Recursion, Dynamic Programming, And Implicit Structures
Asked of: Software Engineer
Last updated
What's being tested
These problems probe mastery of recursion on an implicit tree: compute and use subtree sizes given a Fibonacci-like recurrence, then map preorder indexes to tree paths with index arithmetic. Interviewers check correctness, off-by-one handling, and efficient traversal without materializing the whole tree.
Patterns & templates
- Compute subtree sizes with the Fibonacci recurrence and memoize (
`getSize(k)`); this is O(k) to build, constant-time lookups thereafter. - Preorder index navigation: compare target index to
`left_size`+ 1 to decide left/root/right; iterate until leaf — O(height) steps. - Iterative recursion: replace recursive descent with a loop that updates node rank and subtree order to avoid stack depth issues.
- Path encoding: emit directions (
`L`/`R`) while descending; reconstruct node-to-node path by computing LCA via index-to-path conversion. - Dynamic programming on indices: cache computed path segments or sizes across queries to answer multiple path requests in O(height) each.
- Guard against overflow: cap Fibonacci sizes at
`INT64_MAX`and clamp indices; check for invalid indexes early.
Common pitfalls
Pitfall: Off-by-one errors when treating
`left_size`, root position, and right subtree start — always test small k (1..4) to validate indexing.
Pitfall: Assuming tree height is log(n); for Fibonacci trees height ≈ index k, so complexity must be in terms of k, not total nodes.
Pitfall: Using recursion without tail-call elimination can blow the stack for deep k — prefer iterative descent or explicit stack.
Practice these
The practice cards below cover the canonical variants — solve all of them and time yourself.
Practice questions
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