# L25post - Previous Lecture: Linear Search Bubble Sort,...

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± Previous Lecture: ± Linear Search ± Bubble Sort, Insertion Sort ± Today’s Lecture: ± “Divide and conquer” strategies ± Binary search ± Merge sort ± Recursion ± Announcements: ± Section this week in classrooms, and attendance is not required . Go if you can but for sure do the exercise. ± P7 posted. Due Dec 3rd.

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Nov 24, 2009 Lecture 25 3 function x = insertSort(x) % Sort vector x in ascending order with insertion sort n = length(x); for i= 1:n-1 % Sort x(1:i+1) given that x(1:i) is sorted j= i; need2swap= x(j+1) < x(j); while need2swap % swap x(j+1) and x(j) temp= x(j); x(j)= x(j+1); x(j+1)= temp; j= j-1; need2swap= j>0 & x(j+1) end end S o rt i n g s d e - p l a c . m t r u f B b
Nov 24, 2009 Lecture 25 4 An ordered (sorted) list The Manhattan phone book has 1,000,000+ entries. How is it possible to locate a name by examining just a tiny , tiny fraction of those entries?

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Nov 24, 2009 Lecture 25 5 % Linear Search % f is index of first occurrence of value x in vector v. % f is -1 if x not found. k= 1; while k<=length(v) && v(k)~=x k= k + 1; end if k>length(v) f= -1; % signal for x not found else f= k; end 12 15 35 33 42 45 v x 31 S ea r c h i n g a u s ort ed l t
Nov 24, 2009 Lecture 25 6 Key idea of “phone book search”: repeated halving To find the page containing Pat Reed ’s number… while (Phone book is longer than 1 page) Open to the middle page. if Reed ” comes before the first entry, Rip and throw away the 2 nd half. else Rip and throw away the 1 st half. end end

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Nov 24, 2009 Lecture 25 7 What happens to the phone book length? Original: 3000 pages After 1 rip: 1500 pages After 2 rips: 750 pages After 3 rips: 375 pages After 4 rips: 188 pages After 5 rips: 94 pages : After 12 rips: 1 page
Nov 24, 2009 Lecture 25 8 Binary Search Repeatedly halving the size of the “search space” is the main idea behind the method of binary search . An item in a sorted array of length n can be located with just log 2 n comparisons.

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Nov 24, 2009 Lecture 25 9 % Linear Search % f is index of first occurrence of value x in vector v. % f is -1 if x not found. k= 1; while k<=length(v) && v(k)~=x k= k + 1; end if k>length(v) f= -1; % signal for x not found else f= k; end n co mp a r i s o e d wo t ca . = l g h ( v )
Lecture 25 10 Binary Search Repeatedly halving the size of the “search space” is the main idea behind the method of binary search . An item in a sorted array of length

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## L25post - Previous Lecture: Linear Search Bubble Sort,...

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