1. Algorithms CSCI 235, Spring 2019 Lecture 7 Recurrences II

2. Recall Merge Sort
Divide in 1/2
repeatedly
merge in
sorted order

3. Pseudo code for Merge Sort
// MergeSort(A, 1, length[A]) is initial call
MergeSort(A, p, r)
if p < r // if p >= r then empty or single item
q = (p + r)/ // p is the floor of p
MergeSort(A, p, q)
MergeSort(A, q+1, r)
Merge (A, p, q, r)
Size of each subproblem = ?
Number of subproblems = ?
Running time of merge = ?
Equation for merge-sort: ?

4. Example 1 Working toward merge-sort
A simpler equation: T(n) = T(n/2) + 1
We will draw the recursion tree for this in class.

5. Solution for Example 1 Number of levels = ? Cost of each level = ?
Total cost = (# levels)*(cost of each level)
= ?
T(n) = ?

6. Example 2 (working toward merge-sort)
Another equation: T(n) = 2T(n/2) + 1

7. Solution for example 2
T(n) = lg(n)
T(n) = ?

8. Example 3 merge-sort
merge-sort equation: T(n) = 2T(n/2) + n

9. Solving Recursion tree for Merge-Sort
Number of levels = ?
Cost of each level = ?
Total cost = (# levels)*(cost of each level)
= ?
T(n) = ?