The document discusses the fundamentals of algorithmic problem solving. It describes the three main phases of the problem solving process: (1) analyzing the problem by designing an algorithm using pseudocode or flowcharts, (2) implementing the algorithm in a programming language, and (3) maintaining the program if requirements change. It also discusses choosing between exact and approximate algorithms, analyzing algorithms for time and space efficiency, and types of errors like syntax, runtime, and logic errors that can occur when implementing an algorithm.

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Fundamentals of Algorithms
Problem Solving

2. Fundamentals of Algorithmic Problem Solving

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Problem Solving
• Algorithm
 Step-by-step problem-solving process
 Solution achieved in finite amount of time
 Problem Solution by computer

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Problem Solving Process
• Phase 1 - Analyze the problem
 Outline the problem and its requirements
 Design (algorithm) to solve the problem ( Flow chart, pseudo
code)
 Algorithm tracing
• Phase 2 - Implement the algorithm
 Implement the algorithm in code (in Programming Language 
Program)
 Verify that the algorithm works
• Phase 3 - Maintenance
 Use and modify the program if the requirements changes

5. Choosing between Exact and Approximate Problem Solving
• The next principal decision is to choose between
solving the problem exactly (exact algorithm) or
solving the problem approximately (approximation
algorithm).
Exact algorithm
Eg. extracting square roots, solving nonlinear
equations, and evaluating definite integrals.
Approximation algorithm
Eg. Vertex Cover, Traveling Salesman Problem

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Analyze the Problem (1)
Design Algorithm
• Pseudocode - is a mixture of a natural language and
programming language constructs. Pseudo code is usually more
precise than natural language.
• Flow chart - a method of expressing an algorithm by a
collection of connected geometric shapes containing
descriptions of the algorithm’s steps

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Flow Chart Symbols
Start and End
Input / output
Selection
Calculation
Data
Flow
• A Flowchart is
 An algorithm graphical representation.
 Written as a combination of the following graphical
notations:

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• Pseudo-code:
<Algorithm name>
The comment lines “//”
Begin
<data definition>
<actions>
End

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Analyze the Problem (1)
Algorithm Tracing
 Draw flowchart
 Find all possible paths
 Check each path with appropriate input data
 Observed Outputs not conform to the expected ones  error in
the algorithm.

10. Proving an Algorithm’s Correctness/verification
• Once an algorithm has been specified, you have to prove its
correctness. i.e. you have to prove that the algorithm yields a
required result for every legitimate input in a finite amount
of time.
Analyzing an Algorithm
two kinds of analyzing the algorithm efficiency:
• time efficiency- indicating how fast the algorithm runs
• space efficiency-indicating how much extra memory it uses.
• Range of inputs-These factors are not satisfactory then
redesign the algorithm.

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 Computer Stage: after completing the program, the
computer must do the following:
1.Compilation:
2.Execution: when the program become don’t has errors, the
computer execute it to produce the output

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Implement the algorithm
• Errors are of three types:
. syntax errors
. run-time errors
. logic errors
• Syntax errors: detected by the C compiler
. source code does not conform to one or more of C’s grammar
rules
. examples of syntax errors: undeclared variable, …
• Often one mistake leads to multiple error messages – can
be confusing

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Implement the algorithm
• Run-time errors. detected and displayed by computer during
execution.
- Occur when program directs computer to perform illegal
operation.
- will stop program execution and display message
• Logic errors.
- caused by faulty algorithm
- sign of error: incorrect program output
- cure: thorough testing and comparison with expected results
A logic error is also referred to as a bug, so finding logic errors is
called debugging.