Virtual Labs

Bellman-Ford Algorithm for Single Source Shortest Path

After watching the simulation, why does the algorithm need exactly V-1 iterations?

a: Because the graph can have at most V-1 edges Explanation

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b: Because the longest simple path has at most V-1 edges Explanation

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c: Because it takes V-1 steps to visit all vertices Explanation

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d: Because V-1 is the optimal number found experimentally Explanation

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In the simulation, when an edge is highlighted during relaxation, what is the algorithm doing?

a: Removing that edge from consideration Explanation

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b: Checking if using that edge provides a shorter path Explanation

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c: Marking the edge as part of the final shortest path tree Explanation

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d: Increasing the weight of that edge Explanation

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During the simulation, you notice a vertex's distance value changes from 15 to 12. What does this indicate?

a: The edge weight to that vertex decreased Explanation

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b: A shorter path to that vertex was discovered Explanation

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c: The vertex moved closer to the source Explanation

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d: An error occurred in the algorithm Explanation

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If you observe in the simulation that no distance values change during an entire iteration, what can you conclude?

a: The shortest paths have already converged and no further updates are needed. Explanation

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b: The graph has a negative cycle Explanation

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c: The source vertex is disconnected Explanation

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d: The algorithm has an error Explanation

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Based on the simulation, what happens during the relaxation of edge A→B with weight 3, if distance[A] = 5 and distance[B] = 7?

a: distance[B] remains 7 Explanation

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b: distance[B] becomes 8 Explanation

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c: distance[B] becomes 5 Explanation

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d: distance[B] becomes 3 Explanation

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In the simulation, you see that after V-1 iterations, running one more iteration still updates a distance value. What does this mean?

a: The algorithm needs more iterations to converge Explanation

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b: The graph contains a negative weight cycle Explanation

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c: The implementation has a bug Explanation

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d: The source vertex was chosen incorrectly Explanation

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Watching the simulation with edges: S→A (4), S→B (5), A→B (-6), with distances after iteration 1 being S=0, A=4, B=5. After iteration 2, what will distance[B] become?

a: 5 (unchanged) Explanation

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b: -2 Explanation

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c: -1 Explanation

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d: 0 Explanation

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Consider a graph shown in the simulation: A→B (2), B→C (3), C→A (-8), with source A. What is the final output of Bellman-Ford on this graph?

a: Shortest path from A to C is 5 Explanation

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b: Shortest path from A to B is 2 Explanation

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c: A negative weight cycle exists Explanation

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d: No path exists from A to C Explanation

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In the simulation, edges are processed in order: E1, E2, E3, E4. If you change the order to E4, E3, E2, E1, what happens to the final result?

a: The shortest distances will be different Explanation

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b: The shortest distances will be the same, but convergence may be faster or slower Explanation

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c: The algorithm will fail Explanation

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d: Negative cycles may not be detected Explanation

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After using the simulation, you understand that Bellman-Ford is preferred over Dijkstra when:

a: You need the fastest possible algorithm Explanation

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b: The graph has negative edge weights Explanation

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c: The graph is very large Explanation

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d: You only need the path to one specific vertex Explanation

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A delivery company wants the cheapest routes from one source city to all other cities, and some routes have toll rebates (negative costs). Which algorithm should they use and why?

a: Dijkstra, because it is faster Explanation

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b: Bellman-Ford, because it handles negative edge weights Explanation

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c: Prim's, because it finds minimum spanning trees Explanation

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d: Floyd-Warshall, because it works for all pairs Explanation

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In currency exchange, how can Bellman-Ford be used to detect arbitrage opportunities?

a: By finding the longest path in the exchange graph Explanation

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b: By detecting negative weight cycles that represent profit loops Explanation

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c: By sorting all exchange rates Explanation

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d: By maximizing the number of exchanges Explanation

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