{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

CSE331 Lecture 30

CSE331 Lecture 30 - return a b a 1 = a n-1,…,a[n/2 and a...

This preview shows pages 1–16. Sign up to view the full content.

Lecture 30 CSE 331 Nov 9, 2011

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Online Office Hr @ 10:00- 10:30pm
Possible review session

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Need a scribe volunteer
Integer Multiplication Input: a = ( a n-1 ,.., a 0 ) and b = ( b n-1 ,…, b 0 ) Output: c = a x b a = 11 01 b = 10 01 c = 1110101

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Some notation Dec( a ) = Dec( a 1 ) 2 [n/2] + Dec( a 0 ) a 1 = 11 and a 0 = 01 Dec( a ) = a n-1 2 n-1 + a n-2 2 n-2 +…+ a 1 2 + a 0 a = 11 01 Dec( a ) = 13 a 1 = ( a n-1 ,.., a [n/2] ) a 0 =( a [n/2]-1 ,…, a 0 ) Dec( a ) = a n-1 2 n-1 +…+ a [n/2] 2 [n/2] + a [n/2]-1 2 [n/2]-1 +…+ a 0 = 2 [n/2] ( a n-1 2 n-[n/2]-1 +…+ a [n/2] ) + a [n/2]-1 2 [n/2]-1 +…+ a 0
Today’s agenda Design Divide and Conquer Multiplication Algorithm

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The algorithm so far… Mult over n bits Mult over n bits Multiplication over n/2 bit inputs Multiplication over n/2 bit inputs Shift by O(n) bits Shift by O(n) bits Adding O(n) bit numbers Adding O(n) bit numbers T(n) 4 T(n/2) + cn T(1) c T(n) is O(n 2 ) T(n) is O(n 2 )
The key identity

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The final algorithm Input: a = ( a n-1 ,.., a 0 ) and b = ( b n-1 ,…, b 0 ) If n = 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: return a b a 1 = a n-1 ,…,a [n/2] and a = a [n/2]-1 ,…, a Compute b 1 and b from b Mult ( a , b ) Let p = Mult ( x , y ), D = Mult ( a 1 , b 1 ), E = Mult ( a , b ) T(1) ≤ c T(n) ≤ 3T(n/2) + cn O(n log 3 ) = O(n 1.59 ) run time O(n log 3 ) = O(n 1.59 ) run time (Old) Reading Assignment Sec 5.2 of [KT] Rankings How close are two rankings? Rest of today’s agenda Formal problem: Counting inversions Divide and Conquer algorithm 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 all sub-problems: Mergesort Solve some sub-problems: Multiplication Solve stronger sub-problems: Inversions...
View Full Document

{[ snackBarMessage ]}

Page1 / 16

CSE331 Lecture 30 - return a b a 1 = a n-1,…,a[n/2 and a...

This preview shows document pages 1 - 16. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online