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CSE331 Lecture 31

# CSE331 Lecture 31 - 1,a 2 max(a 1,a 2 a L = a 1,… a n/2 a...

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Lecture 31 CSE 331 Nov 11, 2011

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HW 8 due today Q1 and Q 2 in separate piles I will not take any HW after 1:15pm
Other HW related stuff Solutions to HW 8 on Monday HW 7 should be available for pickup from Monday HW 9 has been posted on the blog

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Review Session Details
Optimal MST algorithms

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

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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
Three kinds of inversion 10 7 21 20 100 1 Non-crossing inversions are counted recursively

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Today’s agenda Divide and Conquer algorithm for counting the # inversions
HW 8 due today Q1 and Q 2 in separate piles I will not take any HW after 1:15pm

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Mergesort-Count algorithm Input: a 1 , a 2 , …, a n Output: Numbers in sorted order+ #inversion MergeSortCount ( a, n ) If n = 2 return ( a1 > a2 , min(a

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Unformatted text preview: 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 Counts #crossing-inversions+ MERGE O(n) O(n) T(2) = c T(n) = 2T(n/2) + cn O(n log n) time O(n log n) time If n = 1 return ( 0 , a 1 ) Rest of 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...
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CSE331 Lecture 31 - 1,a 2 max(a 1,a 2 a L = a 1,… a n/2 a...

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