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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?

Question

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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Solution

True. Since Dijkstra's algorithm has already been run from node A, the shortest path from A to any other node has already been determined. This includes the shortest path from A to Z. Since E is a node on the shortest path from A to Z, the shortest path from E to Z is simply the remainder of the path from A to Z after reaching E. Therefore, you do not need to run Dijkstra's algorithm again from node E.

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Suppose I have a graph whose edges have non-negative weights, and I want to find the longest path from a starting node s to an ending node v. I can negate the weights of the graph and run Dijkstra's algorithm. True or False?

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.

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