This went about as well as an interview can go.
Start by clearly defining the graph representation and BFS algorithm for the base case, emphasizing time and space complexity. Then, for each follow-up, identify the additional constraint, discuss how it changes the problem, and propose modifications to BFS or alternative algorithms, analyzing trade-offs.
Pro tip: Always clarify the graph type (directed/undirected, weighted/unweighted) and constraints upfront; this shows thoroughness and prevents incorrect assumptions. For follow-ups, think aloud about edge cases and potential optimizations before coding.
Ask questions to understand the graph (directed/undirected, weighted/unweighted, cyclic/acyclic), source and target nodes, and any constraints. Confirm that BFS is suitable for unweighted shortest path.
Describe BFS with a queue, visited set, and distance tracking. Walk through an example, and state time complexity O(V+E) and space O(V).
Identify the additional constraint (e.g., weighted edges, obstacles, multiple sources). Discuss why BFS may not suffice and propose modifications (e.g., Dijkstra, multi-source BFS) or alternative algorithms.
Repeat for the second constraint, considering combinations or more complex scenarios (e.g., dynamic obstacles, path reconstruction). Discuss trade-offs and potential optimizations.
Summarize the solutions, compare complexities, and mention testing with edge cases. Offer to code if needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
She showed up 25 minutes late and seemed like she had somewhere else to be.
Clarify the problem constraints (e.g., path definition, negative values) and then propose a recursive post-order traversal that computes the maximum gain from each subtree. At each node, update the global maximum path sum by considering the node's value plus the maximum gains from its left and right subtrees, and return the maximum gain that can be extended to the parent.
Pro tip: Emphasize that the path can start and end at any node, so you must consider the possibility of a path that goes through a node and connects its left and right subtrees. Also, mention that you handle negative values by taking the maximum of the gain and 0 to avoid including negative subtrees.
Ask questions to confirm the definition of a path (e.g., can it start and end at any node? Can it include negative values? Is an empty path allowed?) and the expected output (maximum sum).
Design a helper function that returns the maximum gain from a subtree rooted at a given node, where the gain is the maximum sum of a path starting at that node and going down to any node in its subtree.
For each node, recursively compute the left and right gains. Update the global maximum path sum as the maximum of the current global max and the sum of node's value plus left gain plus right gain.
Return the node's value plus the maximum of left gain and right gain (or 0 if both are negative) to represent the best path that can be extended upward.
State that the time complexity is O(n) and space complexity is O(h) due to recursion stack. Walk through a simple example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.