SophiaPretty

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Category > Computer Science Posted 23 Oct 2017 My Price 10.00

Determine the initial conditions and recurrence equation.

Need help with the following 2 questions:

 

3. 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-O for execution time?
  •  Determine a formula that expresses the height of the tree.
  •  What is the Big-O for memory?

 

4. 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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SophiaPretty
(5)
Status NEW Posted 23 Oct 2017 07:10 AM My Price 10.00

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