My Learning Cart
?
Categories
Account

What happens if Dijkstra's algorithm is run on a graph with a negative weight cy

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: What happens if Dijkstra\'s algorithm is run on a graph with a negative weight cycle?

Options:

  1. It will return the correct shortest path
  2. It will enter an infinite loop
  3. It will terminate with an error
  4. It may return incorrect results

Correct Answer: It may return incorrect results

Solution: 

If Dijkstra\'s algorithm is run on a graph with a negative weight cycle, it may return incorrect results, as the algorithm assumes that once a vertex\'s shortest path is found, it will not change.

What happens if Dijkstra's algorithm is run on a graph with a negative weight cy

Practice Questions

Q1
What happens if Dijkstra's algorithm is run on a graph with a negative weight cycle?
  1. It will return the correct shortest path
  2. It will enter an infinite loop
  3. It will terminate with an error
  4. It may return incorrect results

Questions & Step-by-Step Solutions

What happens if Dijkstra's algorithm is run on a graph with a negative weight cycle?
  • Step 1: Understand what Dijkstra's algorithm does. It finds the shortest path from a starting point to all other points in a graph.
  • Step 2: Know that Dijkstra's algorithm assumes that once it finds the shortest path to a vertex, that path will not change.
  • Step 3: Recognize what a negative weight cycle is. It is a cycle in the graph where the total weight of the edges is negative, meaning you can keep going around the cycle and reduce the total path cost.
  • Step 4: Realize that if Dijkstra's algorithm encounters a negative weight cycle, it can keep finding shorter paths indefinitely by going around the cycle.
  • Step 5: Conclude that because of this, Dijkstra's algorithm will give incorrect results when there is a negative weight cycle in the graph.
  • Dijkstra's Algorithm – An algorithm for finding the shortest paths between nodes in a graph, which assumes non-negative edge weights.
  • Negative Weight Cycle – A cycle in a graph where the sum of the edge weights is negative, leading to potential infinite reductions in path costs.
  • Algorithm Assumptions – Dijkstra's algorithm assumes that once a vertex's shortest path is determined, it will not be updated, which is violated by negative weight cycles.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks