Data Str & Algorithm HW Solutions 74

Data Str & Algorithm HW Solutions 74 - 74 Chap. 11...

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74 Chap. 11 Graphs 23456 11013126 2 2 351 61 2 3 8 15 15 41 1 1 0 53 11.16 The problem is that each entry of the array is set independently, forcing pro- cessing of the adjacency list repeatedly from the beginning. This illustrates the dangers involved in thoughtlessly using an inef f cient access member to a data structure implementation. A better solution is to process the actual edges within the graph. In other words, for each vertex, visit its adjacency list. Set the shortest-paths array by setting the values associated with that edge. If the array is initialized with values of , then any vertices not connected by an edge will retain that value. 11.17 Clearly the algorithm requires at least Ω( n 2 ) time since this much informa- tion must be produced in the end. A stronger lower bound is dif f cult to obtain, and certainly beyond the ability of students at this level. The primary goal of this exercise is for the students to demonstrate understanding of the concept of a lower bound on a problem, in a context where they will not be able to make the lower bound and the algorithm’s upper bound meet.
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