Sparse metrics, Data Structure & Algorithms

Assignment Help:

Q. Define the sparse metrics and also explain the representation of a 4X4 matrix using linked list.        

Ans:

A matrix in which number of zero entries is quite higher than the number of non zero entries is called the sparse matrix. The natural method or technoque of expressing matrices in memory as two-dimensional arrays may not be appropriate for sparse matrices. One can save the space by storing only nonzero entries. For example matrix A (3*3 matrix) which is represented below

 

0    2      0

5   0     0

0   6     9

can be written in sparse matrix form as:

3   3     4

0    1      2

1   0   5

2   2   6

2   3   9

In this the first row represent the dimension of matrix and last column tells us about the total number of non zero values; from the second row onwards it is giving the location and value of non zero number.

Representation of a 4*4 matrix using linked list is given below:

#define MAX1 4

#define MAX2 4

struct cheadnode           /* structure for col

headnode */

{

int colno ;

struct node *down ;

struct cheadnode *next ;

} ;

struct rheadnode          /* structure for row

headnode */

{

int rowno ;

struct node * right ;

struct rheadnode *next ;

} ;

struct node                  /* structure for node to

store element */

{

int row ; int col ; int val ;

struct node *right ;

struct node *down ;

} ;

struct spmat                /* structure for special headnode */

{

struct rheadnode *firstrow ; struct cheadnode *firstcol ; int noofrows ;

int noofcols ;

} ;

struct sparse

{

int *sp ;

int row  ;

struct spmat *smat ;

struct cheadnode *chead[MAX2] ; struct rheadnode *rhead[MAX1] ; struct node *nd ;

} ;

void initsparse ( struct sparse *p )           /*

initializes structure elements */

{

int i ;

for ( i = 0 ; i < MAX1 ; i++ )            /* create row headnodes */

p -> rhead[i] = ( struct rheadnode * ) malloc (

sizeof ( struct rheadnode ) ) ;

for ( i = 0 ; i < MAX1 - 1 ; i++ ) /* initialize and

link row headnodes together */

{

p -> rhead[i] -> next = p -> rhead[i + 1] ;

p -> rhead[i] -> right = NULL ;

p -> rhead[i] -> rowno = i ;

}

p -> rhead[i] -> right = NULL ;

p -> rhead[i] -> next = NULL ;

for ( i = 0 ; i < MAX1 ; i++ )          /* create col headnodes */

p -> chead[i] = ( struct cheadnode * ) malloc (

sizeof ( struct cheadnode ) ) ;

for ( i = 0 ; i < MAX2 - 1 ; i++ )               /*

initialize and link col headnodes together */

{

p -> chead[i] -> next = p -> chead[i + 1] ;

p -> chead[i] -> down = NULL ;

p -> chead[i] -> colno = i ;

}

p -> chead[i] -> down = NULL ;

p -> chead[i] -> next = NULL ;

/* create and initialize special headnode */

p -> smat = ( struct spmat * ) malloc ( sizeof (

struct spmat ) ) ;

p -> smat -> firstcol = p -> chead[0] ;

p -> smat -> firstrow = p -> rhead[0] ;

p -> smat -> noofcols = MAX2 ;

p -> smat -> noofrows = MAX1 ;

}

void create_array ( struct sparse *p )    /* creates, dynamically the matrix of size MAX1 x MAX2 */

{

int n, i ;

p -> sp = ( int * ) malloc ( MAX1 * MAX2 * sizeof (

int ) ) ;

for ( i = 0 ; i < MAX1 * MAX2 ; i++ )        /*

get the element and store it */

{

printf ( "Enter element no. %d:", i ) ;

scanf ( "%d", &n ) ;

* ( p -> sp + i ) = n ;

}

}


Related Discussions:- Sparse metrics

Determine the critical path and the expected completion, The information in...

The information in the table below is available for a large fund-raising project. a. Determine the critical path and the expected completion time of the project. b. Plot the total

The data structure required to evaluate a postfix expression, The data stru...

The data structure needed to evaluate a postfix expression is  Stack

Data structures, I am looking for assignment help on the topic Data Structu...

I am looking for assignment help on the topic Data Structures. It would be great if anyone help me.

Inorder traversal, Inorder traversal: The left sub tree is visited, then t...

Inorder traversal: The left sub tree is visited, then the node and then right sub-tree. Algorithm for inorder traversal is following: traverse left sub-tree visit node

Efficiency of binary search, Each of the comparison in the binary search de...

Each of the comparison in the binary search decrease the number of possible candidates where the key value can be searched by a factor of 2 as the array is divided into two halves

Implement an open hash table, In a chained hash table, each table entry is ...

In a chained hash table, each table entry is a pointer to a collection of elements. It can be any collection that supports insert, remove, and find, but is commonly a linked list.

Stack, implement multiple stacks ina single dimensional array. write algori...

implement multiple stacks ina single dimensional array. write algorithams for various stack operation for them.

The two famous methods for traversing, The two famous methods for traversin...

The two famous methods for traversing are:- a) Depth first traversal b) Breadth first

Exlain double linked list, Double Linked List In a doubly linked list, ...

Double Linked List In a doubly linked list, also known as 2 way lists, each node is separated into 3 parts. The first part is called last pointer field. It has the address of t

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd