repreentstion by: 1] manisha . 2] sanika . 3] payal . 4] ashwini
DESCRIPTION
REPREENTSTION BY: 1] Manisha . 2] Sanika . 3] Payal . 4] Ashwini . 5] Ankita. 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. - PowerPoint PPT PresentationTRANSCRIPT
REPREENTSTION BY:
1] Manisha .2] Sanika .3] Payal .4] Ashwini .5] Ankita .
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.
What is link list???
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.
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.
NODE
DATA LINK
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 ordered so that the first link get connected to second and the second to the third and so on…
Types of link lists
Circular linked listSingly linked listDoubly linked list
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.
What are Polynomials?
Representation
Link of other node
3 14 2 8 1 0 0
8 14 -3 10 10 6 0
coefficient
exponents link
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:
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.
Program:
typedef struct polyNode *polypointer;Typedef struct { int coef; int expon; polypointer link; } polyNode;polypointer a,b;
polypointer padd(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)
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;
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;
/*delete extra initial node */temp=c;c= c ->link;free(temp);return c;}
WHAT IS A SPARSE MATRIX?
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.
next
down right
down right
row col value
REPRESENTATION OF SPARSE MATRIX
ELEMENT NODE
HEADER NODE
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
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.
void mwrite(matrixpointer node) / *print out the matrix in row major form*/ int i; matrixpointer temp,head=node->right; / *matrix dimensions*/ printf(“\ nnumrows=%d,numcols=%d\ n”,node ->u.entry.row, node->u.entry.col); printf(“the matrix by row,column and
value:\ n\ n”); for(i=0; i< node->u.entry.row; i++) / *print out the entries in each row*/
for(temp=head->right ; temp!=head;temp=temp
->right)printf(“%5d%5d%5d\n”,temp-
>u.entry.row u.entry.col ,u.entry.value);
head=head->u.next;/*next row*/}
Erasing a sparse matrixvoid merase (matrixPointer *node){/* erase the matrix, return the nodes to the heap */ matrixPointer x,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);}
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 ;}
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 matrix with it’s representation.
THANK YOU…!!