Algorithmic problem solving

1. V.M.Prabhakaran,
Department of CSE,
KIT- Coimbatore
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2. Definition
• Algorithms are procedural solutions to
problems.
• These solutions are not answers but specific
instructions for getting answers.
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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
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4. Algorithm design and Analysis process
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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.
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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.
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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
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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
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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
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10. 6. Methods of specifying an algorithm
• There are mainly two options for specifying an
algorithm,
– Use of natural language
– Pseudo code and Flowcharts
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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.
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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.
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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.
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