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PROGRAM - BSc IT
SEMESTER - FOURTH
SUBJECT CODE &
NAME - BT0080, Fundamentals of Algorithms
CREDIT - 4
BK ID - B1092
MAX. MARKS – 60
Q1. Explain
recursion with the help of an example. 10
Ans: Recursion: Next, we consider another
important control structure namely recursion. In order to facilitate the
discussion, we recall from Mathematics, one of the ways in which the
factorial of a natural number n is defined.
factorial (1) = 1
Q2. Describe binary search
algorithm with the help of an example. 10
Ans: Binary Search: Let ai, 1 < i < n be a list of elements that are sorted
in non-decreasing order. Consider
the problem of determining whether a given element x is present in the list. If x is present we
are to determine
Q3. Describe the
branch and bound algorithms for travelling salesman problem. 10
Ans:
Travelling Salesman Problem: An O(n22n) dynamic programming
algorithm for the travelling sales person was arrived at in Unit 5. We
now investigate branch-and-bound algorithms for this problem. Although
the worst-case
Q4. Explain trees
and subgraphs with
examples. 5+5 = 10
Ans:
Trees: A tree is
called a binary tree, if it is either empty, or it consists of a node called
the root together with two binary trees called the left subtree and a right
subtree. Now , we make the following observations.
1. It may be noted that the above
definition is a recursive definition, in the sense that definition of binary
tree is given in its own terms (i.e. binary tree).
2. The following are all distinct
and the only binary trees are having two nodes. The following are all distinct
and only binary
Q5. Define spanning
trees. Explain Kruskal’s algorithm to find out minimal cost spanning trees. 10
Ans:
Spanning Trees:
Definition: A tree T is said to be a spanning
tree of a connected graph G if T is a subgraph of G and
T contains all the vertices of G.
i)
Spanning
trees are the largest (with the maximum number of edges) trees among all trees
in G. Spanning tree is also called a
Q6. Define and
explain Hamiltonian circuit and path. 10
Ans:
Hamiltonian Circuit and Path: A Euler line of a connected graph
was characterized by the property of being a closed walk that traverses
every edge of the graph (exactly once).
Hamiltonian Circuit: A Hamiltonian circuit in a
connected graph is defined as a closed walk that traverses
Get fully solved assignment. Buy online from website
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