Trie Insert Operation 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. Each node represents a character, and paths down the tree represent words.

beginner

What does the insert operation do in a Trie?

The insert operation adds a word to the Trie by creating nodes for each character if they don't exist and marking the end of the word.

beginner

In Trie insertion, what does marking the end of a word mean?

It means setting a flag (like isEndOfWord) in the last node of the inserted word to indicate that a complete word ends there.

intermediate

Why do we create new nodes only if the character path does not exist during insertion?

Because existing nodes represent prefixes of other words, so we reuse them to save space and avoid duplication.

intermediate

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

The time complexity is O(n), where n is the length of the word, because we process each character once.

What does each node in a Trie typically represent?

A A character

B A whole word

C An integer value

D A number of words

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

During insertion, if a character node already exists, what should we do?

A Create a new node anyway

B Delete the existing node

C Reuse the existing node

D Skip the character

We reuse existing nodes to represent shared prefixes and save space.

What flag is commonly used to mark the end of a word in a Trie node?

A isWordEnd

B isEndOfWord

C wordComplete

D endFlag

The flag is commonly named isEndOfWord to indicate the end of a word.

What is the worst-case time complexity to insert a word of length n in a Trie?

A O(n)

B O(log n)

C O(n^2)

D O(1)

Insertion requires processing each character once, so O(n).

If you insert the words 'cat' and 'car' into a Trie, how many nodes will be shared?

A 3

B 1

C 0

D 2

The nodes for 'c' and 'a' are shared, so 2 nodes.

Explain step-by-step how to insert the word 'dog' into an empty Trie.

Think about creating nodes for each character and marking the last one.

Describe why Tries are efficient for prefix-based searches and how insertion supports this.

Focus on shared nodes and marking word ends.

Practice

1. What is the main purpose of the insert operation in a Trie data structure?

easy

A. To count the number of words stored in the Trie

B. To delete a word from the Trie

C. To add a new word character by character into the Trie

D. To search for a word in the Trie

Solution

1. Step 1: Understand the insert operation

   The insert operation adds each character of a word into the Trie, creating nodes if they don't exist.

2. Step 2: Differentiate from other operations

   Deleting removes words, searching checks presence, counting totals words. Insert specifically adds words.

3. Final Answer:

   To add a new word character by character into the Trie -> Option C

4. Quick Check:

   Insert = Add word [OK]

Hint: Insert means adding word step-by-step [OK]

Common Mistakes:

• Confusing insert with search or delete
• Thinking insert counts words
• Assuming insert replaces existing words

2. Which of the following is the correct way to declare a Trie node class in C++ for insertion?

easy

A. class TrieNode { public: vector<char> children; bool isEnd; TrieNode() { isEnd = false; } };

B. class TrieNode { public: int children[26]; bool isEnd; TrieNode() { for(int i=0; i<26; i++) children[i] = 0; isEnd = false; } };

C. class TrieNode { public: TrieNode children[26]; bool isEnd; TrieNode() { isEnd = false; } };

D. class TrieNode { public: TrieNode* children[26]; bool isEnd; TrieNode() { for(int i=0; i<26; i++) children[i] = nullptr; isEnd = false; } };

Solution

1. Step 1: Check children type for TrieNode

   Children must be pointers to TrieNode to allow dynamic node creation; hence TrieNode* children[26].

2. Step 2: Verify initialization

   Initialize all children pointers to nullptr and isEnd to false in constructor.

3. Final Answer:

   class TrieNode { public: TrieNode* children[26]; bool isEnd; TrieNode() { for(int i=0; i<26; i++) children[i] = nullptr; isEnd = false; } }; -> Option D

4. Quick Check:

   Children pointers + init nullptr = class TrieNode { public: TrieNode* children[26]; bool isEnd; TrieNode() { for(int i=0; i<26; i++) children[i] = nullptr; isEnd = false; } }; [OK]

Hint: Children must be pointers, initialized to nullptr [OK]

Common Mistakes:

• Using int array instead of pointers
• Not initializing children to nullptr
• Using vector<char> instead of TrieNode pointers

3. What will be the output of the following code snippet after inserting the words "cat" and "car" into an empty Trie?

Trie trie;
trie.insert("cat");
trie.insert("car");
int count = 0;
for(int i = 0; i < 26; i++) {
  if(trie.root->children[i] != nullptr) count++;
}
std::cout << count << std::endl;

medium

A. 1

B. 2

C. 3

D. 0

Solution

1. Step 1: Insert "cat" and "car" into Trie

   Both words start with 'c', so only one child node for 'c' is created at root.

2. Step 2: Count root children nodes

   Only one child at root for 'c' exists, so count is 1.

3. Final Answer:

   1 -> Option A

4. Quick Check:

   Root children count after insert = 1 [OK]

Hint: Count root children after insert; common prefix shares node [OK]

Common Mistakes:

• Counting all characters instead of root children
• Assuming separate root nodes for each word
• Confusing total nodes with root children

4. Identify the error in the following Trie insert function snippet:

void insert(string word) {
  TrieNode* node = root;
  for(char c : word) {
    int index = c - 'a';
    if(node->children[index] == NULL) {
      node->children[index] = new TrieNode();
    }
    node = node->children[index];
  }
  node->isEnd = true;
}

medium

A. No error; the insert function is correct

B. The index calculation should be c - 'A' instead of c - 'a'

C. The root pointer is not initialized before insertion

D. The loop should iterate over indices, not characters

Solution

1. Step 1: Check root initialization assumption

   Assuming root is properly initialized elsewhere, this code correctly uses root pointer.

2. Step 2: Verify index calculation and loop

   Index c - 'a' is correct for lowercase letters; loop over characters is valid.

3. Final Answer:

   No error; the insert function is correct -> Option A

4. Quick Check:

   Code logic matches standard insert [OK]

Hint: Check index and pointer usage carefully [OK]

Common Mistakes:

• Assuming uppercase letters without context
• Thinking loop must use indices
• Forgetting root initialization outside snippet

5. Given a Trie that already contains the words "bat", "ball", and "barn", what will be the effect of inserting the word "bar"?
Choose the correct statement.

hard

A. A new branch is created starting from 'b' node

B. No new nodes are created; only an existing node's isEnd flag is set

C. All existing nodes are duplicated to insert the new word

D. The word "bar" cannot be inserted because "barn" exists

Solution

1. Step 1: Analyze existing Trie structure

   Words "bat", "ball", "barn" share prefix 'ba' and 'bar' prefix exists as part of "barn".

2. Step 2: Effect of inserting "bar"

   Nodes for 'b', 'a', 'r' already exist; only isEnd flag at 'r' node is set to true to mark "bar" as a word.

3. Final Answer:

   No new nodes are created; only an existing node's isEnd flag is set -> Option B

4. Quick Check:

   Insert existing prefix sets isEnd only [OK]

Hint: Insert existing prefix sets isEnd flag only [OK]

Common Mistakes:

• Thinking new nodes are always created
• Assuming duplicates of nodes happen
• Believing insertion fails if prefix exists