Longest Word in Dictionary Using Trie in DSA Typescript - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a Trie data structure?

A Trie is a tree-like data structure that stores a dynamic set of strings, where each node represents a character. It is used for efficient retrieval of words, especially for prefix-based searches.

intermediate

How does a Trie help in finding the longest word in a dictionary?

By inserting all words into a Trie, we can traverse nodes only if they mark the end of a valid word. This ensures that prefixes are valid words, helping us find the longest word built one character at a time.

beginner

What condition must be true for a node to be considered during traversal when finding the longest word?

The node must mark the end of a word (isEnd = true) to ensure the prefix up to that node is a valid word.

intermediate

Why do we prefer lexicographical order when multiple longest words exist?

Choosing the lexicographically smallest word ensures a consistent and predictable result when multiple words have the same maximum length.

intermediate

What is the time complexity of building a Trie with n words of average length m?

The time complexity is O(n * m), since each character of every word is inserted once.

What does each node in a Trie represent?

A A character of a word

B A whole word

C A number

D A sentence

Each node in a Trie represents a single character of a word.

When finding the longest word in a Trie, which nodes do we consider for traversal?

A All nodes regardless

B Only nodes marking the end of a word

C Only root nodes

D Only leaf nodes

We only traverse nodes that mark the end of a valid word to ensure prefixes are valid.

If two words have the same length, which one is chosen as the longest word?

A The lexicographically smaller word

B The lexicographically larger word

C The first inserted word

D The last inserted word

The lexicographically smaller word is chosen for consistency.

What is the main advantage of using a Trie for prefix-based searches?

A Uses less memory than arrays

B Sorts words automatically

C Stores numbers efficiently

D Fast retrieval of words sharing prefixes

Trie allows fast retrieval of words sharing common prefixes.

What is the time complexity to insert one word of length m into a Trie?

A O(m^2)

B O(1)

C O(m)

D O(log m)

Inserting a word requires processing each character once, so O(m).

Explain how a Trie is used to find the longest word in a dictionary where every prefix is also a valid word.

Think about how prefixes relate to valid words in the Trie.

Describe the steps to build a Trie and how to traverse it to find the longest word with all prefixes valid.

Focus on insertion and traversal rules.