清华大学：《数据结构》课程电子教案（PPT课件讲稿）Chapter3 Lists

chapter 3 Lists 8 1 AbStract Data Type(adt) (Definition Data Type = Objects ]U[ Operations Example〗int={0,±1,±2,…, NT MAX, INT MIN} (Definition An Abstract Data Type(ADT)is a data type that is organized in such a way that the specification on the objects and specification of the operations on the objects are separated from the representation of the objects and the implementation on the operations

CHAPTER 3 Lists §1 Abstract Data Type (ADT) 【Definition】Data Type = { Objects }  { Operations } 〖Example〗 int = { 0, 1, 2,   , INT_MAX, INT_MIN }  { +, −, , , ,    } 【Definition】An Abstract Data Type (ADT) is a data type that is organized in such a way that the specification on the objects and specification of the operations on the objects are separated from the representation of the objects and the implementation on the operations

s2 The List ADt ADT. Objects:(item, item,., itemN-1) Operations: 9 Finding the length, N, of a list. Cg Printing all the items in a list 9 Making an empty list C Finding the k-th item from a list,0<k<N. Inserting a new item after the k-th item of a list, 0sk<N. C Deleting an item from a list C Finding next of the current item from a list e Finding previous of the current item from a list

§2 The List ADT Objects: ( item0 , item1 ,  , itemN−1 ) Operations:  Finding the length, N, of a list.  Printing all the items in a list.  Making an empty list.  Finding the k-th item from a list, 0  k < N.  Inserting a new item after the k-th item of a list, 0  k < N.  Deleting an item from a list.  Finding next of the current item from a list.  Finding previous of the current item from a list. ❖ ADT:

1. Simple Array implementation of lists(seqlist) array i=item Address Content array+i item; Sequential mapping -array+i+1 item;1 Maxsize has to be estimated Find Kth takes o(1)time. Insertion and Deletion not only take o(N time, but also involve a lot of data movements which takes time

1. Simple Array implementation of Lists (seqlist) array[ i ] = itemi  MaxSize has to be estimated. Address Content array+i itemi array+i+1 itemi+1 …… …… …… …… Sequential mapping  Find_Kth takes O(1) time.  Insertion and Deletion not only take O(N) time, but also involve a lot of data movements which takes time

Seqlist's(顺序表 definition #define listsize 100 /max length typedef int ListData; typedef struct i ListData x data: //base address int length: //current items lengt th 3 Seqlist

SeqList ’s(顺序表)definition #define ListSize 100 //max length typedef int ListData; typedef struct { ListData * data; //base address int length; //current items’ length } SeqList ;

Basic operation of seqlist Initialize void InitList( Seq list &l)i L data=( ListData *) malloc Listsize s sizeof List Data ))i if (Ldata== NULL)( printf(“存储分配失败!n”); exit (1); length =0

Basic operation of SeqList ◼ Initialize void InitList ( SeqList & L ) { L.data = ( ListData * ) malloc ( ListSize * sizeof ( ListData ) ); if ( L.data == NULL ) { printf ( “存储分配失败!\n” ); exit (1); } L.length = 0; }

Find value find the position of x in the SeqList, return position of x in L, -1 if not found int Find( seqlist &l, listData x)i inti=0 while (i< Length & L data!=x) i++ if (i< Llength ) return 1; else return-l

▪ Find value：find the position of x in the SeqList，return position of x in L,-1 if not found. int Find ( SeqList &L, ListData x ) { int i = 0; while ( i < L.length && L.data[i] != x ) i++; if ( i < L.length ) return i; else return -1; }

Find value whether x is in L int IsIn( Seqlist &l, ListDatax) t inti=0, found=0 while(i< Llength &&l found if(L data!=x)i++ else found=l return found:

Find value：whether x is in L int IsIn ( SeqList &L, ListData x ) { int i = 0, found=0; while ( i < L.length &&!found ) if(L.data[i] != x ) i++; else found=1; return found; }

Solve the length of seq list int Length( Seq list &l)i return Length Find k th: return the k th data in ListData GetData( Seq list &l, int i)t if (i>=0&&i< Llength return Ldata; e print(“参数i不合理!Ⅶn”); eIs

◼ Solve the length of SeqList int Length ( SeqList & L ) { return L.length; } ◼ Find k_th：return the k_th data in l ListData GetData ( SeqList &L, int i ) { if ( i >= 0 && i < L.length ) return L.data[i]; else printf ( “参数 i 不合理！\n” ); }

Findsucceed int Next( Seq List &l, listData x)t int i= Find (x) if(i>0 & i0 & i< Llength )return i-1 else return -l

▪ FindSucceed int Next ( SeqList &L, ListData x ) { int i = Find(x); if ( i >0 && i 0 && i < L.length ) return i-1; else return -1; }

■ Insertion 56 25345716480963 Insert x 50 D 34567 2534575016480963 The average moving number of times(AM if it is equal probability to insert the new element into all positions AMN- I ∑(n-i)=—(n+…+1+0) n+1 n+1 1n(n+1) (n+1)2

▪ Insertion 2 2 ( 1) ( 1) 1 ( 1 0) 0 1 1 ( ) 1 1 = n n n n n n i n n i n = + + =  + + + = + − = + AMN  25 34 57 16 48 09 63  0 1 2 3 4 5 6 7 50 Insert x 25 34 57 50 16 48 09 63  0 1 2 3 4 5 6 7 50 i The average moving number of times(AMN) if it is equal probability to insert the new element into all positions