Courtsey & Copyright: http://csetube.tk DESIGN AND ANALYSIS OF ALGORITHMS Courtsey & Copyright: http://csetube.tk

What is Empirical Analysis? It is performed by running a program implementing the algorithm on a sample of inputs and analyzing the data observed. This involves generating pseudorandom numbers. Define Convex-Hull Problem. A set of points (finite or infinite) on the plane is called convex if for any two points P and Q in the set, the entire line segment with the end points at P and Q belongs to the set What is Divide and Conquer Algorithm It is a general algorithm design technique that solved a problem’s instance by dividing it into several smaller instance, solving each of them recursively, and then combining their solutions to the original instance of the problem.

What are the Features of Algorithm Visualization. Consistent Interactive Very Clear and Concise Emphasize the visual component Define O-Notation. A function t(n) is said to be in O (g(n)), denoted t(n) Є O (g(n)), if t(n) is bounded above by some constant multiple of g(n) for all large n, ie ., if there exist some positive constant c and some nonnegative integer n0 such that t(n) <= cg(n) for all n >= n0 What is Algorithm Visualization? It is defined as the use of images to convey some useful information about algorithms.

Define Static Algorithm Visualization? Static Algorithm Visualization shows an algorithms progress through a series of still images. On other hand, Algorithm animation shows a continuous movie like presentation of an algorithm’s operation. What is Fibonacci Numbers? The Fibonacci numbers are an important sequence of integers in which every element is equal to the sum of its two immediate predecessors. There are several algorithms for computing the Fibonacci numbers with drastically different efficiency. What are the Classification of Algorithm Visualization? Static Algorithm Visualization Dynamic Algorithm Visualization

What is Brute Force? Brute Force is a straightforward approach to solving problem, usually directly based on the problem’s statement and definitions of the concepts involved. . What are the different criteria used to improve the effectiveness of algorithm? Input- Zero or more quantities are externally supplied Output-At least one quantity is produced Definiteness-Each instruction is clear and unambiguous Finiteness-If we trace out the instructions of an algorithm, then for all case the algorithm terminates after a finite number of steps Effectiveness-Every instruction must be very clear

What is recursive call? An algorithm is said to be recursive if the same algorithm invoked in the body. There are 2 types of algorithm. They are Direct Recursive Indirect Recursive What is meant by Direct Recursive call? An algorithm that calls itself is direct recursive call. Eg. int fun(int x) { if(x<=0) return x; return (fun(x-1)); }

14. Define indirect recursive call? Algorithm A is said to be indirect recursive if it calls another algorithm which in turn call A.

List the application areas of algorithm visualization? The 2 application are of algorithm visualization are Research and Education Give some example for animation systems. BALSA TANGO ZEUS Define Interpolation? Interpolation is approach, which deals with values with in the sample’s range. Define Extrapolation? Extrapolation is a approach, which deals with values of n, that are outside of the range of the samples values.

Define profiling? Profiling is an important resource in the empirical analysis of an algorithms running time. Measuring time spent on different segments of a program can pinpoint a bottleneck in the program’s performance that can be missed by an abstract deliberation about the algorithm’s basic operations. The process of getting such data is called profiling. What is meant by basic operations.? A basic operation is the operation that contributes most toward running time . Typically, it is the most time consuming operation in the algorithm’s innermost loop.

What is articulation point? A vertex of a connected graph G is said to be in articulation point, if its removal with all edges incident to it breaks the graph into disjoint pieces. List the advantages of binary search? Less time is consumed The processing speed is fast The number of iterations is less. It takes n/2 iterations. Binary search, which is used in Fibonacci Series, involves addition and subtraction rather than division It is priori analysis, since it can be analyzed before execution

the left and right subtrees of t are also binary search trees. 3. Define binary search Tree? A binary search tree t is a binary tree, either it is empty or each node in the tree contains an identifier and all identifiers in the left subtree of t are less than the identifier in the root node t. all identifier in the right subtree of t are greater than the identifier in the root node t. the left and right subtrees of t are also binary search trees. 4. Explain the principle used in quick sort? It is a partition method using the particular key the given table is partitioned into 2 sub tables so that first, the original key will be its proper position in the sorted sequence and secondly, all keys to the left of this key will be less in value and all keys to the right of it will be greater in values

What is binary search? The binary search algorithm is one of the most efficient searching techniques which requires the list to be sorted in ascending order. To search for an element in the list, the binary search algorithms split the list and locate the middle element of the list. First compare middle key K1, with given key K If K1=K then the element is found. What are the objectives of sorting algorithm? To rearrange the items of a given list To search an element in the list

The principle variations of transform and conquer techniques are 7. Why is bubble sort called by the name? The sorting problem is to compare adjacent elements of the list and exchange them if they are out of order. By doing it repeatedly, we end up bubbling up the largest element to the last position on the list. The next pass bubbles up the second largest element and so on until, after n-1 pass the list is sorted. What are the 3 variations in transform and conquer? The principle variations of transform and conquer techniques are Instance Simplification Representation Change Problem Reduction

Explain principle of Optimality? The principle of optimality says that an optimal solution to any instance of an optimization problem is composed of optimal solution to its sub instances. What is need for finding minimum spanning tree? Spanning tree has many applications. Any connected graph with n vertices mush have at least n-1 edges and all connected graphs with n-1 edges are trees If the nodes of G represent cities and edges represent possible communication links connecting 2 cities, then the minimum number of links needed to connect the n cities is n-1. Therefore, it is necessary for finding minimum spanning tree.

A path of longest length is called critical path. For example, tree What is critical path? A path of longest length is called critical path. For example, tree What is spanning tree? Let G= {V, E} be an undirected connected graph. A sub graph t={V,E} of G is a spanning tree of G, if t is a tree. What is Dynamic programming? Dynamic programming is an algorithm design technique for solving problem with overlapping subprograms. The smaller subprograms are solved only once and recording the results in a table from which the solution to the original problem is obtained.

What is greedy method? The greedy method is the most straight forward design, which is applied for change making problem. The greedy technique suggests constructing a solution to an optimization problem through a sequence of steps, each expanding a partially constructed solution obtained so far, until a complete solution to the problem is reached. On each step, the choice made must be feasible, locally optimal and irrevocable. List the advantage of greedy algorithm Greedy algorithm produces a feasible solution Greedy method is very simple to solve a problem Greedy method provides an optimal solution directly.

Define the term control abstraction? Control abstraction is a procedure whose flow of control is clear but whose primary operations are specified by other procedures whose precise meanings are left undefined. List the applications of minimum spanning tree? Spanning tree are used to obtain an independent set of circuit equations for an electric network. Another application of spanning tree arises from the property that a spanning tree is a minimal sub graph G’ of G such that V(G’)=V(G) and G’ is connected

Define AVL Tree An AVL Tree is a binary search tree in which the balance factor of every node, which the balance factor of every node, which is defined as the difference between the heights of the node’s left and right sub trees is either 0 or +1 or -1 What do you mean by row major and column major? In a given matrix, the maximum elements in a particular row is called row major. In a given matrix, the maximum elements in a particular column is called column major.

20. What is Minimum Cost Spanning Tree? A minimum cost spanning tree of a weighted connected graph is its spanning tree of the smallest weight, where the weight of the tree is defined as the sum of the weights on all its edges.

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