Can Dijsktra Handle Cycle

Question

Answer

Can Dijkstra handle negative weights for Dag?

No, it cannot be used when there are negative weights.

Does Dijkstra’s algorithm always work?

Yes Dijkstra’s always gives shortest path when the edge costs are all positive. However, it can fail when there are negative edge costs.

Can Dijkstra handle self loops?

Like the answers mentioned it really depends on the particular implementation of dijkstra algorithm. This implementation will work fine because it adds the smallest possible edge among all possible parallel edges to the data structure you are using to keep track of the yet to be explored nodes.

Can Dijkstra be used for undirected graphs?

You can use Dijkstra’s algorithm in both directed and undirected graphs, because you simply add nodes into the PriorityQueue when you have an edge to travel to from your adjacency list.

Why Dijkstra fail in negative weights?

It happens because, in each iteration, the algorithm only updates the answer for the nodes in the queue. So, Dijkstra’s algorithm does not reconsider a node once it marks it as visited even if a shorter path exists than the previous one. Hence, Dijkstra’s algorithm fails in graphs with negative edge weights.

Is Dijkstra optimal?

In addition, Best First Search is not optimal [not guaranteed to find the shortest path], and also A*, if you do not use an admissible heuristic function, while Dijkstra’s algorithm is always optimal, since it does not relay on any heuristic.

Is Dijkstra’s algorithm greedy?

Dijkstra Algorithm is a graph algorithm for finding the shortest path from a source node to all other nodes in a graph(single source shortest path). It is a type of greedy algorithm. It only works on weighted graphs with positive weights.

How Dijkstra’s algorithm works?

Dijkstra’s Algorithm finds the shortest path between a given node (which is called the “source node”) and all other nodes in a graph. This algorithm uses the weights of the edges to find the path that minimizes the total distance (weight) between the source node and all other nodes.

Does Dijkstra work for multiple edges?

Dijkstra’s Algorithm can only work with graphs that have positive weights. This is because, during the process, the weights of the edges have to be added to find the shortest path. If there is a negative weight in the graph, then the algorithm will not work properly.

Is Bellman-Ford algorithm greedy?

The graph may contain negative weight edges. We have discussed Dijkstra’s algorithm for this problem. Dijkstra’s algorithm is a Greedy algorithm and time complexity is O((V+E)LogV) (with the use of Fibonacci heap).