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2 cards from this section. Quick, good the night before a test.
Define what is meant by All-pairs Shortest Paths.
Consider the necessity of comparing distances for multiple vertex pairs.
What is a weighted graph?
Think about how distances are represented in a graph.
What is the primary goal of the Floyd-Warshall algorithm?
Consider what the algorithm is focused on.
True or False: The Floyd-Warshall algorithm can handle graphs with negative cycles.
Think about the impact of cycles on path definitions.
Design a graph with vertices A, B, C, D, and edges with various weights including negative ones. Apply the Floyd-Warshall algorithm and determine all-pairs shortest paths.
Start initializing your weights based on direct edges then iterate through the vertex combinations.
Discuss the implications of allowing negative weights in graphs. What types of real-world scenarios can affect the shortest path calculations?
Think about situations like city planning where costs might fluctuate or topographical changes could affect distances.
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