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I got the basic structure down pretty quickly, nodes with a map of character to child node, a flag for end-of-word.
Start by clarifying the requirements and constraints, then describe the trie node structure and the algorithms for each operation. Discuss time/space complexity and potential optimizations like using a hash map for children or storing full keys at terminal nodes for efficient enumeration.
Pro tip: Mention that you would store the full key at the terminal node to avoid reconstructing it during enumeration, and discuss memory trade-offs. Also, consider using a compressed trie (radix tree) if memory is a concern, but note the added complexity.
Ask about expected key characteristics (e.g., alphabet size, key length, number of keys) and performance requirements. Confirm whether operations need to be thread-safe or if there are memory constraints.
Define a node with a map (or array) of children, a boolean flag indicating end of key, and optionally the full key string. Explain the choice of data structure for children based on alphabet size.
Describe insertion, lookup, and prefix check by traversing the trie character by character. For enumeration, perform a depth-first search from the prefix node, collecting keys when the end flag is true.
State time complexity O(L) for insert/lookup/prefix check and O(L + K) for enumeration, where L is key length and K is number of keys with prefix. Discuss space complexity and possible optimizations like compression or using arrays for small alphabets.
Address empty strings, duplicate insertions, and deletion if required. Mention potential extensions like autocomplete, wildcard search, or thread safety.
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I talked about prefix sharing saving memory versus storing full keys in a hash map, and O(m) lookup where m is key length.
Start by defining the use case and key characteristics (e.g., key length, alphabet size, operations). Then compare trie and hash map in terms of time complexity for lookup, insert, delete, and space overhead, highlighting scenarios where each excels. Conclude with a recommendation based on trade-offs like prefix operations, memory constraints, and worst-case guarantees.
Pro tip: Mention that tries enable ordered traversal and prefix-based queries, which hash maps cannot do efficiently, but hash maps offer O(1) average time with less memory overhead for random keys. Also note that tries can degrade to O(m) time where m is key length, which is independent of the number of keys, making them suitable for large datasets with long keys.
Ask or state assumptions about the key set: are keys fixed-length or variable? What operations are needed (lookup, insert, delete, prefix search)? What are the expected number of keys and key length?
Compare average and worst-case time for lookup, insert, and delete. Hash maps: O(1) average, O(n) worst-case. Tries: O(m) where m is key length, independent of number of keys, but with constant factors depending on alphabet size.
Discuss memory usage: hash maps store keys and values with overhead for buckets and load factor. Tries store nodes per character, which can be memory-heavy for large alphabets or sparse data, but can be compressed (e.g., radix trie) to save space.
Highlight that tries support ordered traversal and prefix queries (e.g., autocomplete) efficiently, while hash maps do not. Hash maps may require additional structures for such operations.
Based on the use case, recommend one over the other. For example, if prefix searches are needed, trie is better; if memory is tight and keys are random, hash map is preferable. Mention hybrid approaches if applicable.
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Knew the concept well enough to describe collapsing single-child chains into edge labels.
Start by defining the problem of space inefficiency in standard tries and then systematically describe compaction strategies like path compression and level compression. For implementation, outline the key design decisions for a radix tree or Patricia tree, focusing on node structure, insertion/deletion algorithms, and trade-offs between memory and speed.
Pro tip: Mention real-world systems that use these structures (e.g., Linux kernel's radix tree for page cache, HTTP routers) to show practical awareness. Also, discuss how you would handle edge cases like long common prefixes and concurrency if relevant.
Explain that standard tries can have many nodes with a single child, leading to wasted space. Compaction strategies aim to reduce this overhead.
Cover path compression (merging chains of single-child nodes) and level compression (replacing full subtrees with arrays). Mention Patricia trees as a specific implementation of path compression.
For a radix tree, describe node structure (e.g., storing a prefix and a map of children), insertion (splitting nodes when prefixes diverge), and deletion (merging nodes when a node has one child).
Compare memory usage, lookup speed, and update complexity. For example, path compression reduces memory but may increase insertion complexity due to node splitting.
Summarize when to use each strategy, such as Patricia trees for IP routing and radix trees for databases or file systems.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.