Dijkstra's algorithm will always return the correct answer (relaxing each edge at most once) for any shortest-path queries on the following types of graphs (select all that apply):Unweighted TreesWeighted Graphs (connected, non-negative edge weights)Weighted Graphs (connected)Weighted Graphs with no negative weight cycles (connected)Continue
Question
Dijkstra's algorithm will always return the correct answer (relaxing each edge at most once) for any shortest-path queries on the following types of graphs (select all that apply):Unweighted TreesWeighted Graphs (connected, non-negative edge weights)Weighted Graphs (connected)Weighted Graphs with no negative weight cycles (connected)Continue
Solution
Dijkstra's algorithm will always return the correct answer for the following types of graphs:
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Unweighted Trees: Yes, Dijkstra's algorithm will work correctly on unweighted trees. Since all edges have the same weight, the shortest path between two nodes is simply the path with the fewest edges.
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Weighted Graphs (connected, non-negative edge weights): Yes, Dijkstra's algorithm will work correctly on weighted graphs with non-negative edge weights. The algorithm is designed to find the shortest path in such graphs.
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Weighted Graphs (connected): This depends on the weights of the edges. If there are negative edge weights, Dijkstra's algorithm may not return the correct answer. This is because the algorithm assumes that a shorter path will not be found once a node has been visited, which is not true if there are negative weights.
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Weighted Graphs with no negative weight cycles (connected): Yes, Dijkstra's algorithm will work correctly on weighted graphs with no negative weight cycles. Even if there are negative weights, as long as there are no negative cycles, the algorithm will still return the correct shortest path.
Similar Questions
Which algorithm is used to find the shortest path between nodes in a weighted graph with non-negative weights?Bellman-Ford algorithmDijkstra's algorithmKruskal's algorithmFloyd-Warshall algorithm
What is a crucial requirement for Dijkstra’s algorithm (for finding shortest path) to work correctly?Select one:a. All edge weights in the graph must be equal.b. The graph must be fully connected.c. The graph must be a tree.d. The graph must not contain any negative edge weights.
Which algorithm is used to find the shortest path in a weighted graph with non-negative edge weights?A) Bellman-FordB) Kruskal'sC) Prim'sD) Breadth-First Search (BFS)
The shortest path in a graph with weighted edges can be found using:A. Depth-first searchB. Breadth-first searchC. Dijkstra's algorithmD. Kruskal's algorithm
Suppose I have a huge graph with nodes (A~Z) whose edges have non-negative weights. Using Dijkstra's algorithm, we came up with the shortest path tree starting from node A. With this tree, we found out the shortest path from node A to node Z, which looks like A -> C -> E -> G -> J -> L -> Z. Now, I want to find out the shortest path from node E to Z. I can find out this without running Dijkstra's algorithm from node E. True or False?
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