Left Side View of Binary Tree in DSA Python - Deep Dive

Overview - Left Side View of Binary Tree

What is it?

The Left Side View of a Binary Tree is the set of nodes visible when you look at the tree from its left side. It shows the first node you see at each level of the tree, starting from the root down to the leaves. This view helps understand the structure of the tree from a specific angle.

Why it matters

Without the left side view, we might miss how a tree looks from different perspectives, which is important in many applications like graphical displays, tree traversals, and understanding hierarchical data. It helps in visualizing and debugging tree structures by focusing on nodes that are most visible from one side.

Where it fits

Before learning this, you should understand basic binary trees and tree traversal methods like breadth-first search (BFS) or depth-first search (DFS). After this, you can explore other tree views like right side view, top view, and bottom view, or advanced tree algorithms.

Mental Model

Core Idea

The left side view of a binary tree is the first node encountered at each level when looking from the left side.

Think of it like...

Imagine standing on the left side of a row of tall buildings of different heights. The buildings you see first at each height level are like the left side view nodes of the tree.

Binary Tree Levels:
Level 0:        1
Level 1:      /   \
Level 2:     2     3
Level 3:    / \     \
Level 4:   4   5     6

Left Side View: 1 -> 2 -> 4 -> null

Build-Up - 6 Steps

1

Foundation

Understanding Binary Tree Structure

Concept: Learn what a binary tree is and how nodes are connected.

A binary tree is a structure where each node has up to two children: left and right. The top node is called the root. Each child can also have its own children, forming levels.

Result

You can visualize a tree as a set of nodes connected by branches, with a clear top (root) and levels below.

Understanding the basic shape and connections in a binary tree is essential before exploring views or traversals.

2

Foundation

Level Order Traversal Basics

Concept: Learn how to visit nodes level by level from top to bottom.

Level order traversal visits nodes one level at a time, from left to right. It uses a queue to keep track of nodes to visit next.

Result

For the tree: 1 / \ 2 3 The traversal order is: 1, 2, 3

Level order traversal helps us process nodes level-wise, which is key to finding the left side view.

3

Intermediate

Identifying Leftmost Nodes per Level

🤔Before reading on: do you think the left side view always includes the left child of each node? Commit to yes or no.

Concept: The left side view includes the first node visited at each level during level order traversal.

When doing level order traversal, the first node you visit at each level is the leftmost node visible from the left side. You record this node and ignore others at the same level for the view.

Result

For the tree: 1 / \ 2 3 / \ 4 5 Left side view nodes: 1, 2, 4

Knowing that the left side view depends on the first node per level, not just left children, clarifies how to capture the view correctly.

4

Intermediate

Implementing Left Side View Using BFS

🤔Before reading on: do you think a queue or a stack is better for left side view? Commit to your answer.

Concept: Use a queue to perform BFS and capture the first node at each level for the left side view.

Start with the root in a queue. For each level, process all nodes in the queue. The first node processed at that level is added to the left side view. Add children to the queue for the next level.

Result

Left side view for example tree: [1, 2, 4]

Using BFS with a queue naturally processes nodes level by level, making it easy to pick the leftmost node.

5

Advanced

Left Side View Using DFS with Level Tracking

🤔Before reading on: do you think DFS can find the left side view as easily as BFS? Commit to yes or no.

Concept: DFS can find the left side view by visiting nodes in preorder and tracking the first node visited at each depth.

Start DFS from root with level 0. For each node, if this is the first time visiting this level, record the node. Recurse left child first, then right child. This ensures leftmost nodes are recorded first.

Result

Left side view for example tree: [1, 2, 4]

DFS with level tracking offers an alternative to BFS, useful when recursion is preferred or queue is unavailable.

6

Expert

Handling Edge Cases and Sparse Trees

🤔Before reading on: do you think missing left children affect the left side view? Commit to yes or no.

Concept: The left side view depends on the first visible node at each level, even if left children are missing.

In sparse trees, if a left child is missing, the right child might be the first visible node at that level. The algorithm must handle this by recording the first node encountered at each level regardless of position.

Result

For tree: 1 \ 3 Left side view: [1, 3]

Understanding that the left side view is about visibility, not just left children, prevents errors in sparse or unbalanced trees.

Under the Hood

The left side view algorithms work by traversing the tree level by level or depth by depth, recording the first node encountered at each level. BFS uses a queue to process nodes in order, while DFS uses recursion with level tracking. Internally, the tree nodes are visited in a controlled sequence to ensure the leftmost nodes are captured.

