Why Bottom View of Binary Tree in DSA Javascript?

The Big Idea

Discover how to see the hidden branches of a tree from the ground without missing a single one!

The Scenario

Imagine you have a tall tree in your backyard and you want to see which branches are visible if you look at the tree from the bottom. You try to write down all the branches you see from the ground, but the tree is big and some branches hide others. Doing this by just looking and guessing is confusing and you might miss some branches.

The Problem

Trying to figure out the bottom view of a tree by hand is slow and error-prone because you have to remember which branches are hidden behind others. It's easy to forget or mix up branches, especially when the tree has many layers and branches overlap. This manual method doesn't scale well for big trees.

The Solution

The bottom view of a binary tree uses a smart way to track which nodes are visible from the bottom by using their horizontal positions. It automatically finds the lowest visible nodes at each horizontal position, so you don't have to guess or remember. This method is fast and works perfectly even for big trees.

Before vs After

✗ Before

function bottomViewManual(tree) {
  // Try to guess visible nodes by checking levels manually
  // This is confusing and incomplete
  return [];
}

✓ After

function bottomView(tree) {
  // Use horizontal distances and a map to track bottom nodes
  // Return nodes visible from bottom
  return bottomNodes;
}

What It Enables

This concept lets you quickly find and print all nodes visible from the bottom of a binary tree, no matter how big or complex the tree is.

Real Life Example

In city planning, if buildings are arranged like a tree, bottom view helps find which buildings are visible from street level when looking up, helping design better views and sunlight access.

Key Takeaways

Manual observation of bottom view is confusing and error-prone.

Bottom view uses horizontal positions to find visible nodes automatically.

This method works efficiently for any size of binary tree.

Practice

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

easy

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

B. Nodes visible when the tree is viewed from the top

C. Nodes visible when the tree is viewed from the bottom

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

Solution

1. Step 1: Understand the bottom view concept

   The bottom view shows nodes visible when looking at the tree from below, meaning the lowest nodes at each horizontal distance.

2. Step 2: Compare with other views

   Top view shows nodes from above, left and right views show nodes from sides, so bottom view is unique for bottom perspective.

3. Final Answer:

   Nodes visible when the tree is viewed from the bottom -> Option C

4. Quick Check:

   Bottom view = nodes visible from below [OK]

Hint: Bottom view shows lowest nodes at each horizontal distance [OK]

Common Mistakes:

• Confusing bottom view with top view
• Thinking bottom view shows all leaf nodes
• Mixing bottom view with side views

2. Which of the following JavaScript code snippets correctly initializes a Map to store horizontal distances and nodes for bottom view?

easy

A. const map = new Map();

B. const map = {};

C. const map = new Array();

D. const map = new Set();

Solution

1. Step 1: Identify suitable data structure for key-value pairs

   Map is ideal for storing horizontal distance as key and node data as value with easy insertion and retrieval.

2. Step 2: Check other options

   Object ({}) can be used but Map is preferred for ordered keys and better methods; Array and Set are not suitable for key-value pairs.

3. Final Answer:

   const map = new Map(); -> Option A

4. Quick Check:

   Use Map for horizontal distance mapping [OK]

Hint: Use Map() for key-value storage in bottom view [OK]

Common Mistakes:

• Using Array instead of Map for key-value pairs
• Using Set which stores only unique values, not key-value
• Using plain object without considering key types

3. Consider the following binary tree and code snippet to print its bottom view:

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

const root = new Node(20);
root.left = new Node(8);
root.right = new Node(22);
root.left.left = new Node(5);
root.left.right = new Node(3);
root.right.right = new Node(25);
root.left.right.left = new Node(10);
root.left.right.right = new Node(14);

// Bottom view logic omitted for brevity
// Assume correct implementation

// Output bottom view nodes in order of horizontal distance
// What is the bottom view output?

medium

A. [5, 8, 3, 14, 25]

B. [5, 10, 3, 14, 25]

C. [5, 10, 3, 22, 25]

D. [8, 10, 3, 14, 25]

Solution

1. Step 1: Assign horizontal distances and track bottom nodes

   Assign horizontal distances: 20(0), 8(-1), 22(1), 5(-2), 3(0), 25(2), 10(-1), 14(1). Bottom view keeps last node at each horizontal distance.

2. Step 2: Determine bottom nodes at each horizontal distance

   At -2: 5; at -1: 10 (overwrites 8); at 0: 3 (overwrites 20); at 1: 14 (overwrites 22); at 2: 25.

3. Final Answer:

   [5, 10, 3, 14, 25] -> Option B

4. Quick Check:

   Bottom view nodes = [5,10,3,14,25] [OK]

Hint: Track last node at each horizontal distance [OK]

Common Mistakes:

• Using first node instead of last at horizontal distance
• Mixing horizontal distances incorrectly
• Ignoring overwriting nodes at same horizontal distance

4. The following code attempts to print the bottom view of a binary tree but produces incorrect output. What is the main issue?

function bottomView(root) {
  const map = new Map();
  const queue = [];
  queue.push({ node: root, hd: 0 });

  while (queue.length > 0) {
    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 Array.from(map.values());
}

medium

A. It stores only the first node at each horizontal distance, not the bottom-most

B. It uses shift() which is inefficient for queue

C. It does not handle null root input

D. It uses Map instead of Object for storage

Solution

1. Step 1: Analyze map update condition

   The code sets map value only if horizontal distance key is not present, so it keeps first node encountered at that hd.

2. Step 2: Understand bottom view requirement

   Bottom view requires last node at each horizontal distance (lowest level), so map should update value every time a node at same hd is found.

3. Final Answer:

   It stores only the first node at each horizontal distance, not the bottom-most -> Option A

4. Quick Check:

   Bottom view needs last node per hd, code keeps first [OK]

Hint: Update map value for every node at horizontal distance [OK]

Common Mistakes:

• Not updating map on repeated horizontal distances
• Confusing top view logic with bottom view
• Ignoring queue inefficiency but that doesn't affect correctness

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

hard

A. Display the node with the smallest value at that horizontal distance

B. Display the leftmost node at that horizontal distance and level

C. Display the rightmost node at that horizontal distance and level

D. Display the node encountered last in level order traversal at that horizontal distance

Solution

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

   When nodes share horizontal distance and level, bottom view shows the one visible from bottom, which is the one encountered last in level order traversal.

2. Step 2: Reason about traversal order

   Level order traversal processes nodes left to right at each level, so last encountered node at hd and level overwrites previous.

3. Final Answer:

   Display the node encountered last in level order traversal at that horizontal distance -> Option D

4. Quick Check:

   Bottom view uses last node in level order per hd [OK]

Hint: Use last node in level order traversal for bottom view [OK]

Common Mistakes:

• Choosing leftmost or rightmost arbitrarily
• Choosing node by value instead of position
• Ignoring traversal order impact