BT0080 - Fundamental of Algorithms

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ASSIGNMENT

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

1. Describe insertion sort algorithm with the help of an example.

Answer: It is a simple Sorting algorithm which sorts the array by shifting elements one by one. Following are some of the important characteristics of Insertion Sort.

1.       It has one of the simplest implementation

2.       It is efficient for smaller data sets, but very inefficient for larger lists.

3.       Insertion Sort is adaptive, that means it

4.        

5.        

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

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 the

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 tree.

Q5. Define spanning trees.  Explain Kruskal’s algorithm to find out minimal cost spanning trees.

Answer: In the mathematical field of graph theory, a spanning tree T of an undirected graph G is a subgraph that includes all of the vertices of G that is a tree. In general, a graph may have several spanning trees, but a graph that is not connected will not contain a spanning tree (but see Spanning forests below). If all of the edges of G are also edges of a

Q.6 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

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