passing through each node (or a word count at terminal nodes) to avoid unnecessary deletions and make the operation more efficient. Also, discuss the trade-off between recursive and iterative approaches, and consider memory management in languages without garbage collection.
Ask whether the word is guaranteed to exist, whether we need to handle deletion of a prefix, and whether the trie supports other operations concurrently. Confirm if the trie uses a count of words per node or just a boolean flag.
Recursively or iteratively traverse the trie following the characters of the word. If any character is missing, the word doesn't exist; handle that case appropriately.
At the terminal node, unset the end-of-word flag (or decrement a word count). If the node has other children or represents another word, stop deletion here.
On the way back up, for each node, if it has no children and is not the end of another word, remove it from its parent. Continue until you reach a node that is either a word end or has other children.
State that time complexity is O(L) where L is the word length, and space is O(L) for recursion stack. Mention optimizations like using a word count to avoid unnecessary checks, or iterative deletion with a stack.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the problem: fuzzy matching within one edit of the prefix means we need to find all words in a dictionary that are within Levenshtein distance 1 of the given prefix. Discuss using a trie with depth-limited search or a BK-tree, and analyze trade-offs between preprocessing time, query time, and space.
Pro tip: Mention that for a single-character edit, you can often use a simpler approach like generating all possible edits of the prefix and checking if they exist in a hash set or trie, which is efficient for small edit distances. Also, consider if the dictionary is static or dynamic, as that affects data structure choice.
Confirm the definition of 'one character edit' (insertion, deletion, substitution) and whether transpositions count. Ask about the size of the dictionary, expected query frequency, and if the dictionary is static.
Propose a trie for efficient prefix-based search, or a BK-tree for metric-space indexing. For small edit distance, generating all possible edits of the prefix and checking against a hash set is also viable.
For trie: perform DFS with a budget of 1 edit, pruning branches when edit distance exceeds 1. For BK-tree: use triangle inequality to prune. For edit generation: create all strings within one edit of the prefix and check membership.
Compare time and space complexity: trie search is O(n * m) where n is number of words and m is prefix length, but with pruning it's faster. Edit generation is O( (alphabet size) * (prefix length) ) but requires a hash set. BK-tree is efficient for larger edit distances but may be overkill for distance 1.
Consider empty prefix, very long prefixes, and words that are shorter than the prefix. Also discuss if the match should be exact prefix match or if the entire word must be within one edit of the prefix.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.