Consider an undirected connected graph G = (V, E) with n nodes and m edges; define...

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Consider an undirected connected graph G = (V, E) with n nodes and m edges; define a special source node s € V in the graph G. Describe a data structure which can achieve the following: • the data structure can be constructed in O(n +m) worst-case time; • the space consumption of the data structure (excluding the graph G) is O(n) in the worst case; for any query node q E V other than s, it can report the shortest distance between s and q in the graph G in O(1) worst-case time, where the shortest distance between s and q is defined as the length, (i.e., the number of edges) of the shortest path from s to q in G. You will need to justify the above complexities of your algorithm with appropriate analysis. [1 mark for data structure and the algorithm, and 1 mark for the analysis] Activate Windows Consider an undirected connected graph G = (V, E) with n nodes and m edges; define a special source node s € V in the graph G. Describe a data structure which can achieve the following: • the data structure can be constructed in O(n +m) worst-case time; • the space consumption of the data structure (excluding the graph G) is O(n) in the worst case; for any query node q E V other than s, it can report the shortest distance between s and q in the graph G in O(1) worst-case time, where the shortest distance between s and q is defined as the length, (i.e., the number of edges) of the shortest path from s to q in G. You will need to justify the above complexities of your algorithm with appropriate analysis. [1 mark for data structure and the algorithm, and 1 mark for the analysis] Activate Windows

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To achieve the described requirements we can use a combination of the BFS BreadthFirst Search algori... View the full answer