??????

1
??? ???

• ???
• ???
• ???
• ????
• ????
• ???

????????
????????
?????
2
??? ???
2.1 ???

• ??
• n( ? 0)????????
• L (a1, a2, , an)
• ai???,n?????
• ????????,???????

3

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

4
2.2 ???

• ???????????

LOC ( i ) LOC ( i -1 ) l a il
5

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

6
?????????????

• define maxSize 100
• typedef int T
• typedef struct
• T datamaxSize //??????????
• int last
• SeqList
• typedef int T
• typedef struct
• T data //??????????
• int maxSize, last
• SeqList

7
?????(????)

• ????????????????,???????union
• typedef union
• int val //?data.val??
• char ch //?data.ch??
• float dir //?data.dir??
• union data link //?data.link??
• data //????????data

8
???(SeqList)????

• include ltiostream.hgt //???seqList.h?
• include ltstdlib.hgt
• include linearList.h"
• const int defaultSize 100
• template lt class Egt
• class SeqList public LinearListltEgt
• protected
• E data //????
• int maxSize //??????????
• int last //???????????
• void reSize(int newSize) //????????

9

• public
• SeqList(int sz defaultSize) //????
• SeqList(SeqListltEgt L) //??????
• SeqList() delete data //????
• int Size() const return maxSize //??????
• int Length() const return last1 //?????
• int Search(E x) const
• //??x?????,????????
• int Locate(int i) const
• //??? i ???,????????
• bool getData(int i, E x) const //??i?????
• bool Insert(int i, E x) //??
• bool Remove(int i, E x) //??

10
????????

• include ltstdlib.hgt //??exit????
• include seqList.h //??????seqList.cpp
• template ltclass Egt
• SeqListltEgtSeqList(int sz)
• if (sz gt 0)
• maxSize sz last -1
• data new EmaxSize //???????
• if (data NULL) //??????
• cerr ltlt "??????!" ltlt endl
• exit(1)

11
??????

• template ltclass Egt
• SeqListltEgtSeqList ( SeqListltEgt L )
• maxSize L.Size() last L.Length()-1 E
  value
• data new EmaxSize //??????
• if (data NULL) //??????
• cerr ltlt "??????!" ltlt endl exit(1)
• for (int i 1 i lt last1 i) //??????
• L.getData(i, value) datai-1 value

12
????????

• template ltclass Egt
• int SeqListltEgtSearch(E x) const
• //??????????? x ?????,???
• //?????????????,??????0
• for (int i 0 i lt last i) //????
• if ( datai x ) return
  i1 //??????????1
• return 0 //????

13
??????(??)
x 48 x 50
14
???????????(??????)

• ACN(Average Comparing Number) (???????n,?n
  last 1)

??????i?????pi,????ci
??????
?????pi ??,?
?????????n?
15
??????
16
???????

• template ltclass Egt
• bool SeqListltEgtInsert (int i, E x)
• //????x??????i (1ilast2) ????
• //?? if (last maxSize-1) return false
  //??
• if (i lt 1 i gt last2) return false
  //??i???
• for (int j last j gt i-1 j--)
  //????
• dataj1 dataj
• datai-1 x //??(? i ???datai-1?)
• last return true //????

17
??????????(????)
???? i ?????,?datai-1 ?data last
????,??n-1-(i-1)1 n-i1? (???????n,?n last
1)
????????AMN(Average Moving Number)????????????
?????n1?????,????n/2?
18
????????
19
???????

• template ltclass Egt
• bool SeqListltEgtRemove (int i, E x)
• //?????? i (1ilast1) ???,?????
• //?? x ??????? if (last -1) return false
  //??
• if (i lt 1 i gt last1) return
  false//??i???
• x datai-1
• for (int j i j lt last j)
  //????,??
• dataj-1 dataj
• last-- return true

20
????????????(????)
??? i ???,??? i1 ??? last1?????,???????
n-(i1)1 n-i (???????n,?n last 1)
????????AMN(Average Moving Number)?n???????????
?????n?????,????(n-1)/2?
21
??????
????????????
void Union ( SeqListltintgt LA,
SeqListltintgt LB ) int n
LA.Length ( ) int m LB.Length ( )
int x for ( int i 1 i lt m i )
LB.getData(i, x) //?LB????? int k
LA.Search (x) //?LA???? if ( k 0 )
//??????? LA.Insert (n,
x) n
22
????????????
void Intersection ( SeqListltintgt LA,
SeqListltintgt LB )
int n LA.Length ( ) int m LB.Length (
) int i 1 int x while ( i lt n )
LA.getData (i, x) //?LA????? int k
LB.Search (x) //?LB???? if ( k 0 )
LA.Remove (i,x) n-- //???,?LA???? else
i
23
2.3 ???

