Prefix Search Using Trie in DSA C - 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. It allows fast retrieval of words by their prefixes.

beginner

How does prefix search work in a Trie?

Prefix search in a Trie involves traversing the tree nodes following the characters of the prefix. If traversal succeeds, all words under that node share the prefix.

intermediate

What is the time complexity of searching a prefix in a Trie?

The time complexity is O(m), where m is the length of the prefix, because we traverse one node per character.

intermediate

Why is Trie preferred over hash tables for prefix search?

Trie allows efficient prefix search by sharing common prefixes in nodes, while hash tables do not support prefix queries efficiently.

beginner

What does each node in a Trie typically contain?

Each node contains an array or map of child nodes for each possible character and a boolean flag indicating if the node marks the end of a word.

What does a Trie node usually store?

A A hash of the word

B Only the character it represents

C Pointers to child nodes and end-of-word flag

D The entire word string

Trie nodes store pointers to child nodes for each character and a flag to mark if a word ends at that node.

What is the main advantage of using a Trie for prefix search?

A Fast prefix lookup by traversing nodes

B Uses less memory than arrays

C Stores words in sorted order automatically

D Supports fast numeric calculations

Trie allows fast prefix lookup by following nodes matching prefix characters.

If a prefix is not found in a Trie, what does it mean?

A No word in the Trie starts with that prefix

B All words start with that prefix

C The Trie is empty

D The prefix is a complete word

If traversal for the prefix fails, no word in the Trie starts with that prefix.

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

A O(log n)

B O(1)

C O(n^2)

D O(n)

Insertion requires traversing or creating nodes for each character, so O(n).

Which data structure is NOT suitable for prefix search?

A Trie

B Hash Table

C Prefix Tree

D Radix Tree

Hash tables do not support efficient prefix search as they do exact key lookups.

Explain how prefix search works using a Trie data structure.

Think about walking down the tree following prefix letters.

Describe the structure of a Trie node and its role in prefix search.

Focus on what each node stores and how it helps find prefixes.

Practice

1. What is the main purpose of using a Trie data structure in prefix search?

easy

A. To perform arithmetic operations quickly

B. To sort words alphabetically

C. To store numbers in sorted order

D. To efficiently find all words that start with a given prefix

Solution

1. Step 1: Understand the role of Trie in prefix search

   A Trie stores characters of words in a tree structure, allowing quick prefix lookups.

2. Step 2: Identify the main use case

   It helps find all words starting with a prefix efficiently, unlike sorting or arithmetic.

3. Final Answer:

   To efficiently find all words that start with a given prefix -> Option D

4. Quick Check:

   Trie = Prefix search efficiency [OK]

Hint: Trie is built for prefix-based word retrieval [OK]

Common Mistakes:

• Confusing Trie with sorting algorithms
• Thinking Trie is for arithmetic
• Assuming Trie stores numbers only

2. Which of the following is the correct way to declare a Trie node structure in C for prefix search?

easy

A. typedef struct TrieNode { int data; struct TrieNode* next; } TrieNode;

B. typedef struct TrieNode { char* word; struct TrieNode* child; } TrieNode;

C. typedef struct TrieNode { struct TrieNode* children[26]; int isEndOfWord; } TrieNode;

D. typedef struct TrieNode { int value; struct TrieNode* left; struct TrieNode* right; } TrieNode;

Solution

1. Step 1: Identify Trie node components

   A Trie node has an array of pointers for each alphabet letter and a flag for word end.

2. Step 2: Match with given options

   typedef struct TrieNode { struct TrieNode* children[26]; int isEndOfWord; } TrieNode; matches this structure with 26 children pointers and an end-of-word flag.

3. Final Answer:

   typedef struct TrieNode { struct TrieNode* children[26]; int isEndOfWord; } TrieNode; -> Option C

4. Quick Check:

   Trie node = children array + end flag [OK]

Hint: Trie nodes have 26 children pointers for letters a-z [OK]

Common Mistakes:

• Using linked list pointers instead of array for children
• Confusing Trie node with linked list or binary tree node
• Missing end-of-word flag

3. Given the following code snippet inserting words "cat", "car", and "dog" into a Trie, what will be the output of searching prefix "ca"?

insert("cat");
insert("car");
insert("dog");
searchPrefix("ca");

medium

A. ["cat", "car"]

B. ["dog"]

C. ["cat"]

D. []

Solution

1. Step 1: Insert words into Trie

   Words "cat", "car", and "dog" are inserted, building branches for 'c' and 'd'.

2. Step 2: Search prefix "ca"

   Both "cat" and "car" start with "ca", so they are returned by searchPrefix.

3. Final Answer:

   ["cat", "car"] -> Option A

4. Quick Check:

   Prefix "ca" matches cat and car [OK]

Hint: Words starting with prefix are returned [OK]

Common Mistakes:

• Returning only one matching word
• Returning words not matching prefix
• Empty result for existing prefix

4. Consider this buggy C code snippet for inserting a word into a Trie. What is the main error?

void insert(TrieNode* root, char* word) {
  TrieNode* node = root;
  for (int i = 0; word[i] != '\0'; i++) {
    int index = word[i] - 'a';
    if (node->children[index] == NULL) {
      node->children[index] = malloc(sizeof(TrieNode));
    }
    node = node->children[index];
  }
  node->isEndOfWord = 1;
}

medium

A. New nodes are not initialized after malloc

B. Index calculation is incorrect

C. Loop condition should be i < strlen(word)

D. isEndOfWord flag is set too early

Solution

1. Step 1: Analyze node creation

   malloc allocates memory but does not initialize children pointers or isEndOfWord flag.

2. Step 2: Identify impact

   Uninitialized children pointers can cause undefined behavior during traversal or insertion.

3. Final Answer:

   New nodes are not initialized after malloc -> Option A

4. Quick Check:

   malloc needs initialization [OK]

Hint: Always initialize new Trie nodes after malloc [OK]

Common Mistakes:

• Assuming malloc zeroes memory
• Ignoring initialization of isEndOfWord
• Misunderstanding loop condition

5. You want to find all words in a Trie that start with prefix "app" and have length exactly 5. Which approach correctly combines prefix search and length filtering?

hard

A. Collect all words in Trie, then filter those starting with "app" and length 5

B. Traverse Trie to node for "app", then collect words of length 5 from there

C. Search for "app" as a full word, then check length 5

D. Use binary search on sorted word list for prefix "app" and length 5

Solution

1. Step 1: Use Trie prefix traversal

   Traverse the Trie to the node representing the prefix "app" to limit search space.

2. Step 2: Collect words of length 5 from that node

   From this node, recursively collect words that complete to length 5.

3. Final Answer:

   Traverse Trie to node for "app", then collect words of length 5 from there -> Option B

4. Quick Check:

   Prefix traversal + length filter = Traverse Trie to node for "app", then collect words of length 5 from there [OK]

Hint: Start at prefix node, then filter by length [OK]

Common Mistakes:

• Filtering all words instead of prefix subtree
• Searching prefix as full word
• Using binary search on Trie data