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Unformatted text preview: algorithm B has a running time of 2 ) 4 / ( ) ( n n aS n S + = . What is the largest integer value for a such that B is asymptotically faster than A (i.e. such that ) ( n S has an asymptotically slower growth rate than ) ( n T .) ? 4. (1 Points) Let G be an acyclic graph with n vertices, m edges, and k connected components. Show that k n m-= . (Hint: use the fact that 1 | ) ( | | ) ( |-= T V T E for any tree T , from the induction handout.) 5. (1 Point) (Appendix B.4 problem 3) Show that any connected graph G satisfies 1 ) ( ) (- G V G E . (Hint: use induction on the number of edges.)...
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This note was uploaded on 12/03/2009 for the course CS CS101 taught by Professor Agoreback during the Spring '09 term at American College of Gastroenterology.
- Spring '09