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ECE165_2007FALL_EXAM1__[0]

# ECE165_2007FALL_EXAM1__[0] - Data Structures and Algorithms...

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Unformatted text preview: Data Structures and Algorithms D F.U2007 Midterm Name:----------------- E-mail: _ Write all of your answers directly within this test booklet. You may use whatever scrap paper you like, but do not hand it in. Please also write your name at the top of each page. ,(1) Consider the following network flow graph (i.e., flow network): , The labels of edges represent their capacities. Start by pumping 3 units along the path s--+ b--+ c-+ t. (a) Draw the residual graph althis stage. (b) At this point, what augmenting path allows the biggest increase in flow, and how much flow can you pump through it? (c) What is that maximum flow that can be pumped through this flow network? (d) Simply prove that you can not do any better than your answer to part (c), using only the original graph. In other words, I do not want you to carry out the entire Ford- Fulkerson method and show that it stops at this point; I want you to point to something in the original graph that shows you can not do any better than your answer to (c). (2) Consider the following leftist heaps: Leftist heap A: 10 19 o / \ 1 1\ 088808 Leftist heap B: (a) Label each node...
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• Spring '08
• Faculty
• Shortest path problem, Flow network, Maximum flow problem, Max-flow min-cut theorem, Graph algorithms, null path length

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ECE165_2007FALL_EXAM1__[0] - Data Structures and Algorithms...

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