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Objects : ( item 0 , item 1 ,  , item N  1 )

CHAPTER 4 Lists. 4.1 The List ADT:. Objects : ( item 0 , item 1 ,  , item N  1 ). Operations :  Finding the length , N , of a list.  Printing all the items in a list.  Making an empty list.  Finding X item from a list, 0  k < N .

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Objects : ( item 0 , item 1 ,  , item N  1 )

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  1. CHAPTER 4 Lists 4.1 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 X 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.

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

  3. 4.2 Singly Linked Lists • Linked list • an ordered sequence of nodes with links represented as arrows • Insert mat after cat : • Delete mat from list :

  4. The capabilities to make linked representation: • Define a node's structure----self-referential structures • Create a new node ---- malloc function • Remove nodes ---- free function 〖example〗list of words ending in at define a node typedef struct listNode *listPointer; structure typedef struct listNode { char data [ 4 ]; listPointer link; }; create a new list listPointer ptr = NULL; ( #define IS_EMPTY(ptr) ( ! ( ptr )) ) create new nodes ptr = (listPointer) malloc ( sizeof (listNode )); place a word into the list strcpy ( ptr ->data, "bat"); ptr -> link = null; Free point free(ptr);

  5. x first ... ... a1 ai ai+1 an b NULL temp 〖example〗List insertion  temp->link = x-> link  x-> link = temp Question: What will happen if the order of the two steps is reversed? Read Program 4.2 on p.153 and answer the question: Why is first passed as a pointer to listPointer?

  6. 〖example〗List insertion #define IS_FULL (ptr ) ( ! (ptr )) void insert(listPointer *first, listPointer x) { /* insert a new node with data = 50 into the list ptr after node */ list_pointer temp; temp = (listPointer)malloc(sizeof(listNode)); if ( IS_FULL(temp) ) { fprintf(stderr, "The memory is full\n'); exit(1); } temp->data = 50; if ( *first) { temp->link = x->link; x->link = temp; } else { temp->link = NULL; *first= temp; } }

  7. trail first ... ... b an b ai a1 ai+1 NULL node x 〖example〗list deletion  trail-> link = x-> link  free ( node ) Question: How can we delete the first node from a list? Read Program 4.3 on p.155 and find the answer.

  8. List after the function call delete(&ptr, NULL, ptr) List after the function call delete(&ptr, ptr, prt->link) 〖example〗list deletion void delete(listPointer *first, listPointer trail, listPointer x) { /* delete node from the list, trail is the preceding node ptr is the head of the list */ if ( trail ) trail->link = x->link; else *first= (*first)->link; free(x); }

  9. 〖example〗Printing out a list void print_list(listPointer first) { printf("The list contains: "); for ( ; first; first= first->link ) printf("%4d”,first->data); printf("\n"); }

  10. STACK temp top top top item item item item NULL    4.3 Dynamically Linked Stacks and Queues Push:  temp->link = top • Linked Stacks  top = temp Pop:  temp = top  top = top->link  item = temp->item Read Program 4.5 and Program 4.6 on p.158 about implementation of push and pop item  free ( temp )  return item Question: How to represent n stacks? Answer: stackPointer top [ n ] ;

  11. Program : Add to a linked stack #define MAX_STACKS 10 /*maximum number od stacks */ typedef struct { int key ； /* other fields */ } element; typedef struct stack *stackPointer; typedef struct stack { element item; stackPointer link； }; stackPointer top [ MAX_STACKS ]; void push(inti, element item) { /* add an element to the top of the stack */ stackPointer temp = (stackPointer)malloc(sizeof(stack)); if ( IS_FULL(temp) ) { fprintf( stderr, "The memory is full\n"); exit(1); } temp->item = item; temp->link = top[i]; top[i] = temp; }

  12. Program : Delete from a linked stack element pop(inti) { /* delete an element from the stack */ stackPointer temp = top[i]; element item; if ( IS_EMPTY(temp) ) { fprintf(stderr, "The stack is empty\n"); exit(1); } item = temp->item; top[i] = temp->link; free(temp); return item; } • the boudary condition for the stacks: • top [ i ] = NULL, iff the i th stack is empty 0 <= i < MAX_STACKS • IS_FULL ( temp) iff the memory is full

  13. QUEUE front rear front temp temp rear NULL item  item    item item Linked Queues addq:  rear->link= temp NULL  temp-> link = NULL  rear = temp deleteq:  temp = front  front = temp-> link item Read Program 4.7 and Program 4.8 on p.159-160 about implementation of addq and deleteq  item = temp->item  free ( temp )  return item Question: How to represent n queues? Answer: queuePointer front[n], rear[n];