Why designed this way?

The design leverages natural tree traversal methods to efficiently find visible nodes without extra complex data structures. BFS aligns with the concept of levels, while DFS with level tracking offers a recursive alternative. This avoids scanning the entire tree multiple times.

┌─────────────┐
│    Root     │
│     1       │
└─────┬───────┘
      │
┌─────▼───────┐
│ Level Order │
│ Traversal   │
└─────┬───────┘
      │
┌─────▼─────────────┐
│ For each level:    │
│ Pick first node    │
└─────┬─────────────┘
      │
┌─────▼─────────────┐
│ Collect nodes for  │
│ Left Side View     │
└───────────────────┘

Myth Busters - 3 Common Misconceptions

Quick: Is the left side view always the left child of each node? Commit to yes or no.

Common Belief: The left side view is just the left child nodes of each parent.

Reality: The left side view is the first visible node at each level, which may be a right child if the left child is missing.

Why it matters: Assuming only left children leads to missing nodes in the view, causing incorrect results especially in sparse trees.

Quick: Does the left side view require visiting all nodes? Commit to yes or no.

Common Belief: You only need to visit left children to get the left side view.

Reality: You must visit all nodes at each level to find the first visible node, because left children might be missing.

Why it matters: Skipping nodes can cause incomplete views and bugs in tree visualization or algorithms relying on the view.

Quick: Can DFS without level tracking produce the left side view? Commit to yes or no.

Common Belief: Any DFS traversal will give the left side view.

Reality: DFS must track levels and record the first node per level to correctly produce the left side view.

Why it matters: Without level tracking, DFS may miss nodes or record wrong nodes, leading to incorrect views.

Expert Zone

1

The order of child traversal in DFS (left before right) is critical to capture the correct left side view.

2

In BFS, the queue size at each iteration represents the number of nodes at that level, enabling precise level boundary detection.

3

Sparse or unbalanced trees require careful handling to avoid missing visible nodes on the left side view.

When NOT to use

Left side view is not suitable when you need a full tree traversal or views from other angles like right side or top view. For balanced tree operations or searching, use inorder or preorder traversals instead.

Production Patterns

Used in graphical tree visualizations to show structure from the left, in UI components displaying hierarchical data, and in interview problems testing tree traversal mastery.

Connections

Right Side View of Binary Tree

Opposite perspective of the same problem, capturing first visible nodes from the right side.

Understanding left side view helps grasp right side view by symmetry, reinforcing level order and DFS traversal concepts.

Breadth-First Search (BFS)

Left side view uses BFS to process nodes level by level and pick the first node at each level.

Mastering BFS traversal is key to implementing many tree views and level-based algorithms.

Human Visual Perception

The left side view mimics how humans perceive objects from a side, focusing on the first visible elements.

This connection shows how computer algorithms model natural perception to solve visualization problems.

Common Pitfalls

#1 Only visiting left children to find left side view.

Wrong approach:

def left_side_view(root):
result = []
node = root
while node:
result.append(node.val)
node = node.left
return result

Correct approach:

def left_side_view(root):
if not root:
return []
from collections import deque
queue = deque([root])
result = []
while queue:
level_length = len(queue)
for i in range(level_length):
node = queue.popleft()
if i == 0:
result.append(node.val)
if node.left:
queue.append(node.left)
if node.right:
queue.append(node.right)
return result

Root cause:

Misunderstanding that left side view depends on first visible node per level, not just left children.

#2 Using DFS without tracking levels to record first nodes.

Wrong approach:

def left_side_view(root):
result = []
def dfs(node):
if not node:
return
result.append(node.val)
dfs(node.left)
dfs(node.right)
dfs(root)
return result

Correct approach:

def left_side_view(root):
result = []
def dfs(node, level):
if not node:
return
if level == len(result):
result.append(node.val)
dfs(node.left, level + 1)
dfs(node.right, level + 1)
dfs(root, 0)
return result

Root cause:

Not tracking levels causes recording all nodes in preorder, not just first per level.

Key Takeaways

The left side view shows the first visible node at each level when looking from the left side of a binary tree.

Level order traversal (BFS) naturally fits this problem by processing nodes level by level and picking the first node.

DFS can also find the left side view if it tracks levels and records the first node visited at each depth.

The left side view depends on visibility, not just left children, so algorithms must consider missing nodes carefully.

Understanding this concept helps in tree visualization, debugging, and mastering tree traversal techniques.

