grid47 Exploring patterns and algorithms
Oct 17, 2024
8 min read
Solution to LeetCode 208: Implement Trie (Prefix Tree) Problem
Implement a Trie data structure that supports inserting words, searching for exact matches, and checking if any word starts with a given prefix.
Problem
Approach
Steps
Complexity
Input: You are given a list of operations to perform on the Trie data structure. Each operation corresponds to one of the Trie methods: insert, search, or startsWith.
• Each string in the Trie has a length between 1 and 2000.
• All characters in the strings are lowercase English letters.
• At most 30,000 operations will be performed.
Output: The output consists of the results of the operations in the order they are performed. For each 'insert' operation, the output is 'null'. For 'search' and 'startsWith' operations, the output is a boolean value indicating whether the operation was successful.
Goal: The goal is to implement the Trie class and handle the operations insert, search, and startsWith efficiently.
Steps:
• Use a nested structure where each node contains an array representing child nodes and a boolean flag indicating if the node corresponds to a complete word.
• For 'insert', iterate through each character of the word and create nodes as necessary.
• For 'search', traverse the Trie and check if the entire word exists.
• For 'startsWith', traverse the Trie to check if there exists a word that begins with the given prefix.
Goal: Constraints ensure the number of operations and string lengths are manageable within the problem's limits.
Steps:
• The number of nodes in each string is between 1 and 2000.
• The total number of operations is at most 30,000.
Assumptions:
• All input strings contain only lowercase English letters.
• No cycles are present in the Trie.
• Input: Example 1
• Explanation: In this example, the operations are performed in sequence, with the insertions and searches occurring as expected, demonstrating how the Trie handles prefixes and exact word matches.
• Input: Example 2
• Explanation: This example shows how the Trie works with a simple dataset where only the word 'dog' is inserted and then searched for both fully and by prefix.
Approach: The approach involves implementing the Trie data structure using a node-based approach where each node holds a collection of child nodes and a flag to indicate if it represents a word.
Observations:
• A Trie is ideal for operations like searching and prefix matching due to its tree-like structure.
• We need to efficiently implement the insert, search, and startsWith methods to handle up to 30,000 operations.
Steps:
• Define a Node class that contains an array for child nodes and a boolean flag indicating if the node represents a complete word.
• Define a Trie class that manages the root node and implements the insert, search, and startsWith operations.
• For insert, iterate over the word and create new nodes if necessary.
• For search, check if all characters of the word exist and if the node at the last character is marked as a complete word.
• For startsWith, traverse the Trie to check if the prefix exists.
Empty Inputs:
• If no words are inserted, all search and startsWith operations should return false.
Large Inputs:
• Handle cases where strings are of maximum length (2000 characters) and when the number of operations is large (30,000).
Special Values:
• Handle cases where words have overlapping prefixes, like 'app' and 'apple'.
Constraints:
• Ensure that the solution performs efficiently within the given constraints.
