BT0080,Fundamental of Algorithms

Dear students get fully solved assignments

Send your semester & Specialization name to our mail id :

“ help.mbaassignments@gmail.com ”

or

Call us at : 08263069601

(Prefer mailing. Call in emergency )

ASSIGNMENT

PROGRAM	BSc IT
SEMESTER	FOURTH
SUBJECT CODE & NAME	BT0080,Fundamental of Algorithms
CREDIT	4
BK ID	B1092
MAX. MARKS	60

Q.1 Define and explain recursion with the help of an example.

Answer: - A recursive definition of a function defines values of the functions for some inputs in terms of the values of the same function for other inputs. For example, the factorial function n!.

Recursion has also been described more simply as the ability to place one component inside another component of the same kind. A function that calls itself is known as recursive function and this technique is known as recursion in C programming.

A linguistic element or grammatical structure that can be used repeatedly in sequence is said to be recursive.

Q.2 State the concept of divide and conquer strategy with the help of an example.

Answer: - Divide and conquer (D&C) is an algorithm design paradigm based on multi-branched recursion. A divide and conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same (or related) type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem.

This technique is the basis of efficient algorithms for all kinds of problems, such as sorting (e.g., quicksort, merge sort), multiplying large numbers (e.g. Karatsuba), syntactic analysis (e.g., top-down parsers), and computing the discrete Fourier

Q.3 Explain knapsack problem. Write algorithm for it.

Answer: - The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a mass and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.

The problem often arises in resource allocation where there are financial constraints and is studied in fields such as combinatorics, computer science, complexity theory, cryptography and applied mathematics.

Q.4 Explain trees and sub graphs with examples.

Answer:-Tree: - A tree is a connected graph without any cycles, or a tree is a connected acyclic graph. The edges of a tree are called branches. It follows immediately from the definition that a tree has to be a simple graph (because self-loops and parallel edges both form cycles). Figure 4.1(a) displays all treewith fewer than six vertices.

An AVL tree is another balanced binary search

Q.5 Define and explain Hamiltonian circuit and path.

Answer: - A graph that contains a Hamiltonian cycle is called a Hamiltonian graph. Similar notions may be defined for directed graphs, where each edge (arc) of a path or cycle can only be traced in a single direction (i.e., the vertices are connected with arrows and the edges traced "tail-to-head").

Hamiltonian path: - a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a Hamiltonian path that is a cycle. Determining whether such paths and cycles exist in graphs is the Hamiltonian path problem, which is NP-complete.

Q.6 (1) Show that the Clique problem is an NP-Complete problem.

Answer: - Clique Problem is an NP-Complete problem: - The clique problem refers to any of the problems related to finding particular complete sub graphs ("cliques") in a graph, i.e., sets of elements where each pair of elements is connected.

For example, the maximum clique problem arises in the following real-world setting. Consider a social network, where the graph’s vertices represent people, and the graph’s edges represent mutual acquaintance. To find a largest subset of people who all know each other, one can systematically inspect all subsets, a process that is too time-consuming to be practical for social networks comprising more than a few dozen people. Although this brute-

2. Show that the Vertex cover problem is NP-Complete.

Answer:-Vertex cover problem is an NP-Complete:- a vertex cover (sometimes node cover) of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set. The problem of finding a minimum vertex cover is a classical optimization problem in computer science and is a typical example of an NP-hard optimization problem that has an approximation algorithm. Its decision version, the vertex cover problem, was one of Karp's 21 NP-complete problems and is therefore a classical NP-complete problem in computational complexity theory. Furthermore, the vertex cover problem is fixed-parameter tractable and a central problem in

Dear students get fully solved assignments

Send your semester & Specialization name to our mail id :

“ help.mbaassignments@gmail.com ”

or

Call us at : 08263069601

(Prefer mailing. Call in emergency )