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

Recall & Review

beginner

What is a Trie data structure?

A Trie is a tree-like data structure used to store a dynamic set of strings where keys are usually strings. Each node represents a character, and paths from root to nodes represent prefixes of words.

intermediate

How does a Trie help in finding the longest word in a dictionary where all prefixes are also words?

A Trie allows efficient prefix checking by storing all words. We can traverse the Trie to find the longest word such that every prefix of that word is also marked as a complete word in the Trie.

beginner

What is the key condition to consider a word valid when searching for the longest word in the Trie?

Every prefix of the word must be a valid word in the Trie, meaning each node along the path must be marked as an end of a word.

intermediate

Why do we prefer DFS (Depth First Search) over BFS (Breadth First Search) in finding the longest word in a Trie?

DFS allows exploring deeper paths first, which helps in finding the longest word by going as far as possible along valid prefixes before backtracking.

advanced

What is the time complexity of inserting all words into a Trie and then finding the longest word where all prefixes are valid?

Inserting all words takes O(N * L) where N is number of words and L is average length. Finding the longest word by DFS also takes O(N * L) in worst case.

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.

Which traversal method is best to find the longest word in a Trie where all prefixes are valid?

A Depth First Search (DFS)

B Inorder Traversal

C Level Order Traversal

D Breadth First Search (BFS)

DFS explores deeper paths first, helping find the longest valid word.

What must be true about prefixes of the longest word in the dictionary for this problem?

A They can be partial words

B They don't matter

C They must all be present as words in the dictionary

D Only the first prefix matters

All prefixes must be valid words for the longest word to qualify.

What is the main advantage of using a Trie over a hash set for this problem?

A Trie stores words in sorted order automatically

B Trie allows efficient prefix checking

C Trie uses less memory

D Trie is faster for all operations

Trie allows checking prefixes efficiently, which is key here.

If two words have the same length and all prefixes are valid, which one should be chosen as the longest word?

A Any one of them

B The lexicographically larger word

C The one inserted first

D The lexicographically smaller word

The problem usually requires choosing the lexicographically smallest word if lengths tie.

Explain how a Trie can be used to find the longest word in a dictionary such that every prefix of the word is also a valid word.

Think about checking prefixes and using depth-first search.

Describe the steps to insert words into a Trie and then find the longest word with all prefixes valid.

Focus on insertion and traversal phases.

Practice

1. What is the main purpose of using a Trie data structure when finding the longest word in a dictionary?

easy

A. To efficiently store and search words by their prefixes

B. To sort words alphabetically

C. To count the total number of words

D. To reverse the words in the dictionary

Solution

1. Step 1: Understand Trie usage

   A Trie stores words by breaking them into characters and linking nodes for prefixes.

2. Step 2: Relate Trie to longest word search

   This structure allows quick prefix checks, which helps find the longest word built from other words.

3. Final Answer:

   To efficiently store and search words by their prefixes -> Option A

4. Quick Check:

   Trie = prefix search [OK]

Hint: Trie is best for prefix-based word searches [OK]

Common Mistakes:

• Thinking Trie sorts words alphabetically
• Confusing Trie with simple lists
• Assuming Trie counts words only

2. Which of the following is the correct way to insert a word into a Trie node in Python?

easy

A. node.children[char] = TrieNode() if char not in node.children else node.children[char]

B. node.children.add(char)

C. node.children.append(char)

D. node.children[char] = char

Solution

1. Step 1: Understand Trie children structure

   Trie children are stored in a dictionary mapping characters to TrieNode objects.

2. Step 2: Correct insertion method

   We check if character exists; if not, create new TrieNode and assign it to children dictionary.

3. Final Answer:

   node.children[char] = TrieNode() if char not in node.children else node.children[char] -> Option A

4. Quick Check:

   Insert uses dictionary with TrieNode [OK]

Hint: Use dictionary keys for children, not list or set [OK]

Common Mistakes:

• Using add() or append() on dictionary
• Assigning character instead of TrieNode
• Not checking if child exists before insertion

3. Given the words: ["a", "app", "apple", "apply", "ap"], what is the longest word that can be built one character at a time using the Trie method?

medium

A. "apply"

B. "app"

C. "apple"

D. "ap"

Solution

1. Step 1: Check each word's prefixes

   Words must have all prefixes present: "a", "ap", "app" are present; "apple" and "apply" require "appl" which is missing.

2. Step 2: Identify longest valid word

   "app" is the longest word where all prefixes exist in the list.

3. Final Answer:

   "app" -> Option B

4. Quick Check:

   Longest word with all prefixes = "app" [OK]

Hint: Check all prefixes exist before choosing longest word [OK]

Common Mistakes:

• Assuming "apple" or "apply" are valid without "appl"
• Ignoring prefix requirement
• Choosing shortest word instead

4. What is the error in this Trie insertion code snippet for building the longest word?

for word in words:
    node = root
    for char in word:
        if char not in node.children:
            node.children[char] = TrieNode
        node = node.children[char]
    node.is_word = True

medium

A. The root node should be reset after each character

B. The loop should iterate over characters in reverse

C. node.is_word should be set before the inner loop

D. TrieNode should be called with parentheses to create an instance

Solution

1. Step 1: Identify object creation mistake

   TrieNode is a class; to create an object, parentheses () are needed.

2. Step 2: Understand impact of missing parentheses

   Without (), node.children[char] stores the class itself, not an instance, causing errors on further access.

3. Final Answer:

   TrieNode should be called with parentheses to create an instance -> Option D

4. Quick Check:

   Instantiate TrieNode with () [OK]

Hint: Always use () to create class instances in Python [OK]

Common Mistakes:

• Forgetting parentheses when creating objects
• Setting flags in wrong loop place
• Resetting root incorrectly inside loops

5. You have a list of words: ["w", "wo", "wor", "worl", "world", "banana", "ban", "bana", "banan"]. Using a Trie, which word will be returned as the longest word built one character at a time from other words in the list?

hard

A. "worl"

B. "banana"

C. "world"

D. "banan"

Solution

1. Step 1: Verify prefix chains for each candidate

   "world" prefixes: "w", "wo", "wor", "worl", "world" all exist; "banana" and "banan" missing prefixes like "b", "ba"; "worl" is shorter than "world".

2. Step 2: Choose longest word with all prefixes present

   "world" is longest with all prefixes present in the list.

3. Final Answer:

   "world" -> Option C

4. Quick Check:

   Longest word with full prefix chain = "world" [OK]

Hint: Check full prefix chain exists before longest word [OK]

Common Mistakes:

• Choosing "banana" without full prefix chain
• Ignoring prefix requirement for "banan"
• Picking shorter word "worl" over "world"