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CSCI220 \\
Fall 1992 Midterm Exam \\
October 2, 1992
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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 program!
Follow these steps:
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\item  Invent a loop invariant.  Use {\em Pre} and {\em Post} to guide you.

\item  Prove that what you have invented is indeed a loop invariant.  Does it
hold after initialization? (Remember to use {\em Pre} as well as the
initialization statement for this.)  Does it hold before the $n$th execution of
the {\bf while} loop?

\item  Prove that {\em Post} follows from the loop invariant and the negation
of the {\bf while} condition.
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Problem 2 [part (a): 40 points; part (b): 10 points]
Do exercise 2.3 in the textbook.  Clarification: the array is 
sorted {\em in ascending order} and it contains only integers.
Hint: This analysis is {\em very} similar to that of {\em LinearSearch}.

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