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CSCI220 \\
Fall 1996 Midterm Exam \\
September 30, 1996
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This is an open book exam.
The total maximum attainable score for this exam is 100.  The score for each
question is given so that you can budget your time.
Partial credit may be given.
You will be graded on clarity and
conciseness as well as correctness.
Good luck!
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Problem 1 [50 points].
Do exercise 1.4 in the textbook.
(Do not panic!  This is a very simple algorithm!)

Problem 2 [25 points].
Assuming that n is a power of 2,  solve the following recurrence relation:\\
$T(1) = 1$\\
$T(n) = 1 + (1/2)T(n/2)$.

Problem 3 [25 points].
In one minute, your old computer has just enough time to solve a problem of
size 64.  The complexity of the algorithm you use to solve the problem is
$k_{6} \log_{2} n$.  
You are planning to buy a computer 100 times as fast as your old one.  How
large an input will your new computer be able to process in one minute?

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