Came up twice across different rounds which was a little surprising.
First, clarify the problem to ensure it involves a directed acyclic graph (DAG) and requires a topological ordering. Then, choose between Kahn's algorithm (BFS-based) or DFS-based topological sort, explaining your choice based on factors like cycle detection or lexicographic order. Walk through the algorithm step-by-step, analyze time and space complexity, and discuss edge cases and potential optimizations.
Pro tip: At Google, interviewers value clear communication and the ability to handle ambiguity. Before diving into code, ask clarifying questions about input constraints, whether the graph is guaranteed to be a DAG, and if a specific ordering (e.g., lexicographically smallest) is required.
Ask questions to understand the graph representation, input size, and any constraints. Confirm that the graph is directed and acyclic, and determine if a specific order is needed.
Decide between Kahn's algorithm (BFS-based) and DFS-based topological sort. Explain your choice based on factors like cycle detection, ease of implementation, or lexicographic ordering.
Describe the steps of your chosen algorithm in detail, using a small example to illustrate. Highlight how you handle cycles and ensure all nodes are processed.
State the time and space complexity of your solution. For both algorithms, it's O(V+E) time and O(V) space, but explain why.
Mention edge cases like empty graph, disconnected components, and cycles. Discuss potential optimizations, such as using a priority queue for lexicographic order.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Felt like the easier of the two problems in that round.
Start by clarifying the problem and defining the DP state on the tree, typically involving subtrees and possibly whether a node is included or not. Then derive the recurrence relations, choose a traversal order (post-order DFS), and analyze time and space complexity. Finally, discuss optimizations or edge cases.
Pro tip: Always root the tree arbitrarily and use post-order DFS to compute DP values bottom-up; mention that you can often avoid recursion depth issues by using an iterative stack or increasing recursion limit.
Ask questions to understand the exact problem, constraints, and expected output. Confirm if the tree is rooted or unrooted, and if there are any special conditions.
Define what each DP state represents, such as dp[node][state] where state captures relevant information (e.g., whether the node is selected). Explain why this state is sufficient.
Write the recurrence relations that combine children's DP values to compute the parent's DP value. Consider all cases and transitions.
Use post-order DFS to compute DP values bottom-up. Discuss iterative vs recursive implementation and handle large trees.
State time and space complexity, typically O(n) time and O(n) space. Mention any possible optimizations or trade-offs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the exact interval problem (e.g., merge, insert, intersect) and constraints, then propose a solution using sorting or sweep-line techniques. Walk through the algorithm with a concrete example, analyze time/space complexity, and discuss edge cases and potential optimizations.
Pro tip: Always confirm whether intervals are inclusive/exclusive and if they are pre-sorted; this shows attention to detail and can drastically simplify the solution. Also, mention how you would handle large inputs or streaming data to demonstrate scalability thinking.
Ask questions to understand the exact interval operation, input format, constraints, and edge cases (e.g., overlapping, touching, empty intervals).
Decide between sorting-based, sweep-line, or interval tree approaches based on problem requirements and constraints.
Trace the algorithm on a small example to verify correctness and identify potential pitfalls.
State the time and space complexity of your solution and compare with alternatives if relevant.
Mention how you handle edge cases and propose optimizations or alternative approaches for large-scale inputs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.