Classic tree problem and I still fumbled the base case for a second.
Start by clarifying the problem and edge cases, then explain a recursive DFS solution that returns the LCA by checking if p and q are found in the left and right subtrees. Emphasize the O(n) time and O(h) space complexity, and discuss iterative alternatives if needed.
Pro tip: Mention that the recursive solution assumes both nodes exist; if not guaranteed, you'd need to verify their presence first. Also, note that the problem can be solved iteratively using parent pointers for O(1) space if the tree nodes have parent references.
Confirm that p and q are distinct and both exist in the tree. Ask if the tree is binary (not BST) and if nodes have parent pointers. Clarify that a node can be its own ancestor.
Decide between recursive DFS (simple, O(n) time, O(h) space) or iterative with parent pointers (O(n) time, O(1) space if parents exist). For most interviews, the recursive approach is expected.
Base case: if root is null or root is p or q, return root. Recursively search left and right subtrees. If both return non-null, root is the LCA; otherwise return the non-null result.
Time: O(n) worst-case, as each node is visited once. Space: O(h) for recursion stack, where h is tree height (O(n) worst-case for skewed tree, O(log n) for balanced).
Handle cases where p or q is the root, or one is ancestor of the other. Mention iterative solutions using parent pointers or path-to-root comparison if applicable.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is the house robber dp problem, pretty much verbatim.
Recognize this as the classic House Robber problem and solve it using dynamic programming. Define the state as the maximum amount robbed up to house i, then derive the recurrence: dp[i] = max(dp[i-1], dp[i-2] + nums[i]). Optimize space to O(1) by keeping only the last two values.
Pro tip: After presenting the optimal solution, briefly discuss edge cases (empty array, single house) and how you would test the solution. This shows attention to detail and production-ready thinking, which Amazon values.
Confirm that houses are in a line (not circular), that you cannot rob adjacent houses, and that all amounts are non-negative. Ask if the array can be empty or have one element.
Let dp[i] be the maximum amount that can be robbed from the first i houses. Explain that at each house, you either skip it (take dp[i-1]) or rob it (take dp[i-2] + nums[i]).
Write the recurrence relation: dp[i] = max(dp[i-1], dp[i-2] + nums[i]). Base cases: dp[0] = 0, dp[1] = nums[0].
Observe that only the last two DP values are needed, so replace the array with two variables (prev2 and prev1) to achieve O(1) space.
State time complexity O(n) and space O(1). Walk through a small example (e.g., [2,7,9,3,1]) to verify correctness and discuss edge cases.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.