shortest path

Treat each word as a node and one-letter edits as edges: the shortest ladder becomes a shortest path in an unweighted graph, which means BFS. The detail that decides pass or fail is producing neighbors in O(26 * L) without scanning the entire dictionary. Here is the pattern.

Dijkstra computes 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 requires non-negative weights and how lazy deletion keeps the heap simple. Here is the answer.

Bellman-Ford copes with negative edge weights that break Dijkstra and detects negative cycles, the foundation of currency-arbitrage problems. The signal is the V-1 relaxation rounds plus 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 building up the visited path to prune cycles and ranking paths by cost to land the shortest one.