Tree Traversal And Hierarchical Structures
Asked of: Software Engineer
Last updated

What's being tested
Tree traversal over binary and N-ary hierarchies: choosing DFS vs BFS, preserving ordering, and attaching metadata like depth, column, or path position. Interviewers probe whether you can convert a structural requirement—vertical order, boundary, kth value, indentation—into a clean traversal invariant with correct edge-case handling.
Patterns & templates
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DFS with depth state —
dfs(node, depth)gives indentation, boundary levels, or recursive formatting;O(n)time,O(h)call stack. -
BFS with coordinates — queue
(node, row, col)for vertical traversal; sort bycol, thenrow, then value if required. -
In-order traversal for BSTs —
left -> node -> rightyields sorted order; stop afterkvisits forO(h + k)time. -
Boundary traversal — split into left boundary, leaves, right boundary; avoid duplicating root or leaf nodes across phases.
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N-ary ordered children — child index matters; first child often defines left view/boundary, last child defines right view/boundary.
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Iterative stack template — use
(node, depth, state)when recursion depth may exceed limits; preserves explicit traversal control. -
Complexity discipline — most solutions should be
O(n)time; vertical traversal may addO(n log n)sorting unless grouping order is maintained.
Common pitfalls
Pitfall: Treating vertical traversal as simple BFS without tie-breaking; equal column and row cases must be ordered exactly as specified.
Pitfall: Duplicating nodes in boundary problems, especially when a boundary node is also a leaf.
Pitfall: Forgetting degenerate trees: empty tree, single node, linked-list-shaped tree, or N-ary nodes with zero children.
Practice these
The practice cards below cover the canonical variants — solve all of them and time yourself.
Featured in interview prep guides
Practice questions
- Solve Balanced Permutations and Tree ReversalsUber · Software Engineer · Take-home Project · medium
- Find Kth Smallest in BSTUber · Software Engineer · Technical Screen · medium
- Solve stock profit and vertical tree traversalUber · Software Engineer · Onsite · medium
- Compute outer boundary of an N-ary treeUber · Software Engineer · Technical Screen · medium
- Print directory tree with indentationUber · Software Engineer · Technical Screen · medium
- Simulate views on an n-ary treeUber · Software Engineer · Technical Screen · Medium
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