Summary

We covered three major graph problems in this chapter: first, the graph traversal problem for which two solutions were introduced, breadth-first search (BFS) and depth-first search (DFS). Second, we revisited the minimum spanning tree (MST) problem and solved it using Prim's algorithm. We also compared it with Kruskal's algorithm and discussed the conditions under which one should be preferred over the other. Finally, we introduced the single-source shortest path problem, which finds a minimum-cost shortest path in graphs, and covered Dijkstra's shortest path algorithm.

However, Dijkstra's algorithm only works for graphs with positive edge weights. In the next chapter, we shall seek to relax this constraint and introduce a shortest path algorithm that can handle negative edge weights. We shall also generalize the shortest path problem to find the shortest paths between all the pairs of vertices in graphs.