Binary Tree Right Side View

Data Structures
Medium
Uber
66.1K views

Given the root of a binary tree, imagine yourself standing on the right side of it, return the values of the nodes you can see ordered from top to bottom. Use BFS or DFS.

Why Interviewers Ask This

Uber interviewers ask this to evaluate a candidate's ability to traverse hierarchical data structures efficiently while managing state across levels. It tests if you understand the difference between BFS and DFS trade-offs, specifically regarding space complexity and level-order processing. They want to see if you can translate a visual spatial problem into an algorithmic solution that handles edge cases like skewed trees without unnecessary overhead.

How to Answer This Question

1. Clarify the Problem: Immediately confirm what 'right side view' means by asking for examples with null nodes or single-child branches. 2. Choose Strategy: Propose Breadth-First Search (BFS) as the primary approach because it naturally processes nodes level-by-level, making it intuitive to capture the last node of each layer. Mention Depth-First Search (DFS) as an alternative but note its reliance on depth tracking. 3. Define Data Structures: Explicitly state you will use a Queue for BFS to manage the current level's nodes. 4. Walk Through Logic: Explain iterating through the queue size to process one level at a time. Emphasize capturing the value of the last element in the current level's iteration. 5. Optimize and Validate: Discuss time complexity O(N) and space complexity O(W), where W is the maximum width. Briefly mention handling empty tree inputs first to show robustness typical of Uber's production-grade expectations.

Key Points to Cover

  • Demonstrating clear understanding of Level Order Traversal mechanics
  • Explicitly distinguishing between BFS and DFS trade-offs for this specific geometry
  • Handling edge cases like empty trees or unbalanced structures proactively
  • Correctly identifying the 'last node' logic within a level iteration
  • Articulating Time and Space complexity with precision

Sample Answer

To solve the Binary Tree Right Side View problem, I would start by clarifying that we need the rightmost node at every depth level. Given the requirement to return values top-to-bottom, a Level Order Traversal using Breadth-First Search is the most straightforward approach. I would initialize a queue and add the root node. While the queue is not empty, I would determine the number of nodes currently in the queue, which represents the size of the current level. I would then iterate exactly that many times. Inside this loop, I would dequeue a node and check if it is the last node in the current level. If it is, I add its value to my result list. For non-last nodes, I simply enqueue their children if they exist. This ensures we only capture the rightmost visible node per level. Alternatively, a recursive DFS could work by visiting the right child before the left, keeping track of the current depth and adding the node value only when the depth matches the size of our result list, effectively filling gaps from top to bottom. Both approaches run in O(N) time since we visit every node once. The BFS approach uses O(W) space for the queue, while DFS uses O(H) space for the recursion stack. I prefer BFS here for its clarity in handling level boundaries, which aligns well with systems requiring predictable memory usage patterns.

Common Mistakes to Avoid

  • Using a simple DFS without tracking depth correctly, leading to missing levels or wrong order
  • Forgetting to handle the case where the tree is empty, causing runtime errors
  • Processing all nodes in a level instead of just the last one, resulting in incorrect output
  • Not mentioning space complexity constraints, which is critical for large-scale Uber infrastructure scenarios

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