Algorithms Homework - Computer Science

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 will not matter for comparing algorithms.

3. 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

4. We have two versions of T(n) above depending on whether we use a constant c or not. Explain why the two versions of running time will not make a difference in terms of algorithm analysis using the asymptotic notation.

5. For T(n) = cn*lg(n) + cn, explain, in terms of growth, the condition where cn becomes insignificant and therefore ignorable in comparison to cn*lg(n)