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

October 18, 2020
###### post 3
October 18, 2020

. 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.

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