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  1. Linked Lists 2014, Fall Pusan National University Ki-Joune Li

  2. Problems of Array • Lack of Dynamic Properties • Insertion • Deletion • Moving elements: expensive operation • Max. Size of Array • Linked List • More dynamic data structure than Array • No subscript (or index) • Only Linear Search is possible

  3. 전도연 9 전지현 7 김희선 이영애 강혜정 6 8 5 Linked List : Example Insert (선호도 순으로)

  4. 전도연 9 Linked List : Data Structures Node Data Link to the next node Class LinkedList { private: Node *first; public: insert(DataType data,Node *q); insert(Node *p); delete(Node *p); Node *search(condition); }; Class Node { friend class LinkedList; private:DataType data; Node *next; };

  5. p: node to delete q Delete node Insert after p LinkedList::delete(Node *p,*q) {// delete node p after q if(q==NULL) first=first->next; else q->next=p->next; delete p; }; LinkedList::insert(DataType data,Node *p) { Node *newNode=new Node(data); if(first==NULL) { first=newNode; newNode->next=NULL } else { newNode->next=p->next; p->next=newNode; } }; Search with conditions Node *LinkedList::search(Condition condition) { for(Node *ptr=first;ptr!=NULL; ptr=ptr->next) { if(checkCondition(condition)==TRUE) return ptr; } return NULL; }; Linked List : Operations

  6. Push(Linked List): Insert at first LinkedList::insertFirst(DataType data) { Node *newNode=new Node(data); newNode->next=temp; first=newNode;}; Pop: Remove from the first DataType LinkedList::deleteFirst() { if(first==NULL) ListEmpty(); DataType tmpData=first->data; Node *tmpNode=first; first=first->next; delete tmpNode; return tmpData;}; Stacks by Linked List Class Stack { private: LinkedList *list; public: push(DataType data);DataType pop();}; Top Top Time Complexity: O(1)

  7. Push Pop Stack::push(DataType data) { list->insertFirst(data); }; DataType Stack::pop() { return list->deleteFirst(data); }; Stacks by Linked List Class Stack { private: LinkedList *list; public: push(DataType data);DataType pop();};

  8. Queues by Linked List Class Queue { private: Node *list; public: insert(DataType data);DataType delete();}; Insert: Insert at last LinkedList::insert(DataType data) { Node *newNode=new Node(data); if(first==NULL) { first=newNode; return; } Node *p=first; Node *q; while(p!=NULL) { q=p; p=p->next; } q->next=newNode;}; first Time Complexity: O(n) Why not pointer to the last ?

  9. Insert: Insert at last CircularList::insert(DataType data) { Node *newNode=new Node(data); if(last==NULL) { last=newNode; last->next=last; return; } newNode->next=last->next; last->next=newNode;}; Delete : delete the first DataType CircularList::delete() { if(last==NULL) QueueEmpty(); DataType tmpData=last->data; Node *first=last->next; last->next=first->next; delete first; retun tmpData;}; Circular List O(n) operations to reach to the last node first last O(1) O(1)

  10. Insert: Insert at first (with head node) CircularList::insert(DataType data) { Node *newNode=new Node(data); newNode->next=head->next; head->next=newNode;}; Circular List with Head Node Empty List Head Head Empty node with ptr to next newNode

  11. 3 2 3 Coef 12 7 14 0 8 0 14 Exp N N Application of List: Polynomials a = 3 x 14 + 2 x8 + 3 b = 12 x 14 + 7

  12. 7 3 3 7 2 3 2 12 15 14 8 0 14 5 14 8 5 0 N N N Adding Polynomials a = 3 x 14 + 2 x8 + 3 b = 12 x 14 + 7 x5 c = a + b

  13. Erasing Linked List first Class LinkedList { private: Node *first; public: LinkedList(); ~LinkedList();}; Become garbage void LinkedList::~LinkedList() { Node *ptr=first; while(first!=NULL) { ptr=first->next; delete first; }};

  14. Delete node Insert after p LinkedList::delete(Node *p,*q) {// delete node p after q if(q==NULL) first=first->next; else q->next=p->next; delete p;}; LinkedList::insert(DataType data,Node *p) { Node *newNode=new Node(data); if(first==NULL) { first=newNode; newNode->next=NULL } else { newNode->next=p->next; p->next=newNode; } }; Maintaining Available Node List Destructor void LinkedList::~LinkedList() { Node *ptr=first; while(first!=NULL) { ptr=first->next; delete first; }}; Class LinkedList { private: Node *first; public: LinkedList(); ~LinkedList();}; time consuming operations

  15. Maintaining Available Node List first Class CircularList { private: Node *first; static Node *av=NULL;public: CircularList(); ~CircularList();}; Available Empty Node List av For add operation Node *CircularList::getNode() { Node *newNode; if(av==NULL) newNode=new Node(); else { newNode=av; av=av->next; } return newNode; } void CircularList::~CircularList() { if(first!=NULL) { Node *second=first->next; first->next=av; first=NULL; av=second; } } replace Node *newNode=new Node(data);  Node *newNode=getNode();

