I need help with the follow 2 questions.
1. 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;
return sum(array, first, mid) + sum(array, mid + 1, last);
· Determine a formula that counts the numbers of nodes in the recursion tree.
· What is the Big-Q for execution time?
· Determine a formula that expresses the height of the tree.
· What is the Big-Q for memory?
· Writ an iterative solution for this same problem and compare its efficiency with this recursive solution.
2. Using the recursive method in problem 3 and assuming 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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