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PROGRAM
BSc
IT
SEMESTER
FOURTH
SUBJECT
CODE & NAME
BT0080,
Fundamentals of Algorithms
Qus:1
Describe insertion sort algorithm with the help of an example. Give the
complexity of it.
Answer:
Insertion
sort algorithm:
The insertion sort,
algorithm for sorting a list L of n numbers represented by an array A [1... n]
proceeds by picking up the numbers in the array from left one by one and each
newly picked up number is placed at its
Qus:2
State the concept of divide and conquer strategy with the help of an example.
Answer:
The
concept of divide and conquer strategy:
Given a function to
compute on n inputs, the divide-and-conquer strategy suggests splitting the
inputs into K distinct subsets, 1
Ques
3 Prove the theorem
“A
given connected graph G is a Euler graph all the vertices of G are of even
degree.”
Ans:
Proof: Suppose G is a Euler graph. Then G contains a Euler
line. So, there exists a closed walk running through all the edges of G exactly
once. Let vV be a vertex of G. Now, in tracing the walk, it goes
Ques
4 Explain Adjacency and Incidence Matrix.
Ans:
Definition: Let G be a graph with n vertices v1,
v2, …, vn and no self-loopsand no parallel edges. We define an n n adjacency
matrix A = [ ij a ]n n, as follows:
aij = 1 if vi is
Q5.
State Cook’s theorem.
Prove
the theorem “CNF satisfiability is polynomially transformable to the clique
problem. Therefore, the clique problem is NP complete.”
Answer:
Proof:
Cook’s Theorem
Cook’s theorem
states that satisfiability is in P if and only if P=NP. We now prove this
important theorem. We know that satisfiability in NP. Hence, if P = NP, then
satisfiability is in P. It remains to be shown that if satisfiability is in P,
then P = NP. To do this, we show how to obtain from any
Ques
6 Mention different classification of problems.
Ans:
The
fact of being engaged in solving problems may be the only sure indication of a
living entity being alive (though, the distinction between entities being alive
and not being alive is getting fuzzier day by day). The problems, attempted to
be solved, may be due to the need for survival in a
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