Recursive expression for running time

illustrate the operation of
INSERTION-SORT on the array A =< 30, 41, 59, 26, 41, 20, 68 >. Show intermediate
results for each iteration. What is the running time for INSERTION-SORT with a list
of n integers in Θ notation?

2. (5 points) Express the following functions in Θ notation.
   • n
   3 − 100n
   2 + 50n + 600
   • nlg(n) + 50n + 20
   • 2
   4+2n + 30n
   2 + 100
3. (5 points) p37. 2.3-1. What is the running time for a list of n integers in Θ notation?
4. (10 points) p39. 2.3-3
   Hint: Use k as independent variable instead of n because n is an exact power of 2 and
   there is no case with n+ 1 . First, verify the case for k = 1. Then, assume the formula is
   true for k and use the hypotheses to prove the formula is true for k+1. Finally, conclude
   the formula is true for k.

Sample Solution