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or initially decreasing and bitonic. est bitonic subsequence of A where A

or initially decreasing and bitonic. est bitonic subsequence of A where A

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Question
Recall the definition of a bitonic sequence from assignment 4. Call a sequence \( S = [s_1, s_2, \ldots, s_n] \) an initially increasing bitonic sequence if there is an index \( 1 \leq i \leq n \) such that \( s_1 < s_2 < \ldots < s_i \) and \( s_i > s_{i+1} > \ldots > s_n \). On the other hand, call \( S \) an initially decreasing bitonic sequence if there is an index \( 1 \leq j \leq n \) such that \( s_1 > s_2 > \ldots > s_j \) and \( s_j < s_{j+1} < \ldots < s_n \). \( S \) is bitonic if it is either initially increasing or initially decreasing and bitonic. Let \( A = [5,8,8,2,-3] \) and let \( L \) be a list of length 5 such that \( L[i] \) is the length of the longest bitonic subsequence of \( A \) where \( A[i] \) is the point at which the subsequence changes direction. Determine \( L \) (the full list, not just the maximum value).
Transcribed Image Text:Recall the definition of a bitonic sequence from assignment 4. Call a sequence \( S = [s_1, s_2, \ldots, s_n] \) an initially increasing bitonic sequence if there is an index \( 1 \leq i \leq n \) such that \( s_1 < s_2 < \ldots < s_i \) and \( s_i > s_{i+1} > \ldots > s_n \). On the other hand, call \( S \) an initially decreasing bitonic sequence if there is an index \( 1 \leq j \leq n \) such that \( s_1 > s_2 > \ldots > s_j \) and \( s_j < s_{j+1} < \ldots < s_n \). \( S \) is bitonic if it is either initially increasing or initially decreasing and bitonic. Let \( A = [5,8,8,2,-3] \) and let \( L \) be a list of length 5 such that \( L[i] \) is the length of the longest bitonic subsequence of \( A \) where \( A[i] \) is the point at which the subsequence changes direction. Determine \( L \) (the full list, not just the maximum value).
Let G=(V,E) be a flow network and suppose that you are given a cut (S,T) of minimum capacity x. What else can be said about G? - a. The maximum flow of G is x - b. There are no augmenting paths in \( G_f \), the residual network of G - c. All valid cuts of G have capacity x - d. A and B - e. All of the above.
Transcribed Image Text:Let G=(V,E) be a flow network and suppose that you are given a cut (S,T) of minimum capacity x. What else can be said about G? - a. The maximum flow of G is x - b. There are no augmenting paths in \( G_f \), the residual network of G - c. All valid cuts of G have capacity x - d. A and B - e. All of the above.
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