Lecture 29
CSE 331
Nov 11, 2009
To be strictly enforced
For the rest of the semester on Fridays
SUBMIT
your
HOMEWORKS
by
1:10 PM
Extra Q sessions next week
Monday and Tuesday 4-6pm
CSE 242
Mergesort algorithm
Input: a1, a2, …, an
Output: Numbers in sorted order
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) )
An example run
51
1
100
19
2
8
1
51
19
100
2
8
1
19
51
100
2
1
2
3
4
8
4
3
3
19
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) )
3
4
4
51
8
100
Correctness
Input: a1, a2, …, an
Output: Numbers in sorted order
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
By
induction
on n
Today’s agenda
Show that Mergesort runs in O(n log n) time
Solve recurrences
To be strictly enforced
For the rest of the semester on Fridays
SUBMIT
your
HOMEWORKS
by
1:10 PM