Dijkstra and Bellman-Ford
Relaxation and predecessor pointers; Dijkstra's algorithm traced vertex by vertex on a five-vertex graph with the distance table after each extraction and the shortest-path tree drawn, its cost with an array, binary heap and Fibonacci heap, and a small graph where one negative edge makes it wrong; Bellman-Ford with V - 1 rounds traced under a fixed edge order, early stopping, negative-cycle detection and its dynamic programming recurrence; what shortest paths mean when a negative cycle is reachable.