Practice

1. What does the Left Side View of a binary tree represent?

easy

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

B. Nodes at the deepest level of the tree

C. All leaf nodes of the tree

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

Solution

1. Step 1: Understand the view perspective

   The left side view shows nodes visible when looking at the tree from the left side.

2. Step 2: Identify visible nodes

   Only the first node at each level from the left is visible in this view.

3. Final Answer:

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

4. Quick Check:

   Left side view = nodes visible from left [OK]

Hint: Left side view shows first node at each level from left [OK]

Common Mistakes:

• Confusing left side view with right side view
• Thinking it shows all leaf nodes
• Assuming it shows deepest nodes only

2. Which of the following Python code snippets correctly initializes an empty list to store the left side view nodes?

easy

A. left_view = ()

B. left_view = {}

C. left_view = []

D. left_view = set()

Solution

1. Step 1: Identify the correct data structure

   We need a list to store nodes in order, so an empty list is best.

2. Step 2: Check syntax for list initialization

   Using square brackets [] creates an empty list in Python.

3. Final Answer:

   left_view = [] -> Option C

4. Quick Check:

   Empty list = [] [OK]

Hint: Use [] to create empty list for ordered nodes [OK]

Common Mistakes:

• Using {} which creates a dictionary, not a list
• Using () which creates a tuple, not a list
• Using set() which is unordered

3. What is the output of the following code that prints the left side view of the given binary tree?

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

def left_side_view(root):
    result = []
    def dfs(node, level):
        if not node:
            return
        if level == len(result):
            result.append(node.val)
        dfs(node.left, level + 1)
        dfs(node.right, level + 1)
    dfs(root, 0)
    return result

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

print(left_side_view(root))

medium

A. [1, 2, 3]

B. [1, 2, 4]

C. [1, 3, 5]

D. [1, 4, 5]

Solution

1. Step 1: Trace DFS traversal and level checks

   At level 0, node 1 is added. At level 1, node 2 is added (left child). At level 2, node 4 is added (left child's right child).

2. Step 2: Confirm nodes added only once per level

   Right children at each level are ignored if left child exists at that level.

3. Final Answer:

   [1, 2, 4] -> Option B

4. Quick Check:

   Left side view nodes = [1, 2, 4] [OK]

Hint: Add node if level equals result length during DFS [OK]

Common Mistakes:

• Adding right child nodes before left child nodes
• Appending nodes multiple times per level
• Confusing left and right children order

4. Find the error in the following code that attempts to print the left side view of a binary tree:

def left_side_view(root):
    result = []
    def dfs(node, level):
        if node is None:
            return
        if level < len(result):
            result.append(node.val)
        dfs(node.left, level + 1)
        dfs(node.right, level + 1)
    dfs(root, 0)
    return result

medium

A. The condition should be 'level == len(result)', not 'level < len(result)'

B. The base case should check 'if node' instead of 'if node is None'

C. The recursive calls should swap left and right children

D. The function should return 'result' inside the dfs function

Solution

1. Step 1: Analyze the condition for adding nodes

   The code uses 'level < len(result)' which is incorrect because nodes should be added only when level equals the current result length.

2. Step 2: Correct the condition to add nodes once per level

   Changing condition to 'level == len(result)' ensures only the first node at each level is added.

3. Final Answer:

   The condition should be 'level == len(result)', not 'level < len(result)' -> Option A

4. Quick Check:

   Use '==' to add first node per level [OK]

Hint: Add node only when level equals result length [OK]

Common Mistakes:

• Using '<' instead of '==' in condition
• Returning result inside recursive function
• Swapping left and right child calls unnecessarily

5. Given a binary tree, how would you modify the standard left side view algorithm to return the left side view nodes in reverse order (bottom to top)?

hard

A. Perform the usual left side view traversal, then reverse the result list before returning

B. Traverse the tree from right to left instead of left to right

C. Add nodes to the result list only if they are leaf nodes

D. Use a queue and perform level order traversal from right to left

Solution

1. Step 1: Perform standard left side view traversal

   Use DFS or BFS to collect the first node at each level from left to right.

2. Step 2: Reverse the collected list

   After traversal, reverse the list to get nodes from bottom to top.

3. Final Answer:

   Perform the usual left side view traversal, then reverse the result list before returning -> Option A

4. Quick Check:

   Reverse after left side view traversal [OK]

Hint: Reverse the left side view list after traversal [OK]

Common Mistakes:

• Changing traversal order instead of reversing result
• Collecting leaf nodes only
• Using right to left traversal which gives wrong nodes