Left Side View of Binary Tree in DSA Go - 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 encounter at each level from top to bottom. This view helps understand the structure of the tree from a different perspective than the usual top-down or in-order views.

Why it matters

Without the left side view, we might miss how the tree looks from different angles, which is important in many applications like graphical displays, tree serialization, or understanding hierarchical data. It helps in visualizing and debugging tree structures by showing which nodes are 'blocking' others from the left side.

Where it fits

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

Mental Model

Core Idea

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

Think of it like...

Imagine standing on the left side of a tall bookshelf with books stacked in rows and columns. The left side view is like seeing only the first book on each shelf from your side, hiding the books behind it.

Binary Tree Levels:
Level 0:       1
Level 1:     2     3
Level 2:   4   5 6   7

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

Build-Up - 6 Steps

1

Foundation

Understanding Binary Tree Structure

Concept: Introduce 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 have its own children, forming levels. For example, a root node 1 can have left child 2 and right child 3.

Result

You can visualize a tree with nodes connected by branches, each node having at most two children.

Understanding the basic structure of binary trees is essential before exploring any 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 at the current level before moving to the next. For example, visiting nodes in order: 1, then 2 and 3, then 4, 5, 6, 7.

Result

You can list nodes in the order they appear level-wise.

Level order traversal is the foundation for extracting views like the left side view.

3

Intermediate

Identifying Leftmost Nodes at Each Level

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

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

When traversing level by level, the first node you see at each level is part of the left side view. This might not always be the left child if the left child is missing. For example, if a node has no left child but has a right child, that right child becomes visible from the left side.

Result

You can identify which nodes form the left side view by picking the first node at each level.

Knowing that the left side view depends on the first visible node at each level, not just left children, prevents common mistakes.

4

Intermediate

Implementing Left Side View Using BFS Queue

🤔Before reading on: do you think we need to store all nodes at each level to find the left side view, or just the first one? Commit to your answer.

Concept: Use a queue to perform level order traversal and record the first node at each level for the left side view.

Initialize a queue with the root node. For each level, process all nodes in the queue. The first node processed at that level is added to the left side view. Enqueue children left to right. Repeat until the queue is empty.

Result

You get a list of nodes representing the left side view, e.g., [1, 2, 4].

Understanding that only the first node at each level matters optimizes the process and clarifies the left side view logic.

5

Advanced

Recursive DFS Approach for Left Side View

🤔Before reading on: do you think depth-first search can find the left side view as easily as breadth-first search? Commit to yes or no.

Concept: Use depth-first search (DFS) with tracking of the current level to record the first node visited at each depth.

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

Result

You get the left side view nodes in order, e.g., [1, 2, 4].

Knowing DFS can solve this problem shows multiple ways to approach tree views and deepens understanding of traversal strategies.

6

Expert

Handling Sparse Trees and Edge Cases

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

Concept: Understand how the left side view adapts when nodes are missing or the tree is unbalanced.

In sparse trees, some levels may have only right children. The left side view includes these nodes because they are the first visible at their level. Also, trees with single branches still produce a left side view equal to the branch nodes.

Result

The left side view correctly reflects visible nodes even in irregular trees.

Recognizing how the left side view adapts to tree shape prevents incorrect assumptions and bugs in real-world data.

Under the Hood

The left side view is computed by traversing the tree level by level and selecting the first node encountered at each level. Internally, a queue or recursion stack keeps track of nodes to visit. The traversal ensures nodes are visited in an order that reveals which nodes are visible from the left side. Memory holds nodes temporarily during traversal, and the first node per level is recorded.

Why designed this way?

This approach leverages the natural hierarchy of trees and the concept of levels to simplify visibility determination. Alternatives like checking all nodes for visibility would be inefficient. Using BFS or DFS with level tracking balances simplicity and performance.

┌───────────────┐
│    Root (1)   │
└──────┬────────┘
       │
┌──────┴───────┐
│ Level Order  │
│ Traversal    │
└──────┬───────┘
       │
┌──────┴─────────────┐
│ For each level:     │
│   Pick first node   │
└──────┬─────────────┘
       │
┌──────┴─────────────┐
│ Left Side View List │
└────────────────────┘

Myth Busters - 3 Common Misconceptions

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

Common Belief: The left side view always consists of the left children of nodes.

