CHAPTER 25 Weighted Graphs and Applications Objectives • To ...

priority queues, we can implement the algorithm in O(|E|log|V|) time (see Programming Exercise 25.10),
which is more efficient for sparse graphs.
Dijkstra’s algorithm is a combination of a greedy algorithm and dynamic programming. It is a greedy
algorithm in the sense that it always adds a new vertex that has the shortest distance to the source. It stores
the shortest distance of each known vertex to the source and uses it later to avoid redundant computing, so
Dijkstra’s algorithm also uses dynamic programming.
PEDAGOGICAL NOTE
Go to www.cs.armstrong.edu/liang/animation/ShortestPathAnimation.html to use a GUI interactive
program to find the shortest path between any two cities, as shown in Figure 25.20.
Figure 25.20
The animation tool displays a shortest path between two cities.
Listing 25.9 gives a test program that displays the shortest paths from Chicago to all other cities in
Figure 25.1 and the shortest paths from vertex 3 to all vertices for the graph in Figure 25.3a, respectively.
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