Sorting

1
??

• Sorting

2
????

• ???????,????????
• ?????????
• ????????????
• ????????

3
 ??

• ??(Sorting)???????????????,???????????,???????????
  ???(???)??????????
• ??????????
• ????(Internal Sorting)??????,?????????????
• ????(External Sorting)??????,??????????,?????????
  ???????

4

• ?????????????
• ?????(Insertion Sort)
• ?????(Selection Sort)
• ?????(Bubble Sort)
• ?????(Shell Sort)
• ?????(Quick Sort)
• ?????(Merge Sort)
• ?????(Heap Sort)
• ?????(Radix Sort)

5

• ???????????,?????????,??????????????????
• ??????
• ????????????????????
• ???????????O(n(logn)2)?????????O(Ns),1ltslt2
• ???????????????????????????????O(n2)?

6

• ??????
• ???????????????,???????,???????????,????(Decision
  Tree)???
• ???????????????
• ??????????????O(n2),????????????????????O(nlogn)?
• ??????
• ?????????,????????????O(nlogpk),
• ?????????O(nlogpk) O(n)
• ??p??????(Base,Radix),k???????

7
?????

• (Insertion Sort)

8
??

• ????????????????????????????,?????????????
• ?????????
• ???????????????,???????????????
• ??????????????,?????,??????????????????

9
????
index 0 1 2 3 4 5
i 60 70 15 40 80 99 ??
60 60??
70 60 70?????index?0???
70 60 15 15??
70 60 40 15 40?????index?2???
80 70 60 40 15 80?????index?0???
99 80 70 60 40 15 99?????index?0???
10
???

• gt?????
• ??????
• procedure insertionsort(int data , int n)
  index i, j int item for (i ?1
  n-1) ???datai????????????
• ??????????? ??????????? ?????????
  ??

11

• gtC?????
• insertionsrot(int data , int n) index i,
  j ,item for (i1 iltn i) /?n1?/
  itemdatai
• ji /?datai??????????,?????????/while
  (jgt0 aj-1gtitem)
• datajdataj-1 j- -
  dataj item /?ai??????/

12

• gt???????
• ??????????
• ??????????????O(n2)
• ??????????

13
????-????

• include ltstudio.hgt
• void insertion_sort ( int , int )
• void main ( )
• int data 20
• int size 0, i
• printf ( \nPlease enter number to sort (enter 0
  when end)\n )
• printf ( Number )

14

• do
• scanf ( d , data size )
• while (data size ! 0 )
• for ( i 0 i lt 60 i ) printf ( - )
• printf ( \nSorting )
• for ( I 0 I lt size i )
• printf ( d , data i )

15

• void insertion_sort (int data , int size )
• int base, compare, temp, i
• for (base 1 base lt size base )
• temp data base
• compare base
• while ( compare gt 0 data compare 1 gt temp)

16

• data compare data compare 1
• compare - -
• data compare temp
• printf ( Access )
• for ( I 0 i lt size i )
• printf ( d , data i)
• printf ( \n )

17
?????

• (Bubble Sort)

18
??

• ????????????????
• ??????(Swap sort)???
• ???????????????,???????????,???????????????,??????
  ????????????,?????????

19
????

• ?????????????????????
• ?????????????,????????????,????????????????????,??
  ???

20
index 0 1 2 3 4 5
i 60 70 15 40 80 99 (a) ????
70 60 15 40 80 99 (b) ?????
70 60 15 40 80 99 (c) ?????
70 60 40 15 80 99 (d) ?????
70 60 40 80 15 99 (e) ?????
70 60 40 80 99 15 (f) ?????
70 60 80 99 40 15 ?????
70 80 99 60 40 15 ?????
80 99 70 60 40 15 ?????
99 80 70 60 40 15 ?????(??)
21
???

• gt?????
• Bubble_sort(int a , int size)
• for (pass size-1 to 1)
• for ( j 1 to size 1)
• if (a j gta j1
• ??a j , a j1

22

• gtC?????
• Bubble_sort(int a , int size)
• int i , j , t
• for (i size-1 igt0 i- -)
• for ( j 0 jlt1 j )
• if (a j gta j1
• ta j
• a j a j1
• a j1 t

23

• gt???????
• ??????????
• ??????????????O(n2),
• ??????????

24
????

• include ltstdio.hgt
• define n 10            // ??????
• void bubble(int )       // ???????
• void show(int )         // ????
• void main()
• int datan 9,1,7,3,4,8,6,2,5,0
• printf("The default is ")
• show(data)              // ??????
• bubble(data)            // ???????
• printf("The answer is ")
• show(data)              // ????

