Trie Node Design and Initialization in DSA Javascript - Time & Space Complexity

Time Complexity: Trie Node Design and Initialization

O(1)

Understanding Time Complexity

We want to understand how much work it takes to create a single node in a trie.

This helps us see how the trie grows as we add words.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

class TrieNode {
  constructor() {
    this.children = {};
    this.isEndOfWord = false;
  }
}
    

This code creates a trie node with an empty children map and a flag for word end.

Identify Repeating Operations

Look for any loops or repeated steps inside the constructor.

• Primary operation: Creating an empty object and setting a boolean.
• How many times: This happens once per node creation.

How Execution Grows With Input

Each node creation takes the same small amount of work, no matter what.

Input Size (n)	Approx. Operations
1 node	2 simple steps
10 nodes	20 simple steps
100 nodes	200 simple steps

Pattern observation: The work grows directly with the number of nodes created.

Final Time Complexity

Time Complexity: O(1)

This means creating one trie node always takes the same small amount of time, no matter what.

Common Mistake

[X] Wrong: "Creating a trie node takes longer if the trie is big already."

[OK] Correct: Each node is made fresh with no loops, so its creation time does not depend on trie size.

Interview Connect

Knowing that node creation is quick helps you focus on where the real work happens when adding or searching words.

Self-Check

"What if the children were stored in an array of fixed size instead of an object? How would the time complexity change?"