Content: CS / CS41 / CS / CS / Design and Analysis of Algorithms May / June Question Paper CSE,I 4th Semester. CS Design and Analysis of Algorithms Anna university subject notes lecturer notes unit wise unit 1, unit 2 unit 3 unit 4 unit 5. Click The Below Link To. Anna University Syllabus For UG and PG Regulation CS DESIGN ANALYSIS OF ALGORITHMS question paper NOVEMBER.
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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 operation at a time. Accordingly, algorithms designed to be executed on such machines are called Sequential algorithms. What are Parallel Algorithms? 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? 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?
An algorithm design technique is a general approach to solving problems algorithmically that is applicable to a variety of problems from different areas of computing. A Pseudo code is a mixture of a natural language and programming language like constructs.
A pseudo code is usually more precise than a natural language, and its usage often yields more succinct algorithm descriptions. 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.
Optimality is about the complexity of the problem that algorithm solves. The sorting problem asks us to rearrange the items of a given list in ascending order or descending order The searching problem deals with f cs251 a given value, called a search key, in a given wyllabus. In this running time wi l l be the longest. In this running time wi ll be the smallest. It turns out that in some si tuations a single syllabud can be expensive ,but the total time for an entire sequence of n such operations is always signi f icantly ysllabus than the worst case ef ficiency of that single operation multipl ied 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 cw2251 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?
The notations O, W and Q and are used to indicate and compare the asymptotic orders of growth of functions expressing algorithm efficiencies. Describe briefly the notions of complexity of an algorithm.
Explain with an example. A[n-l] 4 What can we say about the average case efficiency of binary search?
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Since the binary tree definition itself divides a binary tree into two smaller structures of the same type, the left subtree and the right subtree, many problems about binary trees can be solved by applying the divide-conquer technique. 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 ccs2251 be feasible, locally optimal and irrevocable. All 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.
Can I complete the major?
Typically, these subproblems arise from a recurrence relating a solution to a given problem with solutions to its smaller 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 used to f ind the distances the lengths of the shortest paths from each vertex to all other vertices of a weighted connected graph.
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 ci ties and visit the remaining cities exactly once and come back to the city where he started his journey in such a manner that either the distance is minimum or cost is minimum. This is known as traveling salesman problem. In this case, the algorithm backtracks to replace the last component of the partially constructed solution with its next option 2 Explain State Space Tree If it is convenient to implement backtracking by constructing a tree of choices being made, the tree is called a state space tree.
Its root represents an initial state before the search for a solution begins. A Hamiltonian Circuit in the traveling salesman problem.
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The shortest Hamiltonian Circuit Syllabus most valuable subset of items that fit the knapsack 9 Mention two reasons to terminate a search path at the current node in a state-space tree of a branch and bound algorithm. Sylllabus node 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 vertices of a graph so that no two adjacent vertices are the same color.
Apply backtracking technique to solve the following instance of subset sum problem: Explain Graph coloring with example. Explain about Knapsack Problem using back tracking with example. 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. Going to the nearest unvisited city in the traveling salesman problem is a good illustration for Heuristic 10 Explain NP-Hard problems The notion of an NP-hard problem can be defined more formally by extending the notion of polynomial reducability to problems that are not necessary in class NP including optimization problems.
When the search necessarily involves the examination of every vertex in the object being searched it is called a traversal. Breadth first search Depth first search 13 What is articulation point.
A vertex v in a connected graph G is an articulation point if and only if the deletion of vertex v together with all edged incident to v disconnects the graph in to two or more nonempty components. Explain about biconnected components with example. You are commenting using your WordPress. You are commenting using your Twitter account. You are commenting using your Facebook account. Notify me of new comments via email. Create a free website or blog at Syllabu.
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