25

• void bubble(int data)
• int temp,i,j,flag
• for (in-1igt0i--)                // ??i??
• flag 0                // ???????0?
• for (j0jlt ij)
• if(dataj gt dataj1)           // ?dataj gt
  dataj1????
• printf("\ndatad gt datad",j ,j1)
• printf(" datad,datad swap,",j ,j1)
• temp dataj1
• dataj1 dataj
• dataj temp
• flag 
• // ????????flag

26

• else                           // ?dataj lt
  dataj1???
• printf("\ndatad ltdatad",j ,j1)
• printf(" datad,datad not swap",j,j1)
• if(flag0)               
• //flag?0???????,?????????
• break

27

• printf("\nThe d time is ",-(i-n))      //
  ??????
• show(data)                    // ????????????
• printf("\n")
• void show(int data)
• int i
• for(i0ilt ni)
• printf("d,",(datai))

28
?????

• (Selection Sort)

29
??

• ???????????????(???)??,???????,??????(???)????????
  0??,???????????????????????

30
?????
31

• ???????????,???????????????????,????????,?????????
  ?????,???????????????,??,???????????????????

32
????????
33
????

• ?????(selection sort)??????????????????????(??????
  )?

34
index 0 1 2 3 4 5
i 60 70 15 40 99 80 ????
15 70 60 40 99 80 ?????
15 40 70 60 99 80 ?????
15 40 60 70 99 80 ?????
15 40 60 70 99 80 ?????
15 40 60 70 80 99 ?????(??)
35
???

• gt?????
• select_sort (int a , int size)
• index i , j
• for (i n 1?1)
• ??? data 0
• for ( j 1 ? i)
• if ( a j gt??? )
• ??? a j
• ?a j ? a i ?????

36

• gtC?????
• select_sort(int a , int size)
• int i, j , index, larger
• //?1i???,???????a i ?//
• for (i n-1 Igt0 i--)
• larger a0
• index 0
• for (j1 jlti j )

37

• if(ajgtlarger)
• larger aj
• index
• aindex ai
• ai larger

38

• gt???????
• ???????n-1?,???n-i?,
• ?????????????????????????
• ??????????????,??O(n2 )??????
• ??????????O(n)??

39
????????

• include ltstdio.hgt
• define n 10
• void selection(int )            // ?????????
• void show(int )                 // ????
• void main()
• int datan 9,1,7,3,4,8,6,2,5,0
• printf("The default is ")
• show(data)
• selection(data)
• printf("The answer is ")
• show(data)

40

• void selection(int data)
• int temp,i,j,flag
• for (i0ilt ni)
• for (jijlt nj)
• if(datai gt dataj)         // ?datai gt
  dataj???
• printf("\ndatad gt datad",i ,j)
• printf(" datad,datad swap,",i ,j)
• temp dataj
• dataj datai
• datai temp
• // ?datai lt dataj????

41

• else
• printf("\ndatad ltdatad",i ,j)
• printf(" datad,datad not swap",i ,j)
• printf("\nThe d time is ",i1)
• show(data)
• printf("\n")

42

• void show(int data)
• int i
• for(i0ilt ni)
• printf("d,",(datai))

43
?????

• (Quick Sort)

44
??

• ?C. A. R. Hoare ?????????
• ?????????????,????????
• ??????????????????????????(pivot),
• ??????????????????
• ???????????????,?????????

45
????

• ??????????
• K(1),K(2),,K(n)
• ???????????????????????

46

• ??????
• ?n1,?return
• ????K(p)????????
• ??????????K(i),??K(i)gtK(p)
• ??????????K(j),??K(j)ltK(p)
• ?iltj?K(i)?K(j)??,?????2
• ?i?j,??K(j)?K(p)??,??j?????????????,??????????????
  15?

47
???

• gtC?????
• quick_sort(int a , int l, int r)
• int p, i, j, t
• if ( l lt r)
• i l 1
• j r
• p a l

48

• do
• while (a i lt p)
• i
• while (a j gt p)
• j - -
• if ( i lt j )
• t a i
• a i a j
• a j t

49

• while ( i lt j )
• a l a j
• a j p
• qsort ( a, l, j 1)
• qsort ( a, j 1, r )

50

• gt???????
• ???? ????pivot??????,?????

• ???? ??????pivot????????????????,??????

51

• ???? ?????pivot??????????,?????????
  ?T(j),?T(n-j-1),j?????1?n??????,??
• T(n) O(nlogn)

52
????

• include ltstudio.hgt
• void quick_sort ( int , int )
• void main ( )
• int data 20
• int size 0, i
• printf ( \nPlease enter number to sort (enter 0
  when end)\n )
• printf ( Number )
• do
• scanf ( d , data size )
• while (data size ! 0 )
• for ( i 0 i lt 60 i ) printf ( - )
• printf ( \nSorting )
• for ( I 0 I lt size i )
• printf ( d , data i )

53

• void quick_sort (int data , int left, int
  right, int size )
• int lbase, rbase, compare, temp, i
• for (base 1 base lt size base )
• temp data base
• compare base
• while ( compare gt 0 data compare 1 gt temp)
• data compare data compare 1
• compare - -
• data compare temp
• printf ( Access )
• for ( I 0 i lt size i )
• printf ( d , data i)
• printf ( \n )