1. Algorithms CSCI 235, Spring 2019 Lecture 8 Recurrences III

2. Other examples T(n) = T(n/2) + n T(n) = 2T(n/2) + n2
3. T(n) = T(n/3) + T(2n/3) + n

3. Practice with recurrences
Example 1: T(n) = T(n/2) + n
We will draw the tree in class

4. Solving example 1 Cost of level k = ? T(n) = ? A lower bound:
An upper bound:
T(n) = ?

5. Example 2 Another equation: T(n) = 2T(n/2) + n2
We will draw this tree in class

6. Solution for example 2 Cost of level k = ? T(n) = ? Lower bound:
Upper bound:
T(n) = ?

7. Example 3 Practice equation 3: T(n) = T(n/3) + T(2n/3) + n
We will draw this tree in class

8. Solving Recursion tree for example 3
Number of levels = ?
Cost of each level = ?
Total cost if tree is full = ?
Some paths will be shorter, so cost will be less.
Total cost is at most?
T(n) = ?