1. Lecture 31
CSE 331
Nov 12, 2010

2. HW 8 due today I will not take any HW after 1:15pm
Q1 in one pile and Q 2 in another
I will not take any HW after 1:15pm

3. Graded HW 7 Individual pickups Atri: Fri office hours
Jeff: Recitations and Wed office hours
Alex: Tuesday and Thursday office hours

4. HW 9
Posted on the webpage/blog

5. Mergesort algorithm Input: a1, a2, …, an
Output: Numbers in sorted order
MergeSort( a, n )
If n = 1 return the order a1
aL = a1,…, a[n/2]
aR = a[n/2]+1,…, an
return MERGE ( MergeSort(aL, [n/2]), MergeSort(aR, n-[n/2]) )
If n = 2 return the order min(a1,a2); max(a1,a2)

6. Inductive step follows from correctness of MERGE
Input: a1, a2, …, an
Output: Numbers in sorted order
By induction on n
MergeSort( a, n )
If n = 2 return the order min(a1,a2); max(a1,a2)
aL = a1,…, an/2
aR = an/2+1,…, an
return MERGE ( MergeSort(aL, n/2), MergeSort(aR, n/2) )
Inductive step follows from correctness of MERGE

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

8. HW 8 due today I will not take any HW after 1:15pm
Q1 in one pile and Q 2 in another
I will not take any HW after 1:15pm