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?
It will return the correct shortest path
It will enter an infinite loop
It will terminate with an error
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.
