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# s09-hwex - CS 473 Homework 0(due Spring 2009 CS 473...

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CS 473 Homework 0 (due January 27, 2009) Spring 2009 2. (a) [ 5 pts ] Solve the following recurrences. State tight asymptotic bounds for each function in the form Θ( f ( n )) for some recognizable function f ( n ) . Assume reasonable but nontrivial base cases. If your solution requires a particular base case, say so. Do not submit proofs —just a list of five functions—but you should do them anyway, just for practice. A ( n ) = 10 A ( n / 5 ) + n B ( n ) = 2 B n + 3 4 + 5 n 6 / 7 - 8 r n log n + 9 log 10 n - 11 C ( n ) = 3 C ( n / 2 ) + C ( n / 3 ) + 5 C ( n / 6 ) + n 2 D ( n ) = max 0 < k < n ( D ( k ) + D ( n - k ) + n ) E ( n ) = E ( n - 1 ) E ( n - 3 ) E ( n - 2 ) [Hint: Write out the first 20 terms.] (b) [ 5 pts ] Sort the following functions from asymptotically smallest to asymptotically largest, indicating ties if there are any.
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s09-hwex - CS 473 Homework 0(due Spring 2009 CS 473...

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