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PROGRAM-
BSc IT
SEMESTER-
FOURTH
SUBJECT
CODE & NAME- BT0080,
Fundamentals of Algorithms
CREDIT-4
BOOK
ID- B1092
MAX.
MARKS- 60
Q.1:
Define and explain recursion with the help of an example.
ANS:
This definition
suggests the following procedure/ algorithm for computing thefactorial of a
natural number n:
Q.2: Describe insertion
sort algorithm with the help of an example. Give the complexity of it.
ANS:
The insertion sort,
algorithm for sorting a list L of
n numbers represented byan
array A [1... n] proceeds by
picking up the numbers in the array from leftone by one and each newly picked
up number is placed at its relativeposition, w.r.t. the sorting order, among
the earlier ordered ones. Theprocess is repeated till
Q.3:
ANS:
Q.4:State the backtracking strategy. Also define explicit and
implicit constraints.
Ans:
In many applications
of the backtrack method, the desired solution is expressible as an ntuple (x1,……..,xn) where the xis
are chosen from some finite set isoften
the problem to be solved calls for finding one vector that maximizes a
criterion function p(x1,....xn).
Sometimes it seeks all vectors that
Q.5 Explain lower bound
theory and ordered searching.
ANS:
Lower Boundary Theory:
If f(n) is the time
for some algorithm, then we write f(n)= (g(n)) to mean that g(n) is a lower
bound for f(n). Formally, this equation can be written if there exist positive
constants C and no such that |f(n)| C|g (n)| for all n>no. In addition to
developing lower bounds to within a constant factor, we are also
Q.6:Explain
trees and subgraphs with examples.
ANS:
A tree is a connected
graph without any circuits. The graph in Fig.A, for instance, is a tree. Trees
with one, two, three and four vertices are shown in Fig.B. A graph must have at
least one vertex, and therefore
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