CS2251 DESIGN AND ANALYSIS OF ALGORITHMS NOTES PDF

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Sumathi Kanna www. What is an Algorithm? An algorithm is a sequence of unambiguous instructions for solving a problem, i. What are Sequential Algorithms? The central assumption of the RAM model is that instructions are executed one after another, one w operation at a time.

Accordingly, algorithms designed to be executed on such machines are called Sequential algorithms. What are Parallel Algorithms? What is Exact and Approximation algorithm? The principal decision to choose solving the problem exactly is called exact algorithm. The principal decision to choose solving the problem approximately is called Approximation algorithm.

What is Algorithm Design Technique? Define Pseudo code. A pseudo code is usually more precise than a natural language, and its usage often yields more succinct algorithm descriptions. Define Flowchart. What is Efficiency of algorithm?

Efficiency of an algorithm can be precisely defined and investigated with mathematical rigor. There are two kinds of algorithm efficiency i. Time Efficiency — Indicates how fast the algorithm runs ii.

Space Efficiency — Indicates how much extra memory the algorithm needs. What is generality of an algorithm? It is a desirable characteristic of an algorithm. Generality of the problem the algorithm solves is sometimes easier to design an algorithm for a problem posed in more general terms. The sorting problem asks us to rearrange the items of a given list in ascending order or descending order w w Ex: if you want to sort a list of numbers in ascending order when the numbers are given i n descending order.

In this running time will be the longest. Ex: if you want to sort a list of numbers in ascending order when the numbers are given i n ascending order. In this running time will be the smallest. It turns out that in some situations a single operation can be expensive ,but the total time for an entire sequence of n such operations is always significantly better than the worst case c efficiency of that single operation multiplied by n.

What is called the basic operation of an algorithm? The most important operation of the algorithm is the operation contributing the most to the total running time is called basic operation of an algorithm. Define order of growth. To compare and rank such orders of growth we use three notations i. O Big oh notation ii. What is the use of Asymptotic Notations?

PART - B 1. Describe briefly the notions of complexity of an algorithm. Explain with an example. It sorts a given array A[ A[n-l] 4 What can we say about the average case efficiency of binary search? A binary tree T is defined as a finite set of nodes that is either empty or consists of s root and two di disjoint binary trees TL, and TR called, respectively the left and right subtree of the root.

The extra nodes shown by little squares are called external. The original nodes shown by littile circles are called internal. On each step, the choice made must be feasible, locally optimal and irrevocable.

All w the principal properties of heaps remain valid for min-heaps, with some obvious modifications. It works by attaching to a previously constructed subtree a vertex to the vertices already in the tree. Explain with example. Typically, these subproblems arise from a recurrence relating a solution to a given problem with solutions to its smaller w subproblems of the same type.

Rather than solving overlapping subproblems again and again, dynamic programming suggests solving each of the smaller sub problems only once and recording the results in a table from which we can then obtain a solution to the original problem. It is convenient to record the lengths of shortest paths in an n by n matrix D called the distance di matrix: the element dij in the ith row and the jth column of this matrix indicates the length of the shortest path from the ith vertex to the jth vertex.

It is used to find the distances the lengths of the shortest paths from each vertex to. If probabilities of searching for elements of a set are known, it is natural to pose a question about an optimal binary search tree for which the average number of comparisons in a search is the smallest possible.

It does this by solving, in the top-down fashion but only once, just necessary sub problems of a given problem and recording their solutions in a table. A salesman has to travel n cities starting from any one of the cities and visit the remaining cities exactly once and come back to the city where he started his journey in such om a manner that either the distance is minimum or cost is minimum. This is known as traveling salesman problem.

Its root represents an initial state before the search for a solution begins. Ex: A Hamiltonian Circuit in the traveling salesman problem. The node in represents no feasible solutions because the constraints of the problem are already violated. The graph coloring problem asks us to assign the smallest number of colors to w vertices of a graph so that no two adjacent vertices are the same color.

Part - B 1. Apply backtracking technique to solve the following instance of subset sum problem : CS - Design and Analysis of Algorithms Question Bank Page 12 of 14 www.

Explain Graph coloring with example. Explain about Knapsack Problem using back tracking with example. UNIT V Part - A 1 Define tractable and intractable problems Problems that can be solved in polynomial time are called tractable problems, problems that cannot om be solved in polynomial time are called intractable problems.

This class of problems is called polynomial. Such problems are called Undecidable. Most decision problems are in NP. First of all, this class includes all the problems in P. This class of problems is called Nondeterministic polynomial. Heuristic di 10 Explain NP-Hard problems The notion of an NP-hard problem can be defined more formally by extending the notion of polynomial in reducability to problems that are not necessary in class NP including optimization problems.

When the search necessarilyinvolves the examination of every vertex in the object being searched it. Explain about biconnected components with example.

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No, take me back! R Data Hiding using Multiple frames for secure tranmission Mrs. Design and Analysis of Algorithms. A[n-l] 4 What can we say about the average case efficiency of algorithma search? The central assumption of the RAM model does not hold for some newer computers that can execute operations concurrently, i. What is Exact and Approximation algorithm?

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Kazilkree What is the use of Asymptotic Notations? You can also share your own study materials and it can cs published in this website after verification and reviewing. To excel in Computer Desing and Engineering programme to pursue their higher studies or to succeed in their profession through quality education. Question paper is give Lab Manual I Sem.

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