What is the optimal time complexity of solving Implement Trie Prefix Tree?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Implement Trie Prefix Tree?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Implement Trie Prefix Tree?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Implement Trie Prefix Tree?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Implement Trie Prefix Tree

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Problem Statement

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A trie (pronounced as 'try') or prefix tree is a tree data structure used to efficiently store and retrieve keys in a dataset of strings. There are various applications of this data structure, such as autocomplete and spellchecker.

Implement the Trie class:

- Trie() Initializes the trie object.

- insert(word: str) Inserts the string word into the trie.

- search(word: str) -> bool Returns True if the string word is in the trie (i.e., was inserted before), and False otherwise.

- startsWith(prefix: str) -> bool Returns True if there is a previously inserted string word that has the prefix prefix, and False otherwise.

Input is a list of operations and arguments. Implement a function trie(operations: list, arguments: list) -> list that returns a list of results (None for constructor/insert, bool for search/startsWith).

Constraints

•1 <= len(word), len(prefix) <= 2000
•word and prefix consist of lowercase English letters
•At most 3 * 10^4 calls will be made in total to insert, search, and startsWith

Examples

Example 1

Input

operations = ["Trie", "insert", "search", "search", "startsWith", "insert", "search"], arguments = [[], ["apple"], ["apple"], ["app"], ["app"], ["app"], ["app"]]

Output

[None, None, True, False, True, None, True]

Explanation

Trie initialized. insert("apple"). search("apple") returns True. search("app") returns False. startsWith("app") returns True. insert("app"). search("app") returns True.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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