Answered>Order 6779
. 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.