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Do my CS 5633 Analysis of Algorithms Assignment


Question - CS 5633: Analysis of Algorithms Spring 2014Homework 1
Please turn in a hard copy at the beginning of class on 1/23/14 .
1. Loop Invariants (10 points) :
Consider the code below with computes log nfor any n 0.
function log(n )
k = n
c = 0
while k >1do
k = k/2
c = c+ 1
end while
return c
end function
(a) State a loop invariant for the while loop that will allow you to prove t he
correctness of the algorithm.
(b) Use the loop invariant to prove the correctness of the algorith m. For this you
need to prove by induction that the invariant holds for each iteratio n of the
loop, and then use the loop invariant after the last iteration of the lo op to
prove the correctness of the algorithm.
(c) What is the runtime of the algorithm?
2. Evaluating R ...Read More

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