The BST property does most of the work here, you just DFS and only follow edges where the child value is larger than the parent.
Use a post-order DFS that returns the longest strictly increasing path starting at each node. At each node, combine the best increasing paths from left and right children if their values are greater than the node's value, and update a global maximum with the sum of the two longest valid branches plus one.
Pro tip: Clarify that the path must follow parent-child edges and be strictly increasing, so you cannot traverse from a child back to its parent. Also, mention that the global maximum can be updated at each node by considering the sum of the two longest increasing branches, which is a common pattern in tree path problems.
Confirm that the path must be strictly increasing and follow parent-child edges, and that the path can go through a node's left and right subtrees. Ask if the path can start and end at any nodes.
Define a DFS function that returns the length of the longest strictly increasing path starting at the current node and going downward. This function will be called recursively on children.
For each child, if the child's value is greater than the current node's value, recursively get the longest increasing path from that child. Keep track of the two longest such paths from left and right children.
At each node, the longest increasing path that passes through the node is 1 + the sum of the two longest valid increasing paths from its children. Update a global maximum with this value.
Return 1 + the maximum of the valid increasing paths from children (or 1 if none) to the parent. The time complexity is O(n) and space complexity is O(h) due to recursion stack, where h is the tree height.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
They said I only needed to explain the approach, no full code.
First, clarify the problem: what operation are we generalizing (e.g., search, validation, insertion)? Then explain that without BST ordering, you must rely on structural traversal and possibly additional data structures or constraints. Discuss trade-offs in time/space complexity and mention alternative approaches like hashing or augmented trees.
Pro tip: Show awareness that the generalization often changes the problem fundamentally—e.g., searching becomes O(n) instead of O(log n)—and that you should ask whether the tree is static or dynamic, as that affects the best solution.
Ask which operation (search, insert, delete, validate) and whether the tree is static or dynamic. This determines the feasible approaches.
Explain that without ordering, you cannot prune subtrees based on value comparisons, so you must traverse all nodes in the worst case.
For search or validation, use DFS/BFS with O(n) time. For insertion/deletion, you may need to define a policy (e.g., insert at first available spot) or use a balanced tree if order is required.
Mention that if frequent searches are needed, you could augment the tree with a hash map or convert to a BST, trading space for time. Also note that some problems (like finding a path) may still be solved efficiently with recursion.
Conclude with the time/space complexity of your generalized approach and mention when a different data structure (e.g., hash table, heap) would be more appropriate.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.