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What happens if Dijkstra's algorithm is applied to a graph with negative weight

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Question: What happens if Dijkstra\'s algorithm is applied to a graph with negative weight edges?

Options:

  1. It will still find the shortest path.
  2. It may produce incorrect results.
  3. It will not terminate.
  4. It will find the longest path.

Correct Answer: It may produce incorrect results.

Solution: 

Dijkstra\'s algorithm may produce incorrect results if applied to graphs with negative weight edges, as it assumes that once a node\'s shortest path is found, it cannot be improved.

What happens if Dijkstra's algorithm is applied to a graph with negative weight

Practice Questions

Q1
What happens if Dijkstra's algorithm is applied to a graph with negative weight edges?
  1. It will still find the shortest path.
  2. It may produce incorrect results.
  3. It will not terminate.
  4. It will find the longest path.

Questions & Step-by-Step Solutions

What happens if Dijkstra's algorithm is applied to a graph with negative weight edges?
  • Step 1: Understand what Dijkstra's algorithm does. It finds the shortest path from a starting node to all other nodes in a graph.
  • Step 2: Know that Dijkstra's algorithm works by assuming that once it finds the shortest path to a node, that path will not change.
  • Step 3: Recognize that negative weight edges can create situations where a shorter path to a node can be found after it has already been processed.
  • Step 4: Realize that because of this, Dijkstra's algorithm may give incorrect shortest path results when negative weight edges are present.
  • Step 5: Conclude that Dijkstra's algorithm is not suitable for graphs with negative weight edges.
  • Dijkstra's Algorithm – An algorithm for finding the shortest paths between nodes in a graph, which assumes non-negative edge weights.
  • Negative Weight Edges – Edges in a graph that have a weight less than zero, which can lead to incorrect results when using Dijkstra's algorithm.
  • Optimal Substructure – A property of an algorithm where an optimal solution can be constructed efficiently from optimal solutions of its subproblems, which Dijkstra's algorithm relies on.
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