Algorithmic problem solving

Nov 22, 201810 likes8,056 views

This document discusses the process of algorithm design and analysis. It outlines 9 key techniques for solving problems algorithmically: 1) Understanding the problem, 2) Ascertaining computational capabilities, 3) Determining exact or approximate solutions, 4) Choosing appropriate data structures, 5) Using algorithm design techniques, 6) Specifying the algorithm, 7) Proving correctness, 8) Analyzing efficiency, and 9) Coding the algorithm. These techniques provide a systematic approach to developing procedural solutions to problems through specific instructions to obtain answers.

V.M.Prabhakaran,
Department of CSE,
KIT- Coimbatore
Problem Solving and Python Programming 1

Definition
• Algorithms are procedural solutions to
problems.
• These solutions are not answers but specific
instructions for getting answers.
Problem Solving and Python Programming 2

Techniques are,
• Understanding the problem
• Ascertain the capabilities of the computational
device
• Exact/approximate solution
• Decide on the appropriate data structure
• Algorithm design technique
• Methods of specifying an algorithm
• Proving an algorithm correctness
• Analyzing an algorithm
• Coding an algorithm
Problem Solving and Python Programming 3

Algorithm design and Analysis process
Problem Solving and Python Programming 4

1.Understanding the problem
• The Problem given should be understood
properly.
• Creating an algorithm is an art which may
never be fully automated.
• An input to an algorithm specifies an instance
of the problem the algorithm solves.
• Correct algorithm should work for all
possible inputs.
Problem Solving and Python Programming 5

2. Ascertain the capabilities of the
computational device
• The second step is to ascertain the capabilities
of a machine.
• This can be done by knowing the type of the
architecture, speed and memory
availability.
• Computational device of the algorithm is
intended for sequential algorithms and
parallel algorithms.
Problem Solving and Python Programming 6

3. Exact/approximate solution
• Once algorithm is devised, it is necessary to
show that it compute answer for all the
possible inputs.
• The solution is stated in two forms:
• Solving the problem exactly is called an Exact solution
• Solving it approximately is called approximate
solution.
• Examples: Finding a square root of number
Problem Solving and Python Programming 7

4. Decide on the appropriate data
structure
• Data structures remain important for both
design and analysis of algorithms.
• Data structures can be defined as a particular
scheme of organizing related data items.
• Some of the elementary data structures are
arrays, lists, set.
• Algorithm + Data Structure= Programs
Problem Solving and Python Programming 8

5. Algorithm design technique
• General approach to solving problem
algorithmically that is applicable to a variety of
problems from different areas of computing.
• Some important design techniques are,
– Brute force
– Greedy method
– Divide and conquer
– Dynamic programming
– Backtracking
– Linear programming
Problem Solving and Python Programming 9

6. Methods of specifying an algorithm
• There are mainly two options for specifying an
algorithm,
– Use of natural language
– Pseudo code and Flowcharts
Problem Solving and Python Programming 10

7. Proving an algorithm
correctness
• Correctness has to be proved for every algorithm.
• To prove that the algorithm yields a required
result for every legitimate input in a finite
amount of time.
• A proof of correctness requires that the solution to
be stated in two forms : Assertions that deals
about input and output variables of the program
and Specifications that is expressed in predicate
calculus.
Problem Solving and Python Programming 11

8. Analyzing an algorithm
• There are two kinds of algorithm efficiency:
time and space efficiency.
• Time Efficiency : Indicates how fast the
algorithm runs.
• Space Efficiency : Indicates how much extra
memory the algorithm needs.
• Simpler algorithms are easier to understand
and program, the resulting programs will be
easier to debug.
Problem Solving and Python Programming 12

9. Coding an algorithm
• Program the algorithm by using programming
language.
• Formally verification is done through small
programs.
• Validity is done through testing and
debugging.
• A good algorithm is a result of repeated effort
and work.
Problem Solving and Python Programming 13

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Algorithmic problem solving

1. V.M.Prabhakaran, Department of CSE, KIT- Coimbatore Problem Solving and Python Programming 1

2. Definition • Algorithms are procedural solutions to problems. • These solutions are not answers but specific instructions for getting answers. Problem Solving and Python Programming 2

3. Techniques are, • Understanding the problem • Ascertain the capabilities of the computational device • Exact/approximate solution • Decide on the appropriate data structure • Algorithm design technique • Methods of specifying an algorithm • Proving an algorithm correctness • Analyzing an algorithm • Coding an algorithm Problem Solving and Python Programming 3

4. Algorithm design and Analysis process Problem Solving and Python Programming 4

5. 1.Understanding the problem • The Problem given should be understood properly. • Creating an algorithm is an art which may never be fully automated. • An input to an algorithm specifies an instance of the problem the algorithm solves. • Correct algorithm should work for all possible inputs. Problem Solving and Python Programming 5

6. 2. Ascertain the capabilities of the computational device • The second step is to ascertain the capabilities of a machine. • This can be done by knowing the type of the architecture, speed and memory availability. • Computational device of the algorithm is intended for sequential algorithms and parallel algorithms. Problem Solving and Python Programming 6

7. 3. Exact/approximate solution • Once algorithm is devised, it is necessary to show that it compute answer for all the possible inputs. • The solution is stated in two forms: • Solving the problem exactly is called an Exact solution • Solving it approximately is called approximate solution. • Examples: Finding a square root of number Problem Solving and Python Programming 7

8. 4. Decide on the appropriate data structure • Data structures remain important for both design and analysis of algorithms. • Data structures can be defined as a particular scheme of organizing related data items. • Some of the elementary data structures are arrays, lists, set. • Algorithm + Data Structure= Programs Problem Solving and Python Programming 8

9. 5. Algorithm design technique • General approach to solving problem algorithmically that is applicable to a variety of problems from different areas of computing. • Some important design techniques are, – Brute force – Greedy method – Divide and conquer – Dynamic programming – Backtracking – Linear programming Problem Solving and Python Programming 9

10. 6. Methods of specifying an algorithm • There are mainly two options for specifying an algorithm, – Use of natural language – Pseudo code and Flowcharts Problem Solving and Python Programming 10

11. 7. Proving an algorithm correctness • Correctness has to be proved for every algorithm. • To prove that the algorithm yields a required result for every legitimate input in a finite amount of time. • A proof of correctness requires that the solution to be stated in two forms : Assertions that deals about input and output variables of the program and Specifications that is expressed in predicate calculus. Problem Solving and Python Programming 11

12. 8. Analyzing an algorithm • There are two kinds of algorithm efficiency: time and space efficiency. • Time Efficiency : Indicates how fast the algorithm runs. • Space Efficiency : Indicates how much extra memory the algorithm needs. • Simpler algorithms are easier to understand and program, the resulting programs will be easier to debug. Problem Solving and Python Programming 12

13. 9. Coding an algorithm • Program the algorithm by using programming language. • Formally verification is done through small programs. • Validity is done through testing and debugging. • A good algorithm is a result of repeated effort and work. Problem Solving and Python Programming 13

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