I got the core DFS part down pretty quickly but fumbled a bit when they asked about large sparse graphs.
Start by clarifying the problem and edge cases, then outline the DFS-based algorithm to find connected components, ensuring nodes within each component are sorted and components are sorted by their smallest node. After presenting the solution, analyze time and space complexity, and discuss strategies for handling large sparse graphs such as using iterative DFS and adjacency lists.
Pro tip: Demonstrate awareness of Amazon's leadership principles by emphasizing customer obsession (e.g., ensuring the solution is efficient for large-scale graphs) and dive deep (e.g., discussing trade-offs between recursive and iterative DFS).
Ask clarifying questions about graph size, sparsity, and whether the graph is guaranteed to be connected or may have isolated nodes. Confirm that components should be sorted by their smallest node and nodes within each component in ascending order.
Explain that you'll build an adjacency list, then iterate through nodes in ascending order. For each unvisited node, perform DFS to collect all nodes in its connected component, sort the collected nodes, and add the component to the result list.
Write the DFS function, either recursively or iteratively using a stack. Ensure that visited nodes are marked to avoid cycles. For iterative DFS, use a stack and push neighbors in reverse order if you want to process them in ascending order, but sorting the component afterward is simpler.
After collecting all components, sort each component's node list in ascending order (if not already), and sort the list of components by their first element (the smallest node).
State that time complexity is O(n + m) for DFS plus O(k log k) for sorting components, where k is the number of components, and space complexity is O(n + m) for the adjacency list and visited array. For very large sparse graphs, recommend iterative DFS to avoid stack overflow, use adjacency lists, and consider streaming or external memory algorithms if the graph doesn't fit in memory.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the problem and constraints, then present clean solutions for both tasks: BFS with level grouping for traversal and a post-order DFS for balance checking. Walk through time/space complexity and discuss trade-offs, then outline test cases including edge cases and large inputs.
Pro tip: Mention that the balance check can be combined with the traversal to avoid redundant work, and that early termination on imbalance improves average-case performance. Also, relate the solutions to real-world scenarios like tree serialization or database indexing to show practical insight.
Ask about input size, tree properties (e.g., binary search tree?), and expected output format. Confirm whether recursion depth is a concern and if iterative solutions are preferred.
Use BFS with a queue, processing nodes level by level. For each level, record the number of nodes, dequeue them, add their children, and collect values into a sublist.
Use post-order DFS to compute subtree heights bottom-up. At each node, check if the absolute difference between left and right heights exceeds 1; if so, propagate an error (e.g., return -1).
For traversal: O(n) time, O(w) space where w is max width. For balance check: O(n) time, O(h) space for recursion stack. Discuss iterative vs recursive trade-offs and early termination benefits.
Cover empty tree, single node, balanced/unbalanced trees, skewed trees, and large trees. Include cases where balance is violated at different levels and where traversal groups are empty.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.