  14. Program: Add to the rear of a linked queue #define MAX_QUEUES 10 /*maximum number of queues */ typedefstruct queue *queuePointer; typedefstruct queue { element item; queuePointer link: }; queuePointer front [MAX_QUEUES], rear [MAX_QUEUES ]; void addq(inti, element item) { /* add an element to the rear of the queue */ queuePointer temp = (queuePointer)malloc(sizeof(queue)); if ( IS_FULL(temp) ) { fprintf(stderr, "The memory is full\n"); exit(1); } temp->item = item; temp->link = NULL; if ( front[i] ) rear[i]->link = temp; else front[i] = temp; rear[i] = temp; }

  15. Program: Delete from the front of a linked queue element deleteq(inti) { /* delete an element from the queue */ queuePointer temp = front[i]; element item; if ( IS_EMPTY(front[i]) ) { fprintf(stderr, "The queue is empty\n"); exit(1); } item = temp->item; front[i] = temp->link; free(temp); return item; } • the boudary condition for the queues: • front [ i ] = NULL, iff the i th queue is empty 0 <= i < MAX_QUEUES • IS_FULL ( temp) iff the memory is full

  16. 4.5 Additional List Operations 1. operations for chains a)Inverting a singly linked list b) Concatenating singly linked lists 2. operations for circularly linked lists a) Inserting at the front of a list b) Finding the length of a circular list

  17. a) Inverting a singly linked list listPointer invert (listPointer lead ) { /* invert the list pointed to by lead */ listPointer middle, trail ; middle = NULL ; trail=NULL; /* middle is head of the inverted chain */ while ( lead ) { middle = lead ; lead = lead->link; middle->link= trail ; trail = middle ; } /* end while-loop */ return middle ; } middle middle middle lead lead lead 2 2 3 1 1 3 1 3 2          trail trail trail NULL NULL NULL NULL NULL NULL Tinvert= O( length of lead )

  18. b) Concatenating singly linked lists listPointerconcatenatelistPointer ptr1, listPointer ptr2) { /* produce a new list hat contains the list ptr1 followed by the list ptr2. The list pointed to by ptr1 is changed permanently */ listPointertemp; if ( IS_EMPTY(ptr1) ) return ptr2; else { if ( !IS_EMPTY(ptr2) ) { for ( temp = ptr1; temp->link; temp = temp->link ) ; temp->link = ptr2; } return ptr1; } } Tconcatenate= O( length of ptr1 )

  19. a) Inserting at the front of a circularly linked list void insertFront listPointer *last, listPointer node) /* insert node at the front of the circular list last, where last is the last node in the list */ { if ( IS_EMPTY(*last) ) { /* list is empty, change ptr to point to new entry */ *last= node; node->link = node; } else { /* list is not empty, add new entry at front */ node->link = (*last)->link; (*last)->link = node; } }

  20. b) Finding the length of a circular list int length(listPointer last) { /* find the length of the circular list last */ list_pointer temp; int count = 0; if (last) { temp = last; do { count ++; temp = temp->link; } while ( temp != last); } return count; }

  21. llink rlink  item         item1 item2 item3    H H 4.8 Doubly Linked lists typedef struct node *nodePointer; typedef struct node { nodePointer llink; element item; nodePointer rlink; }; Uhhh ... Then I’ll have to go from the 1st node again. But hey, why do I wantta find the previous node? Don’t we have enough headache already? Why do we need the doubly linked lists? ptr = ptr->llink->rlink = ptr->rlink->llink I’ll go from the 1st node to the m-th node. Suppose you have a list 1->2->3->…->m. Now how would you get the m-th node? Why do you ask me? :-) Maybe you wantta delete the m-th node? A doubly linked circular list with head node: Then you are asked to find its previous node m 1? An empty list :

  22. Program : Insertion into a doubly linked circular list void dinsert(nodePointer node, nodePointernewnode) { /* insert newnode to the right of node */ newnode->llink = node; newnode->rlink = node->rlink; node->rlink->llink = newnode; node->rlink = newnode; }

  23. Program: Deletion from a doubly linked circular list void ddelete(nodePointer node, nodePointer deleted) { /* delete from the doubly linked list */ if ( node == deleted ) printf("Deletion of head node not permitted.\n"); else { deleted->llink->rlink = deleted->rlink; deleted->rlink->llink = deleted->llink; free(deleted); } }

  24. Homework-2 1. P112, #4 2. P142, #1 3. P154, #2 4. P154, #6 5. P172, #1 补充： 6. 如果单链表带头结点，请完成CreateList, Insert, Delete函数操作, 可修改Program4.2和Program4.3完成。并请给出相关的数据结构定义。 CreateList：创建带一个头结点的单链表; Insert：在单链表first的X结点后插入元素Item; Delete：删除单链表First中Tail结点后的X结点，并返回其值。

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