Longest Word in Dictionary Using Trie in DSA Go - 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 each node represents a character. It allows fast retrieval of words by prefix.

intermediate

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

By inserting all words into the Trie, we can traverse nodes only if they mark the end of a word, ensuring all prefixes exist. The longest path following this rule gives the longest valid word.

beginner

In the context of the longest word problem, why do we only continue traversal if the current node marks the end of a word?

Because the problem requires that all prefixes of the word must be valid words. If a node is not an end of a word, it means the prefix is missing, so we stop.

intermediate

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

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

beginner

How do you compare two candidate longest words when their lengths are equal in this problem?

You choose the lexicographically smaller word (alphabetically first) as the answer.

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.

Why do we only continue traversal in the Trie if the node marks the end of a word?

A To find the shortest word

B To save memory

C To ensure all prefixes are valid words

D To avoid loops

Continuing only at nodes marking word ends ensures all prefixes exist as words.

What is the main goal when finding the longest word in the dictionary using a Trie?

A Find the longest word where all prefixes are also words

B Find the shortest word

C Find the word with most vowels

D Find the word with the highest ASCII sum

The problem is to find the longest word such that every prefix is also a valid word.

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

A The one with more vowels

B The lexicographically larger word

C The one inserted first

D The lexicographically smaller word

The lexicographically smaller word is chosen when lengths are equal.

What is the time complexity to insert all words into a Trie?

A O(n + m)

B O(n * m)

C O(n^2)

D O(m^2)

Inserting n words each of average length m takes O(n * m) time.

Explain how a Trie can be used to find the longest word in a dictionary where all prefixes are also words.

Think about how prefixes relate to nodes marking word ends.

Describe the traversal strategy in the Trie to find the longest word with all prefixes present.

Focus on conditions to continue traversal.

Practice

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

easy

A. To reverse the words quickly

B. To sort words alphabetically

C. To count the total number of words

D. To efficiently store and search words by their prefixes

Solution

1. Step 1: Understand Trie usage

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

2. Step 2: Connect Trie to longest word search

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

3. Final Answer:

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

4. Quick Check:

   Trie = prefix search [OK]

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

Common Mistakes:

• Confusing Trie with sorting algorithms
• Thinking Trie reverses words
• Assuming Trie counts words only

2. Which of the following Go code snippets correctly initializes a Trie node struct for storing children nodes?

easy

A. type TrieNode struct { children map[int]string; isWord string }

B. type TrieNode struct { children []int; isWord int }

C. type TrieNode struct { children map[rune]*TrieNode; isWord bool }

D. type TrieNode struct { children []string; isWord bool }

Solution

1. Step 1: Identify correct children type

   Children should map characters (rune) to TrieNode pointers for branching.

2. Step 2: Check isWord type

   isWord is a boolean indicating if node ends a valid word.

3. Final Answer:

   type TrieNode struct { children map[rune]*TrieNode; isWord bool } -> Option C

4. Quick Check:

   Children map[rune]*TrieNode and bool isWord [OK]

Hint: Children map uses rune keys and TrieNode pointers [OK]

Common Mistakes:

• Using slices instead of maps for children
• Wrong data types for children or isWord
• Using int or string instead of rune keys

3. Given the following Go code snippet that inserts words into a Trie and finds the longest word, what will be printed?

words := []string{"a", "app", "apple", "apply", "ap"}
trie := NewTrie()
for _, w := range words {
    trie.Insert(w)
}
result := trie.LongestWord()
fmt.Println(result)

medium

A. "app"

B. "apply"

C. "a"

D. "apple"

Solution

1. Step 1: Insert words into Trie

   All words "a", "ap", "app", "apple", "apply" are inserted.

2. Step 2: Find longest word built from prefixes

   "app" has all prefixes "a", "ap", "app" present as words. "apple" and "apply" lack "appl" prefix.

3. Final Answer:

   "app" -> Option A

4. Quick Check:

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

Hint: Longest word with all prefixes present wins, lex order breaks ties [OK]

Common Mistakes:

• Choosing "apple" or "apply" ignoring missing "appl"
• Picking lexicographically later word
• Not inserting all words before search

4. In the following Go code for inserting words into a Trie, what is the bug that prevents correct longest word detection?

func (t *Trie) Insert(word string) {
    node := t.root
    for _, ch := range word {
        if node.children[ch] == nil {
            node.children[ch] = &TrieNode{}
        }
        node = node.children[ch]
    }
    node.isWord = false
}

medium

A. isWord should be set to true, not false

B. children map is not initialized

C. Loop variable ch should be int, not rune

D. Function should return a value

Solution

1. Step 1: Check isWord assignment

   isWord marks end of a valid word and must be true, not false.

2. Step 2: Understand impact on longest word search

   Setting isWord false means no word end is recognized, breaking longest word logic.

3. Final Answer:

   isWord should be set to true, not false -> Option A

4. Quick Check:

   isWord = true marks word end [OK]

Hint: Set isWord true at word end to mark valid words [OK]

Common Mistakes:

• Setting isWord false instead of true
• Not initializing children map before use
• Ignoring rune type for characters

5. You have a list of words: ["w", "wo", "wor", "worl", "world", "banana", "ban", "bana", "banan"]. Using a Trie, which word will be the longest word in the dictionary where every prefix is also a word? Assume ties are broken by lexicographical order.

hard

A. "worl"

B. "world"

C. "banana"

D. "banan"

Solution

1. Step 1: Check prefixes for each candidate

   "world" has prefixes "w", "wo", "wor", "worl" all present.

2. Step 2: Check "banana" and its prefixes

   "banana" lacks prefixes like "b", "ba", so it fails.

3. Step 3: Compare longest valid words

   "world" (length 5) is longest with all prefixes present; "banana" (6) invalid, "banan" also invalid.

4. Final Answer:

   "world" -> Option B

5. Quick Check:

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

Hint: Check all prefixes exist; longest with lex order wins [OK]

Common Mistakes:

• Ignoring missing prefixes for banana
• Choosing shorter words
• Not applying lexicographical tie-break