lect02 - Lecture 2 Sorting Sorting Problem Input : A...

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Lecture 2 Sorting
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Sorting Problem . ' ' ' such that sequence input of } ' ,..., ' , ' { n permutatio A : Output }. ,..., , { numbers of sequence A : Input 2 1 2 1 2 1 n n n a a a a a a a a a n Insertion Sort, Merge Sort 6. 5, 4, 3, 2, 1, : Output 3. 1, 6, 4, 2, 5, : Input e.g.,
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Efficiency Running time from receiving the input to producing the output. ) log ( ) ( 2 n n O n O Insertion Sort Merge Sort Running time
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Sort in place Satellite data are usually carried around with the key during sorting the key. A sorting algorithm sorts in place if only a constant number of elements of input array are ever stored outside the array.
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key i A i i i A i A key i A i j i j A key A length j + - + - ] 1 [ 1 ] [ ] 1 [ do ] [ and 0 while 1 ] [ do ] [ to 2 for Insertion Sort A array input
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for. - end ; ] 1 [ while; - end ; 1 ]; [ ] 1 [ begin do ] [ and 0 while ; 1 ]; [ begin do ] [ to 2 for key i A i i i A i A key i A i j i j A key A length j + - + -
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Insertion Sort sorts in place.
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Merge Sort end ); , 1 , ( Sort - Merge begin Program Main ]. ... [ subarray in elements sorts which procedure a be ) , , ( Sort - Merge Let n A r p A r p A
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Procedure   then. - end ); , , , ( Merge ); , 1 , ( Sort - Merge ); , , ( Sort - Merge ; 2 / ) ( begin then if ) , , ( Sort - Merge r q p A r q A q p A r p q r p r p A + + <
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]; [ ] [ do to 1 for ]; 1 [ ] [ do to 1 for 1]; .. 1 [ and 1] .. 1 [ array create ; ; 1 ) , , , ( Merge 2 1 2 1 2 1 j q A j R n j i p A i L n i n R n L q r n p q n r q p A + - + + + - + -
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; 1 and ] [ ] [ else 1 and ] [ ] [ hen t ] [ ] [ if do to for ; 1 ; 1 ; ) 1 ( ; ) 1 ( 2 1 + + + + j j j R k A i i i L k A j R i A r p k j i n R n L
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Is there a sorting algorithm
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lect02 - Lecture 2 Sorting Sorting Problem Input : A...

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