MCA4040- ANALYSIS AND DESIGN OF ALGORITHM

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ASSIGNMENT

PROGRAM	MCA(REVISED FALL 2012)
SEMESTER	FOURTH
SUBJECT CODE & NAME	MCA4040- ANALYSIS AND DESIGN OF ALGORITHM
CREDIT	4
BK ID	B1480
MARKS	60

Answer all questions

Q1 . List and explain the properties of Algorithms.

Answer: Data structure  - Define an algorithm. What are the properties of an algorithm? - Feb 27, 2010, 11:15 am by Rajmeet Ghai

Define an algorithm. What are the properties of an algorithm? What are the types of algorithms?

An algorithm is a series of steps or methodology to solve a problem.

Properties of an algorithm:-

It is written in simple English. 

Q2. Write a note on sequential search.

Answer: When data items are stored in a collection such as a list, we say that they have a linear or sequential relationship. Each data item is stored in a position relative to the others. In Python lists, these relative positions are the index values of the individual items. Since these index values are ordered, it is possible for us to visit them in sequence. This process gives rise to our first searching technique, the sequential search.

Q3. Explain topological sort with an example.

Answer: In computer science, a topological sort (sometimes abbreviated topsort or toposort) or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering. For instance, the vertices of the graph may represent tasks to be performed, and the edges may represent constraints that one task must be performed before another; in this application, a topological ordering is just a valid sequence for the tasks. A topological ordering is possible if and only if the graph has no directed cycles, that is, if it is a directed acyclic graph (DAG). Any DAG has at least one topological ordering, and algorithms are known for constructing a

Q. 4. Explain good-suffix and bad-character shift in Boyer-Moore algorithm.

Answer: In computer science, the Boyer–Moore string search algorithm is an efficient string searching algorithm that is the standard benchmark for practical string search literature. It was developed by Robert S. Boyer and J Strother Moore in 1977. The algorithm preprocesses the string being searched for (the pattern), but not the string being searched in (the text). It is thus well-suited for applications in which the pattern is much shorter than the text or where it persists across multiple searches. The Boyer-Moore algorithm uses information gathered during the preprocess step to skip sections of the text, resulting in a

Q. 5. Solve the Knapsack problem using memory functions.

Item 1 2 3 4

Weight 2 6 4 8

Value (in Rs.) 12 16 30 40

Knapsack capacity is given as W=12. Analyze the Knapsack problem using memory functions with the help of the values given above.

Answer:The classical Knapsack Problem (KP) can be described as follows. We are given a set N={1,…,n} of items, each of them with positive profit pj and positive weight wj, and a knapsack capacity c. The problem asks for a subset of items whose total weight does not exceed the knapsack capacity, and whose profit is a maximum. It can be formulated as the following Integer Linear Program (ILP):

(KP)max∑j∈Npjxj(1)

∑j∈Nwjxj≤c(2)

xj∈{0,1},j∈N.(3)

Each variable xj takes value 1 if and only if item j is

Q. 6. Describe Variable Length Encoding and Huffman Encoding.

Answer:Variable Length Encoding:In coding theory a variable-length code is a code which maps source symbols to a variable number of bits.Variable-length codes can allow sources to be compressed and decompressed with zero error (lossless data compression) and still be read back symbol by symbol. With the right coding strategy an independent and identically-distributed source may be compressed almost arbitrarily close to its entropy. This is in contrast to fixed length coding methods, for which data compression is only possible for large blocks of data, and any compression beyond the logarithm of the total number of possibilities comes with a finite (though perhaps arbitrarily small) probability of failure.Some examples of well-known variable-length coding strategies are Huffman coding, Lempel–Ziv coding and

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