Vertical Order Traversal of a Binary Tree

Question

The question asks the candidate to implement a function that performs a vertical order traversal of a binary tree, returning the nodes in a specific order based on their vertical positions.

Codemia · Accepted Answer

To solve the vertical order traversal of a binary tree, we can use a breadth-first search (BFS) approach. We will traverse the tree level by level while keeping track of the horizontal distance of each node from the root. Nodes that are at the same horizontal distance will be grouped together. We can use a queue to facilitate the BFS and a dictionary to store nodes by their horizontal distance.

1. Initialize a queue to hold nodes along with their horizontal distance from the root.
2. Use a dictionary to map horizontal distances to lists of node values.
3. Perform BFS: for each node, add its value to the corresponding list in the dictionary based on its horizontal distance.
4. After traversal, sort the dictionary by keys (horizontal distances) and return the values as the result.

Here is a sample Python implementation:
```python
from collections import deque, defaultdict

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def verticalOrder(root):
    if not root:
        return []
    column_table = defaultdict(list)
    queue = deque([(root, 0)])
    while queue:
        node, column = queue.popleft()
        column_table[column].append(node.val)
        if node.left:
            queue.append((node.left, column - 1))
        if node.right:
            queue.append((node.right, column + 1))
    return [column_table[x] for x in sorted(column_table.keys())]
```

The time complexity of this algorithm is O(N), where N is the number of nodes in the binary tree, as we visit each node once. The space complexity is also O(N) due to the storage of nodes in the queue and the dictionary.

Consider edge cases such as an empty tree, where the output should be an empty list. Additionally, handle trees with only one child or all nodes being in a straight line (skewed trees). These scenarios test the robustness of the algorithm.

Interviewers are looking for clarity in your explanation, the ability to write clean and efficient code, and a strong understanding of the underlying data structure. They also appreciate candidates who can discuss the trade-offs and complexities of their solutions.

Vertical Order Traversal of a Binary Tree

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