Binary Tree Traversals, Vertical Order, And Views

What's being tested

These problems test binary tree traversal with positional state: tracking depth for side views, column index for vertical order, and sometimes row/order for tie-breaking. Interviewers are probing whether you can choose BFS vs DFS, preserve required ordering, handle empty/single-node trees, and explain O(n) or sorting-related complexity clearly.

Patterns & templates

• Right side view via BFS — process level by level; append the last node seen per level; O(n) time, O(w) space.

• Left and right views in one pass — during level-order traversal, record first and last node per level; avoid two separate traversals.

• DFS depth tracking — visit right-first for right view or left-first for left view; record first value at each depth; O(h) recursion space.

• Vertical order traversal — assign root column 0, left col - 1, right col + 1; group values by column in a dict.

• BFS for vertical order tie-breaking — when ties are by breadth-first visitation order, use a queue of (node, col) instead of DFS.

• Column output ordering — track min_col and max_col during traversal for O(k) ordered output, or sort column keys for O(k log k).

• BST to doubly linked list — use in-order traversal to relink left as prev and right as next; preserve sorted order.

Common pitfalls

Pitfall: Using DFS for vertical order when the expected tie-break is BFS order; this can silently produce the wrong sequence within a column.

Pitfall: Appending every node at a depth for right view instead of only the last visible node per level.

Pitfall: Forgetting that recursion depth can be O(n) on a skewed tree; call this out or use iterative traversal if stack overflow matters.

Practice these

The practice cards below cover the canonical variants — solve all of them and time yourself.