Trie Insert Operation in DSA Typescript - Time & Space Complexity

Time Complexity: Trie Insert Operation

O(m)

Understanding Time Complexity

We want to understand how the time to add a word to a trie grows as the word gets longer.

How does the number of steps change when the word length increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class TrieNode {
  children: Map = new Map();
  isEndOfWord: boolean = false;
}

function insert(root: TrieNode, word: string): void {
  let node = root;
  for (const char of word) {
    if (!node.children.has(char)) {
      node.children.set(char, new TrieNode());
    }
    node = node.children.get(char)!;
  }
  node.isEndOfWord = true;
}
    

This code adds each character of a word into the trie, creating new nodes if needed.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through each character of the word.
• How many times: Exactly once per character in the word (word length).

How Execution Grows With Input

Each added character means one more step in the loop, so the work grows directly with word length.

Input Size (word length)	Approx. Operations
10	About 10 steps
100	About 100 steps
1000	About 1000 steps

Pattern observation: The time grows linearly as the word gets longer.

Final Time Complexity

Time Complexity: O(m)

This means the time to insert depends directly on the length of the word being added.

Common Mistake

[X] Wrong: "The insert time depends on the number of words already in the trie."

[OK] Correct: The insert only loops through the new word's characters, not all stored words, so existing size doesn't affect insert time.

Interview Connect

Knowing this helps you explain why tries are efficient for prefix searches and insertions, a common topic in coding interviews.

Self-Check

What if we changed the data structure to use an array of fixed size 26 for children instead of a map? How would the time complexity change?

Practice

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

easy

A. To add a word character by character into the Trie

B. To delete a word from the Trie

C. To search for a word in the Trie

D. To count the number of words in the Trie

Solution

1. Step 1: Understand the insert operation

   The insert operation adds each character of a word into the Trie one by one, creating new nodes if needed.

2. Step 2: Differentiate from other operations

   Deleting removes words, searching finds words, counting totals words. Insert specifically adds words.

3. Final Answer:

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

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 words

2. Which of the following is the correct TypeScript syntax to start inserting a word into a Trie node named root?

easy

A. let node = root;

B. node = root;

C. const node = root()

D. var node == root;

Solution

1. Step 1: Understand variable declaration in TypeScript

   Using let declares a variable that can be reassigned, suitable for traversal nodes.

2. Step 2: Check syntax correctness

   let node = root; uses correct assignment with let. node = root; misses declaration keyword. const node = root() wrongly calls root as a function. var node == root; uses invalid comparison operator.

3. Final Answer:

   let node = root; -> Option A

4. Quick Check:

   Correct variable declaration = let node = root; [OK]

Hint: Use let for variable assignment in TypeScript [OK]

Common Mistakes:

• Missing let or const keyword
• Using == instead of = for assignment
• Calling node as a function

3. Given the following TypeScript code snippet for inserting the word "cat" into an empty Trie, what will be the printed output after insertion?

class TrieNode {
  children: Map = new Map();
  isEndOfWord = false;
}

const root = new TrieNode();

function insert(word: string) {
  let node = root;
  for (const char of word) {
    if (!node.children.has(char)) {
      node.children.set(char, new TrieNode());
    }
    node = node.children.get(char)!;
  }
  node.isEndOfWord = true;
}

insert("cat");

console.log(Array.from(root.children.keys()));

medium

A. ["cat"]

B. ["c", "a", "t"]

C. []

D. ["c"]

Solution

1. Step 1: Trace insertion of "cat" into Trie

   Starting at root, 'c' is not present, so a new node for 'c' is created. Then move to 'c' node, 'a' is added as child, then 't' as child of 'a'.

2. Step 2: Check root's children keys

   Root only has one child node for 'c'. The keys of root.children are ['c'].

3. Final Answer:

   ["c"] -> Option D

4. Quick Check:

   Root children keys after insert = ["c"] [OK]

Hint: Root children keys show first letters only [OK]

Common Mistakes:

• Expecting all letters at root level
• Confusing keys with full words
• Ignoring Map keys method

4. Identify the error in the following TypeScript code snippet for inserting a word into a Trie:

function insert(word: string) {
  let node = root;
  for (const char of word) {
    if (!node.children.has(char)) {
      node.children.set(char, new TrieNode());
    }
    node = node.children.get(char);
  }
  node.isEndOfWord = true;
}

medium

A. Using 'let' instead of 'const' for node

B. Missing parentheses when creating new TrieNode

C. Not checking if node.children.get(char) is undefined

D. Not marking isEndOfWord as false initially

Solution

1. Step 1: Check new object creation syntax

   In TypeScript, when creating a new object, parentheses are required even if no arguments are passed. new TrieNode should be new TrieNode().

2. Step 2: Verify other parts

   Using 'let' for node is fine since node changes. The get method is safe here because we just set the key if missing. isEndOfWord is set at the end, initial value doesn't cause error.

3. Final Answer:

   Missing parentheses when creating new TrieNode -> Option B

4. Quick Check:

   new object needs () [OK]

Hint: Always use () when calling constructors [OK]

Common Mistakes:

• Omitting () after new keyword
• Confusing let and const for variables
• Ignoring possible undefined from get()

5. You want to insert multiple words ["bat", "ball", "batman"] into a Trie. After inserting all, which of the following statements is true about the Trie structure?

hard

A. The node for 'b' has children 'a' and 'm' directly

B. Each word creates a separate branch from root

C. The node for 'b' has children 'a' only, and 'a' has children 't' and 'l'

D. The node for 't' is the end of word for both "bat" and "batman"

Solution

1. Step 1: Analyze common prefixes in words

   Words "bat", "ball", and "batman" share prefix 'b' -> 'a'. From 'a', 't' leads to "bat" and "batman", 'l' leads to "ball".

2. Step 2: Understand Trie branching

   Node 'b' has child 'a'. Node 'a' branches to 't' and 'l'. 'm' is child of 'a'->'t'->'m' for "batman". So 'm' is not direct child of 'b'.

3. Final Answer:

   The node for 'b' has children 'a' only, and 'a' has children 't' and 'l' -> Option C

4. Quick Check:

   Trie branches at shared prefixes [OK]

Hint: Words share nodes for common prefixes only [OK]

Common Mistakes:

• Assuming all words start new branches at root
• Thinking 'm' is direct child of 'b'
• Confusing end of word nodes