Model the social network as an unweighted graph and use BFS to find the shortest path between the two people, as BFS guarantees the minimum number of edges. Discuss the algorithm's time and space complexity, and consider optimizations like bidirectional BFS for large graphs.
Pro tip: Mention that bidirectional BFS can significantly reduce the search space by exploring from both ends simultaneously, often cutting time complexity from O(b^d) to O(b^(d/2)). Also, clarify assumptions about graph size, memory constraints, and whether the graph is static or dynamic.
Ask about graph size, whether it's directed or undirected, if edge weights are uniform, and if there are any memory or latency constraints. Confirm that 'degree of connection' means the shortest path length in terms of number of edges.
Select BFS for unweighted graphs to find the shortest path. If the graph is very large, consider bidirectional BFS to reduce search space. Avoid DFS as it doesn't guarantee shortest paths.
Describe initializing a queue with the source node, a visited set, and a distance counter. Process nodes level by level, tracking distance, and stop when the target is found or the queue is exhausted.
State time complexity O(V+E) and space O(V) for standard BFS. Discuss edge cases: disconnected nodes, source equals target, and very large graphs requiring distributed or approximate methods.
Mention bidirectional BFS for performance, using adjacency lists for sparse graphs, and handling dynamic graphs with incremental updates. Optionally, discuss weighted graphs (Dijkstra) if edges have weights.
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