Algorithms Questions

    0

    • We proved that the running time of mergesort is T(n)=n*lg(n) under the following condition

      T(n) = 0 if n = 1

      T(n) = 2T(n/2) + n if n > 1

    • 1) Prove by telescoping that T(n) = cn*lg(n) + cn under the following condition:

      T(n) = c if n = 1

      T(n) = 2T(n/2) + cn if n > 1

    • 2) Explain why T(1)’s values above 0 versus c when n = 1 will not matter for comparing algorithms. Give an example of a hypothetical situation when you implement a search engine in terms of the search volume and execution time required to complete the search.
    • 3) Explain why the following two versions of running time will not make a difference in terms of algorithm analysis using the asymptotic notation. Also, explain in terms of growth the condition where cn will not matter in relation to cn*lg(n).

      cn*lg(n) + cn

      n*lg(n)





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