  16. 0 0 11 0 0 13 0 12 0 0 0 0 0 14 0 -4 0 0 0 -8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 2 0 6 0 1 1 2 0 1 0 2 2 6 1 5 5 7 0 -9 0 0 0 0 0 -4 12 14 11 7 13 -8 -9 11 Application of List : Sparse Matrix row col down right if ishead=NO value if ishead=YES down right next

  17. 6 7 7 Application of List : Sparse Matrix Circular Linked List with header node

  18. 6 7 7 Application of List : Sparse Matrix Circular Lined List for the header nodes (using right field)

  19. 0 2 11 Application of List : Sparse Matrix Circular Linked List for the header nodes using down field

  20. 0 0 11 0 0 13 0 12 0 0 0 0 0 14 0 -4 10 0 0 -8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 5 0 1 2 2 2 6 0 6 5 5 2 1 1 2 2 7 0 0 -9 0 0 0 0 0 12 10 -8 13 14 7 9 11 -4 10 List for Sparse Matrix : Insert O (max{r,c})

  21. 14 8 0 0 0 Doubly Linked List Linked List : inefficient to go back Head Why not double links ?

  22. 20 14 8 0 0 0 0 0 8 14 0 Doubly Linked List : Insertion and Deletion Insertion x p void DoublyLinkedList::Insert(DblNode *p,*x) { p->leftLink=x; p->rightLink=x->rightLink; x->rightLink->leftLink=p; x->rightLink=p; } O (1) Deletion

  23. Coef Exp_x Exp_y Exp_z next Coef Exp_x Exp_y next Representation of Polynomial P = x10 y3 z2 + 2 x8 y3 z2 + 3 x8 y2 z2 + x4 y4 z + 6 x3 y4 z + 2 y z P = x10 y3 + 2 x8 y3 + 3 x8 y2 + x4 y4 + 6 x3 y4 + 2 y Depends on the number of variables NOT a General Representation How to represent it in more general way ?

  24. P1(z) P211(x) P212(x) P22 (x) P22(y) P21(y) A General Way to Represent Polynomial P = x10 y3 z2 + 2 x8 y3 z2 + 3 x8 y2 z2 + x4 y4 z + 6 x3 y4 z + 2 y z P = ( (x10 + 2 x8 ) y3 + 3 x8 y2 ) z2 + ( ( x4 + 6 x3 ) y4 + 2 y ) z Nested Polynomial Nested Linked List

  25. Generalized Lists • Definition • A = (a0, a1, a2, an-1) where ai is ATOMIC NODE or a LIST • When ai is a list, it is called SUBLIST. • Linear List • Example • D=() : NULL • A=(a, (b, c)) : Finite • B=(A, A, ()) = ((a, (b, c)), (a, (b, c)), ()) • C=(a, C) = (a, (a, (a, …)))) : Infinite Reusability of Generalized List : Shared List

  26. Class GenListNode { friend class GenList; private: Boolean flag; Node *next; union { GenListNode *dlink; DataType data; }; }; Implementation of Generalized List Data of Node Node Node / List Flag Data Next DLink Pointer to List Class GenList { private: GenListNode *first; public: ...};

  27. N L N N L N N N L L N N N N N L L N N x 3 1 y 2 z y 0 1 x x 6 x 4 2 0 4 8 1 2 8 3 3 2 10 Generalized List : Example P = ( (x10 + 2 x8 ) y3 + 3 x8 y2 ) z2 + ( ( x4 + 6 x3 ) y4 + 2 y ) z

  28. Generalized List : Example D=() A=(a, (b, c)) B=(A, A, ()) C=(a, C) A N a L N b N c B L L L C N a L

  29. Operation of Generalized List: Copy A=((a, b), ((c, d), e)) A L L N a N b L N e void GenList:copy(const GenList& l) { first=copy(l.first); } L c N d GenListNode *GenList:copy(const GenListNode *p) { GenListNode *q=NULL; if(p!=NULL) { q=new GenListNode; q->flag=p->flag; if(p->flat==NODE) q->data=p->data; else q->dlink=copy(p->dlink); q->next=copy(p->next); } return q; } One visit per node : Linear Scan : O(m ) Not Circular like C=(a, C)

  30. Operation of Generalized List: Equal s l=((a, b), ((c, d), e)) l L L m=((a, b), ((c, f), e)) int operator==(const GenList& l,m) { return equal(l.first,m.first); } int equal(GenListNode *s, *t) { x=FALSE; if(s and t are null), return TRUE; if(s and t are not null), { if(s and p are node) { if(s->data==t->data) x=TRUE; else x=FALSE; } else x=equal(s->dlink,t->dlink); } if(x==TRUE) return(s->next,t->next); return FALSE; } N a N b L N e N c N d t m L L N a N b L N e N c N f

  31. Head node with reference counter Shared List A N 3 N a L N b N c Shared Linked List: Reference Counter D=() A=(a, (b, c)) B=(A, A, ()) C=(a, C) Deletion of A with care A N a L N b N c B L L L Delete list when reference counter = 0 C N a L

  32. P Data: Closed Geometry Circle Rectangle Polygon Triangle Example: Design Shape List Total Area of P ?