Reality: The left side view includes 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 are visible causes missing nodes in the view, leading to incorrect results.

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

Common Belief: You must visit every node to find the left side view.

Reality: While all nodes are visited in BFS or DFS, only the first node at each level is recorded, so the view depends on selective recording, not all nodes equally.

Why it matters: Misunderstanding this can lead to inefficient or complicated code that tries to track unnecessary nodes.

Quick: Can DFS fail to find the left side view? Commit yes or no.

Common Belief: DFS is not suitable for finding the left side view because it doesn't process nodes level by level.

Reality: DFS with level tracking and visiting left child first can correctly find the left side view.

Why it matters: Ignoring DFS as a solution limits understanding of traversal flexibility and algorithm design.

Expert Zone

1

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

2

In BFS, the queue size at each level determines how many nodes to process, ensuring the first node is the leftmost.

3

Sparse or unbalanced trees reveal that the left side view depends on visibility, not just node position.

When NOT to use

If you need the full structure or all nodes visible from multiple angles, left side view alone is insufficient. For example, use top view or right side view for other perspectives. Also, for very large trees where memory is limited, streaming or partial views might be better.

Production Patterns

Used in graphical tree visualizations to show hierarchical data from the left perspective. Also used in interview problems to test understanding of tree traversals and level processing. In UI trees, it helps in rendering visible nodes efficiently.

Connections

Breadth-First Search (BFS)

The left side view uses BFS to process nodes level by level.

Understanding BFS traversal is key to extracting level-based views like the left side view.

Depth-First Search (DFS)

DFS with level tracking can also produce the left side view by prioritizing left children.

Knowing DFS can solve level problems broadens algorithmic thinking beyond BFS.

Human Visual Perception

The left side view mimics how humans perceive objects from a side angle, seeing only the front-most parts.

Recognizing this connection helps appreciate why certain nodes are visible and others hidden, linking computer science to real-world perception.

Common Pitfalls

#1 Only collecting left children nodes for the view.

Wrong approach:

func leftSideView(root *Node) []int {
var result []int
var dfs func(node *Node)
dfs = func(node *Node) {
if node == nil {
return
}
result = append(result, node.Val)
dfs(node.Left)
}
dfs(root)
return result
}

Correct approach:

func leftSideView(root *Node) []int {
var result []int
var dfs func(node *Node, level int)
visited := make(map[int]bool)
dfs = func(node *Node, level int) {
if node == nil {
return
}
if !visited[level] {
result = append(result, node.Val)
visited[level] = true
}
dfs(node.Left, level+1)
dfs(node.Right, level+1)
}
dfs(root, 0)
return result
}

Root cause:

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

#2 Not processing nodes level by level, causing incorrect order.

Wrong approach:

func leftSideView(root *Node) []int {
var result []int
if root == nil {
return result
}
queue := []*Node{root}
for len(queue) > 0 {
node := queue[0]
queue = queue[1:]
result = append(result, node.Val) // appending every node
if node.Left != nil {
queue = append(queue, node.Left)
}
if node.Right != nil {
queue = append(queue, node.Right)
}
}
return result
}

Correct approach:

func leftSideView(root *Node) []int {
var result []int
if root == nil {
return result
}
queue := []*Node{root}
for len(queue) > 0 {
levelSize := len(queue)
for i := 0; i < levelSize; i++ {
node := queue[0]
queue = queue[1:]
if i == 0 {
result = append(result, node.Val)
}
if node.Left != nil {
queue = append(queue, node.Left)
}
if node.Right != nil {
queue = append(queue, node.Right)
}
}
}
return result
}

Root cause:

Failing to separate nodes by level causes all nodes to be added, not just the first per level.

Key Takeaways

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

Level order traversal (BFS) is the most straightforward way to find the left side view by recording the first node at each level.

Depth-first search (DFS) with level tracking and left-first traversal can also produce the left side view.

The left side view depends on visibility, not just left children, so right children can appear if left children are missing.

Understanding the left side view deepens your grasp of tree traversals and how different perspectives reveal different parts of data structures.