REPREENTSTION BY: 1] Manisha . 2] Sanika . 3] Payal . 4] Ashwini .

1. REPREENTSTION BY: 1] Manisha . 2] Sanika . 3] Payal . 4] Ashwini . 5] Ankita .

2. CONTENTS: • Defination of link list. • Types of Link List. • Polynomials. • Addition of two polynomials. • What is sparse matrix? • Insertion of an element in sparse matrix. • Deletion of an element in sparse matrix. • Programme • Conclusion.

3. What is link list???

4. In the previous chap. We have studied the representation of sequential mapping using an array in C . This representation had a property that successive nodes of the data object were stored a fixed distance apart.

5. Linked list is a very common data structure often used to store similar data in memory. • This memory is randomly selected by the compiler. • The order of the elements is maintained by explicit links between them.

6. NODE DATA LINK

7. It is a non sequential list-representation. • The above fig. is of a singly link list which also means a chain. • A chain is a singly link list that is comprised of zero or more nodes.when the number of nodes is empty. • The nodes of the non-zero(empty) chain are orderedso that the first link get connected to second and the second to the third and so on…

8. Types of link lists • Circular linked list • Singly linked list • Doubly linked list

9. ADVANTAGES OF LINKED REPRESENTATION OVER SEQUENTIAL REPRESENTATION: 1)In sequential representation the memory is allocated sequentially whereas in linked representation memory is allocated randomly. 2)In sequential representation we does not require address of next element where as in linked representation to access list elements in the correct order,with each element we store the address of the next element in that list… Etc.

10. What are Polynomials?

11. Representation Link of other node

12. Padd( ) : This function adds the node to the resultant list in the descending order of the components of the polynomial. • When padd( ) is called to add the second node we need to compare the exponent value of the new node with that of the first node. • It consist of mainly three conditions:

13. 1) If exponent of 1st polynomial is greater than 2nd polynomial. 2) If exponent of 1st polynomial is smaller than the 2nd . 3) If exponents of 1st polynomial is equal to 2nd polynomial.

14. Program: typedefstructpolyNode *polypointer; Typedefstruct { intcoef; intexpon; polypointer link; } polyNode; polypointera,b;

15. polypointerpadd(polypointer a, polypointer b) { /* Return a polynomial which is the sum of a & b */ polypointer c, rear, temp; int sum; malloc(rear,sizeof(*rear)); c=rear; while(a && b)

16. switch(COMPARE(a->expon,b->expon)) { case -1: /*a->expon< b->expon */ attach(b->coef, b->expon ,&rear); b= b->link; break; case 0: /*a->expon= b->expon */ sum= a->coef + b->coef; if (sum) attach(sum, a->expon ,&rear); a= a->link; b= b->link; break;

17. case 1: /*a->expon> b->expon */ attach(a->coef, a->expon ,&rear); a= a->link; break; } /*copy rest of list a and then list b*/ for(; a; a= a->link) attach(a->coef, a->expon ,&rear); for(; b; b= b->link) attach(b->coef, b->expon ,&rear); rear->link =NULL;

18. /*delete extra initial node */ temp=c; c= c->link; free(temp); return c; }

19. WHAT IS A SPARSE MATRIX?

20. Sparse matrix is that matrix which has more number of zero’s or can also be said as that matrix which consist of less number of non-zero numbers.

21. REPRESENTATION OF SPARSE MATRIX HEADER NODE down right next down right ELEMENT NODE row col value

22. We devised a sequential scheme in which we represented each non-zero term by a node with three fields: row,col,value. • Linked list allows us to efficiently represent structures that varies in size, a benefit that also applies to sparse matrix. • In the above fig the next field links the header nodes together. • Each node has a tag field to distinguish between header nodes and entry nodes. • Each header node has three additional fields: 1]down 2]right 3]next

23. Down field is used to link into column list. • Right field is used to link into row list. • Next field is used to link header nodes together. • Whereas every entry field has five fields: 1]row 2]col 3]value 4]down 5]right • We use the down field to link to the next non-zero term in the same column the right field to link to the next non-zero term of row.

25. for(temp=head->right ; temp!=head;temp=temp ->right) printf(“%5d%5d%5d\n”,temp->u.entry.rowu.entry.col ,u.entry.value); head=head->u.next; /*next row*/ }

26. Erasing a sparse matrix void merase (matrixPointer *node) {/* erase the matrix, return the nodes to the heap */ matrixPointerx,y, head =(*node)->right; int i ; /*free the entry and header nodes by row */ for( i=0; i<(*node) -> u.entry.row; i++) { y = head-> right ; while( y!=head) { x = y; y =y->right; free(x); }

27. x=head ; head=head -> u.next; free(x); } /*free remaining header nodes */ y = head; while( y!=*node) { x = y; y =y->u.next ; free(x); } free(*node) ; *node =NULL ; }

28. LINK LIST AT A GLANCE: • Today we have studied the basics of linked list with the help of node structure. • How to add two polynomials using linked list with it’s representation. • How to insert and delete elements in a sparse matrixwith it’s representation.

29. THANK YOU…!!