← Databricks Interview Insights
The construction itself wasn't too bad once I mapped out the recursion on paper.
Start by clarifying the definition and constraints of the Fibonacci tree, then implement a recursive function that builds the tree by combining F(n-1) and F(n-2). After coding, analyze the time and space complexity, noting the exponential growth due to overlapping subproblems and the potential for memoization to improve efficiency.
Pro tip: Mention that while the recursive solution is straightforward, it's inefficient for large n; you can optimize by reusing subtrees or using memoization, but be careful about shared references if the tree is mutable.
Confirm the definition of Fibonacci tree: F(0) is empty, F(1) is a single node, and for n>=2, F(n) has left subtree F(n-1) and right subtree F(n-2). Ask if nodes can be shared or if each tree must be independent.
Write a function that returns the root of F(n). Base cases: if n=0 return null, if n=1 return new node. Recursive case: create a root, set left = F(n-1), right = F(n-2).
The number of nodes in F(n) is the Fibonacci number Fib(n) (with Fib(1)=1, Fib(2)=1, etc.), which grows as φ^n. The recursive construction visits each node once, so time is O(φ^n), exponential.
The space used is proportional to the number of nodes, O(φ^n), plus recursion stack depth O(n). If memoization is used to avoid rebuilding subtrees, space remains O(φ^n) for the tree, but time can be reduced to O(φ^n) as well (since output size is exponential).
Mention that memoization can avoid redundant subtree construction, but if trees are mutable, sharing subtrees may cause issues. Alternatively, iterative construction or dynamic programming can build the tree bottom-up, but still requires exponential space.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.