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Data Str & Algorithm HW Solutions 93

Data Str & Algorithm HW Solutions 93 - Θ | V | | E...

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93 (b) Fill an array with 2 n + 1 elements, which forces a fi nal growth to an array of size 2 n +1 . Now, do an arbitrarily long series of alternating inserts and deletes. This will cause the array to repeatedly shrink and grow, for bad ( Θ( n 2 ) ) performance. (c) If we shrink the array whenever the space use goes below 25%, we will have the desired performance. 14.17 Each node can be visited only once. Thus, there is initially potential for | V | node visits. We can look at each edge only once (the edges out of a node are visited when the node is visited). Thus, there is potential for | E | edge visits. The initial call to DFS can expend a small part of that potential, or a large part. But, the sum of all the calls to DFS must cost
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Unformatted text preview: Θ( | V | + | E | ) . 14.18 As with Move-to-Front, the contribution of unsuccessful searches requiring comparisons between keys A and B is independent of other keys. We have an unsuccessful search for A if and only if we have had more requests for B so far. Assuming that B is requested R B times and A is requested R A times with R B > R A , we can only have unsuccessful searches twice the number of times that A is requested. This happens at most for R A requests to B occurring before R A requests to A. The remaining requests to B are successful without encountering A. Thus, the Count heuristic can have cost at most twice that of the optimal static ordering....
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