Asymptotic notation O satisfies the transitive propertyi.e. if f(n)=O(g(n)) and g(n)=O(h(n)), then f(n)=O(h(n)). Now weknow that 2n =O(2n-1), 2n-1=O(2n-2?),……. ,2i=O(2i-1?),……. So using ruleof transitivity, we can write 2n=O(2i-1?).We can go extending this, so thatfinally 2n =O(2k?), where k is constant.So wecan write
2n =O(1?). Do you agree to what has beenproved?If not,where is the fallacy? 6 marks (ALGORITHM ANALYSIS ANDDESIGN based problem)
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