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?
Question
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?
Solution
False. Dijkstra's algorithm assumes that all edge weights in the graph are non-negative to work correctly. Negating the weights could result in negative weights, which would break this assumption. Furthermore, Dijkstra's algorithm is designed to find the shortest path, not the longest. For finding the longest path in a graph, other algorithms are needed, and it's a more complex problem, especially if the graph has cycles.
Similar Questions
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?
Suppose I have a directed graph whose edges have all positive weights. My graph is not a tree. I want to find the longest path from a starting node s to an ending node v. I can modify Bellman-Ford to solve this problem. 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.
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
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)
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