shortest path

Words are nodes, one-letter edits are edges, and the shortest ladder is a shortest path in an unweighted graph, so BFS. The make-or-break detail is generating neighbors in O(26 * L) without scanning the whole dictionary. Here is the pattern.

Dijkstra finds single-source shortest paths in O((V+E) log V) with a min-heap, the backbone of routing and network latency problems. The signal is why it needs non-negative weights and how lazy deletion keeps the heap simple. Here is the answer.

Bellman-Ford handles negative edge weights that break Dijkstra and detects negative cycles, the basis of currency-arbitrage problems. The signal is the V-1 relaxation rounds and the extra Vth round that flags a negative cycle. Here is the answer.

An org-chart recursion walks a tree, but a general graph has multiple paths and back-edges. The signal is accumulating the visited path to prune cycles and ranking paths by cost to get the shortest one.