IGNOU MCA III 3rd Samester Solved Assignment 2013 2014
(MCS-031, MCS-032, MCS-033, MCS-034, MCS-035 ,MCSL-036)
MCA (3rd Semester) SOLVED ASSIGNMENT IGNOU MCA III 3rd Samester Solved Assignment 2013 2014 MCS-031 MCS-032 MCS-033 MCS-034 MCS-035
MCS SOLVED ASSIGNMENT SOLUTION QUESTION BY QUESTION
Course Code : MCS-031
Course Title : Design and Analysis of Algorithms
Assignment Number : MCA (3)/031/Assign/13
Question 1:
(a) Show, through appropriate examples or otherwise, that the
following three characteristics of an algorithm are independent
of each other: (i.e., a method may have one of these properties,
without having the other two)
(i) finiteness (ii) definiteness (iii) effectiveness
Need for studying algorithms: The study of algorithms is the cornerstone of computer
science.It can be recognized as the core of computer science. Computer programs would
not exist without algorithms. With computers becoming an essential part of our professional
& personal life’s, studying algorithms becomes a necessity, more so for computer
science engineers.
Another reason for studying algorithms is that if we know a standard set of important
algorithms ,They further our analytical skills & help us in developing new algorithms for
required applications
An algorithm is finite set of instructions that is followed, accomplishes a particular task. In
addition, all algorithms must satisfy the following criteria:
1. Input. Zero or more quantities are externally supplied.
2. Output. At least one quantity is produced.
3. Definiteness. Each instruction is clear and produced.
4. Finiteness. If we trace out the instruction of an algorithm, then for all cases, the algorithm
terminates after a finite number of steps.
5. Effectiveness. Every instruction must be very basic so that it can be carried out, in
principal, by a person using only pencil and paper. It is not enough
that each operation be definite as in criterion 3; it also must be feasible.
Question 2:
Let f (n) denote the nth term of a sequence of integers given (5 marks)
by the equation f(n) = f(n-1) +f(n-2) for n > 2 and f(1) = 1
and f(2) = 1, then using principle of mathematical induction, show
that √ 5 f( n ) = {(1+ √ 5) / 2} n -- {(1 -- √ 5) / 2}n for all n > = 1
(MCS-031, MCS-032, MCS-033, MCS-034, MCS-035 ,MCSL-036)
MCA (3rd Semester) SOLVED ASSIGNMENT IGNOU MCA III 3rd Samester Solved Assignment 2013 2014 MCS-031 MCS-032 MCS-033 MCS-034 MCS-035
MCS SOLVED ASSIGNMENT SOLUTION QUESTION BY QUESTION
Course Code : MCS-031
Course Title : Design and Analysis of Algorithms
Assignment Number : MCA (3)/031/Assign/13
Question 1:
(a) Show, through appropriate examples or otherwise, that the
following three characteristics of an algorithm are independent
of each other: (i.e., a method may have one of these properties,
without having the other two)
(i) finiteness (ii) definiteness (iii) effectiveness
Solution:
Need for studying algorithms: The study of algorithms is the cornerstone of computer
science.It can be recognized as the core of computer science. Computer programs would
not exist without algorithms. With computers becoming an essential part of our professional
& personal life’s, studying algorithms becomes a necessity, more so for computer
science engineers.
Another reason for studying algorithms is that if we know a standard set of important
algorithms ,They further our analytical skills & help us in developing new algorithms for
required applications
An algorithm is finite set of instructions that is followed, accomplishes a particular task. In
addition, all algorithms must satisfy the following criteria:
1. Input. Zero or more quantities are externally supplied.
2. Output. At least one quantity is produced.
3. Definiteness. Each instruction is clear and produced.
4. Finiteness. If we trace out the instruction of an algorithm, then for all cases, the algorithm
terminates after a finite number of steps.
5. Effectiveness. Every instruction must be very basic so that it can be carried out, in
principal, by a person using only pencil and paper. It is not enough
that each operation be definite as in criterion 3; it also must be feasible.
Question 2:
Let f (n) denote the nth term of a sequence of integers given (5 marks)
by the equation f(n) = f(n-1) +f(n-2) for n > 2 and f(1) = 1
and f(2) = 1, then using principle of mathematical induction, show
that √ 5 f( n ) = {(1+ √ 5) / 2} n -- {(1 -- √ 5) / 2}n for all n > = 1
Solution :
Hi,
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