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MCS-31 – Block – 1 Introduction To Algorithmics

Unit-1 Elementary Algorithmics

ByKirit A. D.

(MBA, PMP, ITIL, MCTS, Six Sigma Black Belt)

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Content

• Example of an algorithm• Problems and Instances• Characteristics of an algorithm• Problems, Available tools & Algorithms• Building Blocks of Algorithms• Outline of Algorithmics

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Example of An Algorithm

• Variable = Expression• Find GCD• Euclid’s Algorithm for Finding GCD of Two

Natural Numbers m & n

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Problems And InstancesEl

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Where a, b, c may be any real numbers except the restriction that a ≠ 0

Now, if we take a = 3, b = 4 and c = 1

X = -1/3 or -1

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Characteristics Of An Algorithm

• Finiteness• Definiteness• Inputs• Output• Effectiveness

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Problems, Available Tools & Algorithms

• Multiplication 150 x 12• Standard• Counting 150 twelve times• ‘la russe method’

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Building Blocks of Algorithms

• Variable expression• Direct sequencing ie. Writing of the

instructions, one after the other on successive lines, or even on the some line if there is enough space on a line and separated by some statement separator, by semi-colons and in the order of intended execution

• Procedure and RecursionElem

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Outline of Algorithmics

• The problem, which has at least one algorithmic solution, is called algorithmic or computable problem.• Divide and conquer• Dynamic programming• The greedy approach• Backtracking• Branch and bound• Searches and traversalsEl

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Outline of Algorithmics

• Some of the problem types, enumerated below• Sorting problems• Searching problems• Linear programming problems• Number-theory problems• String processing problems• Graph problems• Geometric problems• Numerical problems

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Outline of Algorithmics

• Understanding the Problem• Analyzing the problem• Capabilities of the computer system• Approximate v/s exact solution• Choice of appropriate data structures• Choice of appropriate design technology• Specification methods for algorithms• Proving correctness of an algorithm• Analyzing and algorithm• Coding he algorithm

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THANK YOU