. Draw the recursion tree when n = 8, where n represents the length of the array, for the following recursive method:

int sum (int[] array, int first, int last) {

if (first == last)

return array[first];

int mid = (first + last) / 2;

ret urn sum ( array, first , mid) + sum( array , mid + 1, last);

}

 Determine a formula that counts the numbers of nodes in the recursion t ree.

 What is the B ig –  for execution time?

 Determine a formula that expresses the heig ht of the tree.

 What is the Big –  for memory?

 Write a iterative solution for this same problem and compare its efficiency with this recursive solution .

4. Using the recursive method in problem 3 and a ssuming n is the length of the array.

 Modify the recursion tree from the previous problem to show the amount of work on each activation and the row sums .

 Determine the initial conditions and recurrence equation.

 Determine the critical exponent.

 Apply the Little Master Theorem to solve that equation.

 Explain whether this algorithm optimal.