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The final exam for CSE 421, Fall 2005 at the University of Washington. The exam consists of 9 problems, covering topics such as recurrences, algorithms, reductions, and subsequence finding. The exam is closed book and closed notes, with a time limit of 1 hour and 50 minutes. The problems are of varying difficulty and the total score is out of 155 points.
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University of Washington December 12, 2005 Department of Computer Science and Engineering CSE 421, Fall 2005
Final Exam, December 12, 2005
Instructions:
Total /
Give solutions to the following recurrences. Justify your answers.
a) T (n) =
{ T (n − 1) + n if n > 0 1 if n = 0
b) T (n) =
{ 17 T (n/17) + n if n > 1 0 if n = 0
c)
T (n) =
{ 3 T (n/4) + n if n > 1 0 if n = 0
Consider the following flow graph G, with an assigned flow f. The pair x/y indicates that the edge is carrying a flow x and has capacity y.