Homework Answers
Statement 3:
In an equation, when n grows larger the lower order terms in the equation have the least effect on the running time of the algorithm.
Even a small fraction of the highest order term is enough to dominate the lower order terms when n is large enough. In general when we calculate algorithms running times we ignore the lower order terms and the coefficient of highest order term as they have a very minimal effect when n is large.
So from the given two equations if we ignore lower order terms and coefficient of the highest order term. So the equations we got
1)n5log3n (We ignored 10n2 as it is a lower order term) (Algorithm A)
2)n6 (We ignored 17 coefficient of n6 and lower order term n4log7n) (Algorithm B)
We know that logn is faster than n.
We can write above two equations like below
1)n5 * log3n
2) n5 * n
So clearly the first equation i.e. n6 is greater than the second equation i.e. n5log3n and takes more time to run. Therefore Algorithm A is faster than Algorithm B
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STATEMENT 3: Algorithm A takes n log, (n) + 10na elementary operations and algorithm B takes...
Design an algorithm for the following description. Solution can be done in pseudo-code or steps of...
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Need to find number of elementary expressions in terms of n, not looking for Big O...
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Question 2 Consider the following algorithm Fun that takes array A and key Kas Fun(AO,...,n -...
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be done in pseudo-code or steps of the algorithm.
Describe and analyze an algorithm that takes an unsorted array A of n integers (in an unbounded range) and an integer k, and divides A into k equal-sized groups, such that the integers in the first group are lower than the integers in the second group, and the integers in the second group are lower than the integers in the third group,...
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Need to find number of elementary expressions in terms
of n, not looking for Big O complexity.
4. Work out the number of elementary operations in the worst possible case and the best possible case for the following algorithm (justify your answer): 0: function Nonsense (positive integer n) 1: it1 2: k + 2 while i<n do for j+ 1 to n do if j%5 = 0 then menin else while k <n do constant number C of elementary operations...
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