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Biju Patnaik University of Technology BPUT
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CS 6402
DESIGN AND ANALYSIS OF
ALGORITHMS
QUESTION BANK
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UNIT I
INTRODUCTION
Fundamentals of algorithmic problem solving – Important problem types – Fundamentals of the analysis
of algorithm efficiency – analysis frame work –Asymptotic notations – Mathematical analysis for
recursive and non-recursive algorithms.
2 marks
1. Why is the need of studying algorithms?
From a practical standpoint, a standard set of algorithms from different areas of computing must be known,
in addition to be able to design them and analyze their efficiencies. From a theoretical standpoint the study
of algorithms is the cornerstone of computer science.
2. What is algorithmic?
The study of algorithms is called algorithmic. It is more than a branch of computer science. It is the core of
computer science and is said to be relevant to most of science, business and technology.
3. What is an algorithm?
An algorithm is a sequence of unambiguous instructions for solving a problem, i.e., for obtaining a required
output for any legitimate input in finite amount of time.
An algorithm is step by step procedure to solve a problem.
4. Give the diagram representation of Notion of algorithm.
5. What is the formula used in Euclid’s algorithm for finding the greatest common divisor of two
numbers?
Euclid‘s algorithm is based on repeatedly applying the equality
Gcd(m,n)=gcd(n,m mod n) until m mod n is equal to 0, since gcd(m,0)=m.
6. What are the three different algorithms used to find the gcd of two numbers?
The three algorithms used to find the gcd of two numbers are
Euclid‘s algorithm
Consecutive integer checking algorithm
Middle school procedure
7. What are the fundamental steps involved in algorithmic problem solving?
The fundamental steps are
Understanding the problem
Ascertain the capabilities of computational device
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Choose between exact and approximate problem solving
Decide on appropriate data structures
Algorithm design techniques
Methods for specifying the algorithm
Proving an algorithms correctness
Analyzing an algorithm
Coding an algorithm
8. What is an algorithm design technique?
An algorithm design technique is a general approach to solving problems algorithmically that is applicable
to a variety of problems from different areas of computing.
9. What is pseudocode?
A pseudocode is a mixture of a natural language and programming language constructs to specify an
algorithm. A pseudocode is more precisethan a natural language and its usage often yields more concise
algorithm descriptions.
10. What are the types of algorithm efficiencies?
The two types of algorithm efficiencies are
Time efficiency: indicates how fast the algorithm runs
Space efficiency: indicates how much extra memory the algorithm needs
11. Mention some of the important problem types?
Some of the important problem types are as follows
Sorting
Searching
String processing
Graph problems
Combinatorial problems
Geometric problems
Numerical problems
12. What are the classical geometric problems?
The two classic geometric problems are
The closest pair problem: given n points in a plane find the closest pair among them
The convex hull problem: find the smallest convex polygon that would include all the points of a
given set.
13. What are the steps involved in the analysis framework?
The various steps are as follows
Measuring the input‘s size
Units for measuring running time
Orders of growth
Worst case, best case and average case efficiencies
14. What is the basic operation of an algorithm and how is it identified?
The most important operation of the algorithm is called the basic operation of the algorithm, the
operation that contributes the most to the total running time.
It can be identified easily because it is usually the most time consuming operation in the algorithms
innermost loop.
15. What is the running time of a program implementing the algorithm?
The running time T(n) is given by the following formula
T(n) ≈copC(n)
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cop is the time of execution of an algorithm‘s basic operation on a particular computer and
C(n) is the number of times this operation needs to be executed for the particular algorithm.
16. What are exponential growth functions?
The functions 2n and n! are exponential growth functions, because these two functions grow so fast that
their values become astronomically large even for rather smaller values of n.
17. What is worst-case efficiency?
The worst-case efficiency of an algorithm is its efficiency for the worst-case input of size n, which is an
input or inputs of size n for which the algorithm runs the longest among all possible inputs of that size.
18. What is best-case efficiency?
The best-case efficiency of an algorithm is its efficiency for the best-case input of size n, which is an input
or inputs for which the algorithm runs the fastest among all possible inputs of that size.
19. What is average case efficiency?
The average case efficiency of an algorithm is its efficiency for an average case input of size n. It provides
information about an algorithm behavior on a ―typical‖ or ―random‖ input.
20. What is amortized efficiency?
In some situations a single operation can be expensive, but the total time for the entire sequence of n such
operations is always significantly better that the worst case efficiency of that single operation multiplied by
n. this is called amortized efficiency.
21. Define O-notation?
A function t(n) is said to be in O(g(n)), denoted by t(n) ε O(g(n)), if t(n) is bounded above by some constant
multiple of g(n) for all large n, i.e., if there exists some positive constant c and some non-negative integer n0
such that
T (n) <=cg (n) for all n >= n0
22. Define Ω-notation?
A function t(n) is said to be in Ω (g(n)), denoted by t(n) ε Ω (g(n)), if t(n) is bounded below by some
constant multiple of g(n) for all large n, i.e., if there exists some positive constant c and some non-negative
integer n0 such that
T (n) >=cg (n) for all n >=n0
23. Define θ-notation?
A function t(n) is said to be in θ (g(n)), denoted by t(n) ε θ (g(n)), if t(n) is bounded both above & below by
some constant multiple of g(n) for all large n, i.e., if there exists some positive constants c1 & c2 and some
nonnegative integer n0 such that
c2g (n) <= t (n) <= c1g (n) for all n >= n0
24. Mention the useful property, which can be applied to the asymptotic notations and its use?
If t1(n) ε O(g1(n)) and t2(n) ε O(g2(n)) then t1(n)+t2(n) ε max {g1(n),g2(n)} this property is also true for Ω
and θ notations. This property will be useful in analyzing algorithms that comprise of two consecutive
executable parts.
25. What are the basic asymptotic efficiency classes?
The various basic efficiency classes are
Constant : 1
Logarithmic : log n
Linear : n
N-log-n : nlog n
Quadratic : n2
Cubic : n3
Exponential : 2n
Factorial : n!
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