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Sparse Matrix

MCA, CS-04 2001 (June)
Q.1 (a). What is sparse matrix? Give example. [12]

Ans. Matrices with a relatively high proportion of zero entries are called sparse matrices. Two general types of n-square sparse matrices which will occur in various applications are pictured in Figure.

The first matrix, all entries above the main diagonal are zero or equivalent, where none-zero entries can only occur on or below the main diagonal is called a lower triangular matrix.

The second matrix, where non-zero entries can only occur on the diagonal or on elements immediately above or below the diagonal is called a tridiagonal matrix.

Fig: 1


Fig:2

One may save space by storing only those entries which may be non-zero.

In space array indices are permitted for a larger set, but those values actually added to the array consume memory. Thus the program can ask for Sparse Array [5] or Sparse Array [200], but the memory be allocated for only a small number of entries.

Example: Suppose we want to place in memory the triangular array B in first Figure. We store only those entries of B in linear array C as indicated by arrows i.e. C[1]=b₁₁, C[2]=b₂₁, C[3]=b₂₂, C[4]=b₄₁, ….

C will contain only 1+2+3+ …+ n = n(n+1)/2 elements, which is about half as many elements as a two-dimensional h x n array.

L is integer in terms of J and K, Where C[L]=b_jk, L represents the number of elements in the list upto and including b_jk. There are

1+2+3+…+(J-1)=J(J-1)/2 elements in rows above b_jk, K elements in row J upto and including b_jk. Accordingly, L = J(J-1)/2+K yields the index that accesses the value b_jk from linear array C.

Admission Open for January 2008 Session

IGNOU has initiated admissions for various Academic Programmes Including BCA and MCA for the session January 2008.

Students who are will to take admission in BCA/MCA or any other course, can obtained The Prospectus from all the regional Centres of IGNOU or from Registrar (SR&E), Maidan Garhi, New Delhi-110068, in person, on payment of Rs. 100/- in cash or through DD/IPO of Rs. 150/- drawn in favour of IGNOU payable at New Delhi/ at the city of the Regional Centre/ Partner Institution concerned. Application form can also be downloaded from the website at http://www.ignou.ac.in and submitted along with DD for Rs. 100/- in addition to the programme fee.

Submission of forms with fee at the concerned Regional Centre is 12th November 2007.

BCA Question Paper of 2006

We are updating our site "IGNOU BCA MCA". We are in process of adding few more question papers. We are starting with adding BCA question papers of year 2006. More question paper will be added in future.

We are also adding the IGNOU BCA questions in our BCA forum where you can post answers if you know and exchange your knowledge with others. We are requesting you all to share your knowledge and post what you know.

Kruskal Algorithm

CS62, December, 2001
Question 4(b): Write Kruskal's Algorithm.

Answer: Kruskal's Algorithm enables us to find a minimal spanning tree T of a connected weighted graph G where n vertices. (In which case T must have n-1 edge.

Steps of Kruskal's Algorithm: The input is a connected weighted graph G wigh n vertices.

Step 1: Arrange the edges of G in order of increasing weights.
Step 2: Starting only with vertices of G and processing sequentially, add each edge which does not result in a cycle until n-1 edges are added.
Step 3: Exit

The algorithm is easily executed when graph G is small.

Adding two integers-CS 62December-1999

Q.1.(a) Write a routine in C for adding two integers represented by doubly linked lists.
Answer: NODEPTR addint (NODPTR p, NODEPTR q)
{
/* check if integers are of like sign */
if(p->info * q ->info >0)
return (addsame(p,q));
/* check which has a larger absolute value */
if(compabs(p,q)>0)
return (addiff(p,q));
else
return (addiff(q,p));
}

Binary Search Tree [CS62 june 2001]

Queation: 1.(c) Define binary search tree. Write a function in C to creat a binary search tree.

Answer: A binary search has porperty that all elements in the left subtree of a node n are less than the contents of n and alll elements in the sight subtree of n are greater than or equal to the contents of n.
If a binary search tree is traversed in inorder (left, root, sight) and the contents of each node are printed as the node is visited, the numbers as the node is visited, the numbers are printed in ascending order.

q=null;
p=tree;
while(p!=null){
if (key ==k(p))
return(p);
q=p;
if(key < key(p))
p=left(p);
else
p=right(p);
}
v=maketree(rec,key);
if(q==null)
tree=v;
else
if(key < k(q))
left(q)=v;
else
right(q)=v;
return(v);

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