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

• ??????(??)
• ?????????????
• ?????????????

24

• ??????
• ????(??)???(Node)???
• ????
• ?????????
• ?????????

25
????????
26
???????

• ?????????(???)?
• ????(ListNode)?
• ??(List)?

27

• ????
• ????
• ????
• ????
• ????

28
?????(????)
struct ListNode //??????
int data //????, ?? ListNode
link //???? class List
//??? public private
ListNode first //????
29
?????(????)
class List //???? class
ListNode //????? friend class List
//???????? private int data
//????, ?? ListNode link
//???? class List
//??? private ListNode first
//????
30
?????(????)
class List //???
public private class ListNode
//????? public int data
//????, ?? ListNode link
//???? ListNode first
//????
31
?????(????)
class ListNode //?????
protected int data //????,
?? ListNode link
//???? class List pubic class LinkNode
//??? public
private ListNode first
//????
32
????????????

• ??
• ?????????????
• newNode-gtlink first
• first newNode

(???) (???)
33

• ????????????
• newNode-gtlink current-gtlink
• current-gtlink newNode

(???) (???)
34

• ????????????
• newNode-gtlink current-gtlink
• current-gtlink newNode

(???) (???)
35
????????

• bool ListInsert(int i, int x)
• //???? x ???? i ??????i ?1??,
• //i 0 ????????????
• if (first NULL i 0) //????????
• LinkNode newNode new LinkNode(x)
  //???????
• newNode-gtlink first first newNode
• //?????????
• else //??,??????
• LinkNode current first int k 1
  

36

• while (k lt i current ! NULL) //??i??
• current current-gtlink k
• if (current NULL first ! NULL)
  //??
• cerr ltlt ???????!\n return false
• else //????????
• LinkNode newNode new LinkNode(x)
• newNode-gtlink current-gtlink
• current-gtlink newNode
• return true

37

• ??
• ????? ?????????
• ????? ?????????

????????ai???
38
????????

• bool ListRemove (int i, int x)
• //?????? i ?????, i ?1???
• LinkNode del //????????
• if (i lt 1) del first first
  first-gtlink
• else
• LinkNode current first k 1
  //?i-1???
• while (k lt i-1 current ! NULL)
• current current-gtlink k
• if (current NULL current-gtlink
  NULL) cout ltlt ???????!\n return false

39

• del current-gtlink //???/???
• current-gtlink del-gtlink
• x del-gtdata delete del //????????
• return true
• ?????????????,???????,????????,???????
• ????,???????????????????
• ???????????????????

40
??????(????)????

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

an
a1
first
first
0
0
??? ??
41
??????????????????
newNode-gtlink current-gtlink
current-gtlink newNode
42
???????????????????
(???)
del current-gtlink current-gtlink
del-gtlink delete del
(??)
43
2.4 ?????????

• ????
• ????

44
???? (Circular List)
????
??????????
45

• ???????
• ??????????? link ??? ? 0 (NULL),??????????
• ?????????????,???????????????

46
????????

• template ltclass Egt
• struct CircLinkNode //???????
• E data
• CircLinkNodeltEgt link
• CircLinkNode ( CircLinkNodeltEgt next
• NULL ) link next
• CircLinkNode ( E x, CircLinkNodeltEgt next
• NULL ) data x link next
• bool Operator(CircLinkNodeltEgt node)
  return data node.data
• bool Operator!(CircLinkNodeltEgt node)
  return data ! node.data

47

• template ltclass Egt //?????
• class CircList public LinearListltEgt
• private
• CircLinkNodeltEgt first, last //???, ???
• public
• CircList(const E x) //????
• CircList(CircListltEgt L) //??????
• CircList() //????
• int Length() const //??????
• bool IsEmpty() return first-gtlink first
• 
  //????
• CircLinkNodeltEgt getHead() const
• 
  //????????

48

• void setHead ( CircLinkNodeltEgt p )
• 
  //????????
• CircLinkNodeltEgt Search ( E x ) //??
• CircLinkNodeltEgt Locate ( int i ) //??
• E getData ( int i )
  //??
• void setData ( int i, E x ) //??
• bool Insert ( int i, E x )
  //??
• bool Remove ( int i, E x)
  //??
• ?????????????,?????????????,?????NULL,?????

49
?????????
?????
??25
50
?????????
template ltclass Egt CircListNodeltEgt
CircListltEgtSearch( E x ) //????????????? x
??? current first-gtlink while (
current ! first current-gtdata ! x )
current current-gtlink return current
51
?????????????

• ????? (?n 8 m 3)

52
??Josephus?????

• include ltiostream.hgt
• include CircList.h
• template ltclass Egt
• void Josephus(CircListltEgt Js, int n, int m)
• CircLinkNodeltEgt p Js.getHead(),
• pre
  NULL
• int i, j
• for ( i 0 i lt n-1 i ) //??n-1?
• for ( j 1 j lt m j) //?m-1??
• pre p p p-gtlink
• cout ltlt ????? ltlt p-gtdata ltlt endl

53

• pre-gtlink p-gtlink delete p
  //??
• p pre-gtlink
• void main()
• CircListlt intgt clist
• int i, n, m
• cout ltlt ????????????
• cin gtgt n gtgt m
• for (i 1 i lt n i ) clist.insert(i,
  i) //????
• Josephus(clist, n, m)
  //???????

54
????(doubly linked list)

• ???????

???? ? ? ????

• ???????????

55

• ??????????
• p p?lLink?rLink p?rLink?lLink

56
??????????

• template ltclass Egt
• struct DblNode //???????
• E data //??????
• DblNodeltEgt lLink, rLink //???????
• DblNode ( DblNodeltEgt l NULL,
• DblNodeltEgt r NULL )
• lLink l rLink r
  //????
• DblNode ( E value, DblNodelt Egt l NULL,
  DblNodeltEgt r NULL)
• data value lLink l rLink r
  //????

57

• template ltclass Egt
• class DblList //?????
• public
• DblList ( E uniqueVal ) //????
• first new DblNodeltEgt (uniqueVal)
• first-gtrLink first-gtlLink first
• DblNodeltEgt getFirst () const return first
• void setFirst ( DblNodeltEgt ptr ) first ptr
  
• DblNodeltEgt Search ( E x, int d)
• //?????d???????????x???,
• //d0?????,d?0?????

58

• DblNodeltEgt Locate ( int i, int d )
• //?????????i(0)???, d0????
• //?,d?0?????
• bool Insert ( int i, E x, int d )
• //??i????????????x????,d0
• //?????,d?0?????
• bool Remove ( int i, E x, int d ) //???i???
• bool IsEmpty() return first-gtrlink first
• //??????
• private
• DblNodeltEgt first //????

59
???????????
60
???????????

• template ltclass Egt
• DblNodelt Egt DblListltEgtSearch (E x, int d)
• //??????????????x????
• DblNodeltEgt current (d 0)?
• first-gtlLink first-gtrLink
  //?d??????
• while ( current ! first current-gtdata ! x
  ) current (d 0) ?
• current-gtlLink current-gtrLink
• if ( current ! first ) return current
  //????
• else return NULL //????

61
??????????? (???)
newNode-gtrLink current-gtrLink current-gtrLink
newNode newNode-gtrLink-gtlLink newNode
newNode-gtlLink current
62
??????????? (??)
first
first
25
???25
newNode
current
current
newNode-gtrLink current-gtrLink
(newNode-gtrLink first) current-gtrLink
newNode newNode-gtrLink -gtlLink newNode
( first-gtlLink newNode )
newNode-gtlLink current
63
???????????

