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DRIVE
SPRING
2017
PROGRAM
Master
of Science in Information Technology(MSc IT)
SEMESTER
2
SUBJECT
CODE & NAME
MIT208-
ANALYSIS AND DESIGN OF ALGORITHMS
Assignment
Set - 1
1 Differentiate algorithm,
pseudocode, and program. Write the properties of an algorithm.
Answer: An algorithm
is a finite set of unambiguous statement to solve a problem in finite amount of
time. It can be natural language expressions designed for any common man. Analysis
of algorithm means to study the specification of the algorithm and come to
conclusions about how the implementation of that algorithm
2 Explain the various types
of basic efficiency classes with suitable examples.
Answer: Even though the efficiency analysis
framework puts together all the functions whose orders of growth differ by a
constant multiple, there are still infinitely many such classes. (For example,
the exponential functions an have different orders of growth for different
values of base a.) Therefore, it may come as a surprise that the time
efficiencies of a large number of algorithms fall into only
3 Describe the procedure to
perform Mergesort using suitable example.
Answer: Merge sort is a sorting technique based
on divide and conquers technique. With worst-case time complexity being Ο(n log
n), it is one of the most respected algorithms. While comparing two sublists
for merging, the first element of both lists is taken into consideration. While
sorting in ascending order, the element
Assignment
Set - 2
1 What is AVL tree? Briefly
explain the four rotations in an AVL tree.
Answer: AVL tree is a self balanced binary
search tree. That means, an AVL tree is also a binary search tree but it is a
balanced tree. A binary tree is said to be balanced, if the difference between
the hieghts of left and right subtrees of every node in the tree is either -1,
0 or +1. In other words, a binary tree is said to be balanced if
2 Define Principle of
Optimality. Explain Knapsack problem with suitable example.
Answer: The principle of optimality states that
an optimal sequence of decisions has the property that whatever the initial
state and decision are, the remaining decisions must constitute an optimal
decision sequence with regard to the state resulting from the first decision.
Because of the use of the principle of
optimality, decision sequences containing subsequences that are suboptimal are
not
3 Discuss an approximation
Algorithms for NP – Hard problems.
Answer: Combinatorial optimization problems lie
within a finite but huge feasible region. In this section, we focus on finding
approximation algorithms for optimization problems that are NP-Hard.
Underlying principles
An NP-Hard problem is one for which the algorithm can be
translated to one that can solve any NP-problem (non-deterministic polynomial
time). Many optimization problems do not have an algorithm that can find a
solution for all instances. Sometimes, when trying to find an optimal solution
to some
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