Top View of Binary Tree in DSA Javascript - Time & Space Complexity

Time Complexity: Top View of Binary Tree

O(n)

Understanding Time Complexity

We want to understand how the time needed to find the top view of a binary tree changes as the tree grows.

How does the number of nodes affect the work done to get the top view?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

function topView(root) {
  if (!root) return [];
  const queue = [{ node: root, hd: 0 }];
  const map = new Map();
  while (queue.length) {
    const { node, hd } = queue.shift();
    if (!map.has(hd)) map.set(hd, node.val);
    if (node.left) queue.push({ node: node.left, hd: hd - 1 });
    if (node.right) queue.push({ node: node.right, hd: hd + 1 });
  }
  return Array.from(map.values());
}
    

This code finds the top view of a binary tree by visiting nodes level by level and tracking their horizontal distance.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that visits each node once.
• How many times: Once for every node in the tree (n times).

How Execution Grows With Input

As the number of nodes grows, the code visits each node once, so the work grows directly with the number of nodes.

Input Size (n)	Approx. Operations
10	About 10 visits
100	About 100 visits
1000	About 1000 visits

Pattern observation: The operations increase linearly as the tree size increases.

Final Time Complexity

Time Complexity: O(n)

This means the time to find the top view grows in direct proportion to the number of nodes in the tree.

Common Mistake

[X] Wrong: "The code visits nodes multiple times, so time is more than linear."

[OK] Correct: Each node is visited exactly once in the queue, so the total work is proportional to the number of nodes.

Interview Connect

Understanding this linear time complexity helps you explain how tree traversal works efficiently in real problems.

Self-Check

"What if we used a recursive approach instead of a queue? How would the time complexity change?"

Practice

1. What does the top view of a binary tree represent?

easy

A. All leaf nodes of the tree

B. Nodes visible when the tree is viewed from the left side

C. Nodes visible when the tree is viewed from the right side

D. Nodes visible when the tree is viewed from above

Solution

1. Step 1: Understand the top view concept

   The top view of a binary tree shows nodes visible from above, ignoring nodes hidden behind others.

2. Step 2: Compare with other views

   Left or right views show nodes from sides, and leaf nodes are only the bottom nodes.

3. Final Answer:

   Nodes visible when the tree is viewed from above -> Option D

4. Quick Check:

   Top view = nodes seen from above [OK]

Hint: Top view shows nodes visible from above only [OK]

Common Mistakes:

• Confusing top view with left or right view
• Thinking top view includes all leaf nodes
• Assuming top view shows all nodes

2. Which JavaScript data structure is best suited to store nodes by their horizontal distance when computing the top view of a binary tree?

easy

A. Set

B. Array

C. Map

D. Stack

Solution

1. Step 1: Identify the need for key-value pairs

   We need to store nodes with their horizontal distance as keys and node values as values.

2. Step 2: Choose the best data structure

   A Map allows storing key-value pairs with efficient lookup and insertion.

3. Final Answer:

   Map -> Option C

4. Quick Check:

   Map stores horizontal distance keys [OK]

Hint: Use Map for key-value horizontal distance storage [OK]

Common Mistakes:

• Using Array which is index-based, not key-based
• Using Set which stores only unique values without keys
• Using Stack which is LIFO, not suitable here

3. What is the output of the following code snippet that prints the top view of the binary tree?

class Node {
  constructor(data) {
    this.data = data;
    this.left = null;
    this.right = null;
  }
}

function topView(root) {
  if (!root) return [];
  const map = new Map();
  const queue = [{ node: root, hd: 0 }];
  while (queue.length) {
    const { node, hd } = queue.shift();
    if (!map.has(hd)) map.set(hd, node.data);
    if (node.left) queue.push({ node: node.left, hd: hd - 1 });
    if (node.right) queue.push({ node: node.right, hd: hd + 1 });
  }
  return [...map.entries()]
    .sort((a, b) => a[0] - b[0])
    .map(entry => entry[1]);
}

const root = new Node(1);
root.left = new Node(2);
root.right = new Node(3);
root.left.right = new Node(4);
root.right.right = new Node(5);

console.log(topView(root));

medium

A. [2, 1, 3, 5]

B. [2, 1, 3]

C. [2, 1, 4, 3, 5]

D. [1, 2, 3, 4, 5]

Solution

1. Step 1: Traverse the tree with horizontal distances

   Start at root (1) with hd=0, add left child (2) hd=-1, right child (3) hd=1, then 4 at hd=0 (ignored since hd=0 exists), 5 at hd=2.

2. Step 2: Collect first nodes at each horizontal distance

   Map stores hd:-1=2, hd:0=1, hd:1=3, hd:2=5. Sorted by hd: -1,0,1,2 gives [2,1,3,5].

3. Final Answer:

   [2, 1, 3, 5] -> Option A

4. Quick Check:

   Top view nodes by hd = [2,1,3,5] [OK]

Hint: First node at each horizontal distance is in top view [OK]

Common Mistakes:

• Including nodes hidden behind others at same hd
• Not sorting by horizontal distance before output
• Adding nodes multiple times for same hd

4. Identify the bug in this top view function and select the correct fix:

function topView(root) {
  if (!root) return [];
  const map = new Map();
  const queue = [{ node: root, hd: 0 }];
  while (queue.length) {
    const { node, hd } = queue.pop();
    if (!map.has(hd)) map.set(hd, node.data);
    if (node.left) queue.push({ node: node.left, hd: hd - 1 });
    if (node.right) queue.push({ node: node.right, hd: hd + 1 });
  }
  return [...map.entries()]
    .sort((a, b) => a[0] - b[0])
    .map(entry => entry[1]);
}

medium

A. Replace queue.pop() with queue.shift() to process nodes in correct order

B. Change map to a Set to avoid duplicate nodes

C. Remove sorting before returning the result

D. Add a visited set to avoid infinite loops

Solution

1. Step 1: Understand queue usage in BFS

   Using queue.pop() removes last element, making it a stack (DFS), not BFS. BFS requires queue.shift() to process nodes in FIFO order.

2. Step 2: Fix the traversal order

   Replacing pop() with shift() ensures nodes are processed level by level, correctly capturing top view nodes.

3. Final Answer:

   Replace queue.pop() with queue.shift() to process nodes in correct order -> Option A

4. Quick Check:

   BFS needs shift(), not pop() [OK]

Hint: Use shift() for BFS queue, pop() is for stack [OK]

Common Mistakes:

• Using pop() causing wrong traversal order
• Using Set instead of Map losing key-value pairs
• Skipping sorting which orders output incorrectly

5. Given a binary tree where multiple nodes share the same horizontal distance and level, how should the top view algorithm decide which node to include in the output?

hard

A. Include the node that appears last in level order traversal at that horizontal distance

B. Include the node that appears first in level order traversal at that horizontal distance

C. Include the node with the maximum value at that horizontal distance

D. Include all nodes at that horizontal distance

Solution

1. Step 1: Understand node conflicts at same horizontal distance and level

   When nodes share horizontal distance and level, top view includes the first encountered node in level order (BFS) traversal.

2. Step 2: Reason why first node is chosen

   Because BFS visits nodes level by level from left to right, the first node at that horizontal distance is visible from top.

3. Final Answer:

   Include the node that appears first in level order traversal at that horizontal distance -> Option B

4. Quick Check:

   Top view = first node at hd in BFS order [OK]

Hint: Pick first node at horizontal distance in BFS [OK]

Common Mistakes:

• Choosing node by max value instead of order
• Including all nodes causing duplicates
• Choosing last node instead of first