• template ltclass Egt
• bool DblListltEgtInsert ( int i, E x, int d )
• //????????x????, ???? d ???
• //??????i??????
• DblNodelt Egt current Locate(i, d)
• //?d???????i???
• if ( current NULL ) return false
  //????
• DblNodeltEgt newNd new DblNodeltEgt(x)
• if (d 0) //???????i?????
• newNd-gtlLink current-gtlLink //??lLink?
• current-gtlLink newNd

64

• newNd-gtlLink-gtrLink newNd //??rLink?
• newNd-gtrLink current
• else //???????i?????
• newNd-gtrLink current-gtrLink //??rLink?
• current-gtrLink newNd
• newNd-gtrLink-gtlLink newNd //??lLink?
• newNd-gtlLink current
• return true //????

65
???????????
???
first
31
48
15
??48
current
first
31
15
current
current-gtrLink-gtlLink current-gtlLink
current-gtlLink-gtrLink current-gtrLink
66
???????????

• template lt class Egt
• bool DblListlt EgtRemove( int i, E x, int d )
• //?????????d???????i????
• DblNodelt Egt current Locate (i, d)
• if (current NULL) return false
  //????
• current-gtrLink-gtlLink current-gtlLink
• current-gtlLink-gtrLink current-gtrLink
• //?lLink??rLink????
• x current-gtdata delete current
  //??
• return true //????

67
2.5 ???????
A(x) 1 - 10x6 2x8 7x14

• n???? Pn(x) ? n1 ??
• ?? a0, a1, a2, , an
• ?? 0, 1, 2, , n??????

68
??????????
??????????

• ??? (??????)
• private
• int degree
• float coef maxDegree1
• Pn(x)?????
• pl.degree n
• pl.coefi ai, 0 ? i ? n

69

• ??? (??????)
• private
• int degree
• float coef
• Polynomial Polynomial (int sz)
• degree sz
• coef new float degree 1
• ???????????????????????????????????????,? P101(x)
  35x50-4x101, ????

70
??? struct term //???????
float coef //?? int exp
//?? static term termArraymaxTerms
//??? static int free, maxTerms
//????????
71
??? // term PolynomialtermArrayMaxTerms //
int Polynomialfree 0 class Polynomial
//????? public private int
start, finish //???????
72
?????????? A(x) 2.0x10001.8 B(x) 1.2
51.3x50 3.7x101
A.start A.finish B.start B.finish free
maxTerms
coef exp
1.8 2.0 1.2 51.3 3.7 0
1000 0 50 101
????????termArray?
73
?????????????
A(x) 1 - 10x6 2x8 7x14
???????
???
???
74

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

75
???(polynomial)??????

• struct Term //???????
• float coef //??
• int exp //??
• Term link //????
• Term (float c, int e, Term next NULL)
• coef c exp e link next
• Term InsertAfter ( float c, int e)
• friend ostream operator ltlt (ostream,
• const Term )

76

• class Polynomial //???????
• public
• Polynomal() first new Term(0, -1) //????
• Polynomal (Polynomal R) //??????
• int maxOrder() //??????
• private
• Term first
• friend ostream operator ltlt (ostream,
• const Polynomal )
• friend istream operator gtgt ( istream,
• Polynomal )

77

• friend void Add ( Polynomial A, Polynomial
  B,
• Polynomial C )
• friend void Mul ( Polynomial A, Polynomial
  B,
• Polynomial C )

78
??????????

• ????????????,????pa?pb??????????????,???????????C,
  ?????pc,?????C??????
• ?pa?pb???????????,????????????
• ????????C?,??????pa??pb?1
• ????????????????????,?????C?,pa?pb?1?
• ?pa?pb???????NULL,???????????????C??

79
????????

• AH 1 - 3x6 7x12
• BH - x4 3x6 - 9x10 8x14
• CH 1 - x4 - 9x10 7x12 8x14

80
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87
2.6 ????

• ?????????????????,??????????
• ?????????????????data?????,link????????
• ????????????????,????????????????????
• ?????????,????????????????????

88
???????
0 1 2 3 4 5
data a3 a4 a1 a5 a2
link 3 2 4 5 -1(0) 1

• 0??????,link?????????
• ???????link 0,???????????????,??????link -1?
• link???????,??????