Top View of Binary Tree in DSA Go - 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.

func topView(root *Node) []int {
    if root == nil {
        return []int{}
    }
    type pair struct {
        node *Node
        hd   int
    }
    queue := []pair{{root, 0}}
    hdMap := map[int]int{}
    minHd, maxHd := 0, 0

    for len(queue) > 0 {
        p := queue[0]
        queue = queue[1:]
        if _, ok := hdMap[p.hd]; !ok {
            hdMap[p.hd] = p.node.data
        }
        if p.node.left != nil {
            queue = append(queue, pair{p.node.left, p.hd - 1})
            if p.hd-1 < minHd {
                minHd = p.hd - 1
            }
        }
        if p.node.right != nil {
            queue = append(queue, pair{p.node.right, p.hd + 1})
            if p.hd+1 > maxHd {
                maxHd = p.hd + 1
            }
        }
    }

    result := []int{}
    for i := minHd; i <= maxHd; i++ {
        result = append(result, hdMap[i])
    }
    return result
}
    

This code finds the top view of a binary tree by doing a level order traversal and tracking horizontal distances.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The while loop that processes each node once in a queue.
• How many times: Exactly once per 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 and checks
100	About 100 visits and checks
1000	About 1000 visits and checks

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 the time is more than linear."

[OK] Correct: Each node is added to the queue once and processed once, so the total work is proportional to the number of nodes.

Interview Connect

Understanding this linear time complexity helps you explain how tree traversals work efficiently and shows you can analyze common tree problems clearly.

Self-Check

"What if we used a depth-first traversal instead of breadth-first? How would the time complexity change?"