I got the core BFS down fine, built the adjacency dict from the pairs without much trouble.
First, clarify the problem requirements and edge cases, then outline the steps to build an adjacency list from the edge pairs. Next, explain how to perform BFS to find the target node, shortest path, or connected component, discussing time and space complexity. Finally, consider trade-offs and potential optimizations.
Pro tip: Demonstrate awareness of graph representations: adjacency list is preferred for sparse graphs due to memory efficiency, but mention adjacency matrix for dense graphs. Also, discuss how BFS guarantees shortest path in unweighted graphs.
Ask questions to understand the graph type (directed/undirected), whether nodes are labeled with integers or strings, and what exactly needs to be found (target node, shortest path, or connected component).
Choose an adjacency list (or map) to represent the graph. Iterate through the edge pairs and add each neighbor to the corresponding list, handling both directions if the graph is undirected.
Use a queue to traverse the graph level by level. Keep track of visited nodes to avoid cycles. Depending on the goal, either stop when the target is found, record the path, or collect all nodes in the component.
State that BFS runs in O(V + E) time and O(V) space, where V is the number of vertices and E is the number of edges. Discuss how this scales with input size.
Mention alternative approaches (e.g., DFS for connected components) and trade-offs (e.g., adjacency matrix for dense graphs). Address edge cases like disconnected graphs, empty input, or self-loops.
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