practice.pdf - Practice Problems 1 Depth-First Search(DFS 2...

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Practice Problems 1. Depth-First Search (DFS) 2. Shortest Path (Dijkstra’s algorithm) 3. Minimum-Spanning Tree (MST) 1 / 10
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Depth-First Search I DPV 3.2. Perform depth-first search on each of the following graphs; whenever there’s a choice of vertices, pick the one that is alphabetically first. F A B C D H G E H A B C D E F G 2 / 10
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Depth-First Search I DPV 3.11. Design a linear-time algorithm which, given an undirected graph G and a particular edge e in it, determines whether G has a cycle containing e . 3 / 10
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Shortest Path (Dijkstra’s algorithm) I DPV 4.1. Suppose Dijstra’s algorithm is run on the following graph, starting at node A . 1. Draw a table showing the intermediate distance values of all the nodes at each iteration of the algorithm. 2. Show the final shortest-path tree. 1 A B C D E F G H 1 2 1 4 8 6 6 2 1 4 5 1 4 / 10
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Shortest Path (Dijkstra’s algorithm) I DPV 4.18. In case where there are several different shortest paths between two nodes(and edges
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