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Searching And Sorting Algorithms Pdf Download

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Partition...the...array...(put...all...value...less...than...the...pivot...in...the...left...part...of...the...array,...then...the...pivot...itself,...then...all...values...greater...than...the...pivot)....(Putting..the..smallest..value..in..A[low]..prevents.."right"..from..falling..off..the..end..of..the..array..in..the..following..steps.)..Initialize:..left..=..low+1;..right..=..high-2..Use..a..loop..with..the..condition:..while..(left..=..the..pivot..Each..time..around..the..loop:..left..is..incremented..until..it.."points"..to..a..value..>..the..pivot..right..is..decremented..until..it.."points"..to..a..value..=..3..int..pivot..=..medianOfThree(A,..low,..high);..//..this..does..step..1..int..left..=..low+1;..right..=..high-2;..while..(..left..0)..right--;..if..(left..=..pivot..recursively..sort..the..left..part..recursively..sort..the..right..part..worst-case..O(N2)..expected..O(N..log..N)...Selection..Sort...It..uses..an..auxiliary..method..with..extra..parameters..that..tell..what..part..of..array..A..each..recursive..call..is..responsible..for..sorting...In....the....worst....case:....1st....iteration....of....outer....loop:....inner....executes....1....time....2nd....iteration....of....outer....loop:....inner....executes....2....times....3rd....iteration....of....outer....loop:....inner....executes....3....times.........

Here's..the..code..for..selection..sort:..public..static..void..selectionSort(Comparable[]..A)..{..int..j,..k,..minIndex;..Comparable..min;..int..N..=..A.length;..for..(k..=..0;..k..=..0)..&&..(A[j].compareTo(tmp)..>..0))..{..A[j+1]..=..A[j];..//..move..one..value..over..one..place..to..the..right..j--;..}..A[j..+..1]..=..tmp;..//..insert..kth..value..in..correct..place..relative..to..previous..//..values..}..}..Here's..a..picture..illustrating..how..insertion..sort..works..on..the..same..array..used..above..for..selection..sort:..What..is..the..time..complexity..of..insertion..sort?..Again,..the..inner..loop..can..execute..a..different..number..of..times..for..every..iteration..of..the..outer..loop...(The..following..assumes..that..the..size..of..the..piece..of..the..array..to..be..sorted..is..at..least..3.)..The..basic..idea..is..to..use..two.."pointers"..(indexes)..left..and..right...Here's..a..picture..illustrating..this..merge..process:..Now..the..question..is,..how..do..we..get..the..two..sorted..arrays..of..size..N/2?..The..answer..is..to..use..recursion;..to..sort..an..array..of..length..N:..Divide..the..array..into..two..halves...Note..that..after..i..iterations,..A[0]..through..A[i-1]..contain..their..final..values..(so..after..N..iterations,..A[0]..through..A[N-1]..contain..their..final..values..and..we're..done!).....Then..the..two..halves..are..(recursively)..sorted...N-1st...iteration...of...outer...loop:...inner...executes...N-1...times...So...we...get:...1...+...2...+.......The....idea....behind....selection....sort....is:....Find....the....smallest....value....in....A;....put....it....in....A[0].....

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