Shortest path

The phrase shortest path is ambiguous, so begin by stating the decision tree. For an unweighted graph, or one where every edge has weight one, breadth-first search is correct because the first visit to a node uses the fewest edges. Initialize dist[source]=0, use a queue, and set an unvisited neighbor to dist[node]+1; keep a parent pointer when reconstruction is required. For non-negative weighted edges, use Dijkstra with an adjacency list and min-heap, skipping stale heap entries. Negative edges invalidate Dijkstra, so use Bellman-Ford and, if relevant, report reachable negative cycles. Always define the unreachable sentinel and whether source equals destination. BFS is O(V+E) time and O(V) extra space; heap Dijkstra is O((V+E) log V) time and O(V+E) space. The important interview move is selecting the algorithm from the graph contract, not guessing from the title.