Left Side View of Binary Tree in DSA Go - Time & Space Complexity

Time Complexity: Left Side View of Binary Tree

O(n)

Understanding Time Complexity

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

Specifically, how does the number of steps grow when the tree has more nodes?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

func leftSideView(root *TreeNode) []int {
    if root == nil {
        return []int{}
    }
    var result []int
    queue := []*TreeNode{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
}
    

This code finds the left side view by visiting nodes level by level and recording the first node at each level.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Visiting each node once in a breadth-first manner.
• How many times: Each node is processed exactly once in the inner loop.

How Execution Grows With Input

As the number of nodes (n) increases, the code visits each node once, so the total steps grow roughly in direct proportion to n.

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

Pattern observation: The number of operations grows linearly with the number of nodes.

Final Time Complexity

Time Complexity: O(n)

This means the time to find the left side view grows directly with the number of nodes in the tree.

Common Mistake

[X] Wrong: "Because we only record one node per level, the time is O(height) or less."

[OK] Correct: Even though we record one node per level, we still visit every node to know which is first at each level, so the time depends on total nodes, not just height.

Interview Connect

Understanding this helps you explain how tree traversal works and how to analyze algorithms that visit all nodes efficiently.

Self-Check

"What if we changed the traversal to depth-first search instead of breadth-first? How would the time complexity change?"