Lecture 34 CSE 331 Nov 19, 2010

HW 9 due today Q1 in one pile and Q 2+3 in another I will not take any HW after 1:15pm

No new HW out this week Solutions to HW 9 at the end of the lecture

Graded HW 8 Individual pickups from next week Jeff: Recitations and Wed office hours Alex: Tuesday and Thursday office hours

My office hour today Canceled after 2:35 pm

Next Monday’s lecture I’ll be out of town: no office hours either Jeff will teach the lecture

Last plug for Feedback Forms Link for the survey on the blog

Counting Inversions Input: n distinct numbers a 1,a 2,…,a n Inversion: (i,j) with i a j Output: Number of inversions

Divide and Conquer Divide up the problem into at least two sub-problems Recursively solve the sub-problems “Patch up” the solutions to the sub-problems for the final solution Solve the stronger problem of counting inversions + sorting

Three kinds of inversion Non-crossing inversions are counted recursively

Mergesort-Count algorithm Input: a 1, a 2, …, a n Output: Numbers in sorted order+ #inversion MergeSortCount( a, n ) If n = 2 return the order ( a1 > a2, 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 (c+c L +c R,a) (c L, a L ) = MergeSortCount(a L, n/2) (c R, a R ) = MergeSortCount(a R, n/2) (c, a) = MERGE-COUNT(a L,a R ) Counts #crossing-inversions+ MERGE O(n) T(2) = c T(n) = 2T(n/2) + cn O(n log n) time

HW 9 due today Q1 in one pile and Q 2+3 in another I will not take any HW after 1:15pm

Today’s agenda MERGE-COUNT Computing closest pair of points

Closest pairs of points Input: n 2-D points P = {p 1,…,p n }; p i =(x i,y i ) Output: Points p and q that are closest d(p i,p j ) = ( (x i -x j ) 2 +(y i -y j ) 2 ) 1/2

Group Talk time O(n 2 ) time algorithm? 1-D problem in time O(n log n) ?

Sorting to rescue in 2-D? Pick pairs of points closest in x co-ordinate Pick pairs of points closest in y co-ordinate Choose the better of the two

Rest of today’s agenda Divide and Conquer based algorithm