1. Lecture 29 CSE 331 Nov 11, 2009

2. To be strictly enforced For the rest of the semester on Fridays SUBMIT your HOMEWORKS by 1:10 PM

3. Extra Q sessions next week Monday and Tuesday 4-6pm CSE 242

4. Mergesort algorithm Input: a 1, a 2, …, a n Output: Numbers in sorted order MergeSort( a, n ) If n = 2 return the order min(a 1,a 2 ); max(a 1,a 2 ) a L = a 1,…, a n/2 a R = a n/2+1,…, a n return MERGE ( MergeSort(a L, n/2), MergeSort(a R, n/2) )

5. An example run MergeSort( a, n ) If n = 2 return the order min(a 1,a 2 ); max(a 1,a 2 ) a L = a 1,…, a n/2 a R = a n/2+1,…, a n return MERGE ( MergeSort(a L, n/2), MergeSort(a R, n/2) ) 151100192834 51119100 11951100 2843 2348 1234 81951100

6. Correctness Input: a 1, a 2, …, a n Output: Numbers in sorted order MergeSort( a, n ) If n = 2 return the order min(a 1,a 2 ); max(a 1,a 2 ) a L = a 1,…, a n/2 a R = a n/2+1,…, a n return MERGE ( MergeSort(a L, n/2), MergeSort(a R, n/2) ) By induction on n Inductive step follows from correctness of MERGE

7. Today’s agenda Show that Mergesort runs in O(n log n) time Solve recurrences

8. To be strictly enforced For the rest of the semester on Fridays SUBMIT your HOMEWORKS by 1:10 PM