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

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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