Algorithms & FlowchartsLecture 10. Algorithm’s CONCEPT.
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Transcript of Algorithms & FlowchartsLecture 10. Algorithm’s CONCEPT.
Algorithms & Flowcharts Lecture 10
Algorithm’s CONCEPTAlgorithm’s CONCEPTAlgorithm’s CONCEPTAlgorithm’s CONCEPT
Solving Problems
When faced with a problem:
1. We first clearly define the problem
2. Think of possible solutions
3. Select the one that we think is the best under the prevailing circumstances
4. And then apply that solution
5. If the solution works as desired, fine; else we go back to step 2
al.go.rithmSequence of steps
that can be taken to solve a given problem
Algorithm (Better Definition)
1st Definition:Sequence of steps that can be taken to
solve a problem
Better Definition:A precise sequence of a limited number
of unambiguous, executable steps that terminates in the form of a solution
Examples
• Addition
• Conversion from decimal to binary
• The process of boiling an egg
• The process of mailing a letter
• Sorting
• Searching
Informal definition of an algorithm used in a computer
Finding the largest integer among five integers
Defining actions in FindLargest algorithm
FindLargest refined
Generalization of FindLargest
THREE BUILDING BLOCKSTHREE BUILDING BLOCKSTHREE BUILDING BLOCKSTHREE BUILDING BLOCKS
Sequences
A sequence of instructions that are executed in the precise order they are written in:
statement block 1
statement block 2
statement block 3
statement block 1
statement block 2
statement block 3
DecisionsSelect between alternate courses of action depending upon the evaluation of a condition
If ( condition = true )
statement block 1
Else
statement block 2
End ifstatement
block 1
conditionTrue False
statementblock 2
Repetitions/Loops
Loop through a set of statements as long as a condition is true
Loop while ( condition = true )
statement block
End Loop
conditionTrue
False
statementblock
Three building blocks
Algorithm TYPESAlgorithm TYPESAlgorithm TYPESAlgorithm TYPES
Greedy Algorithm
• An algorithm that always takes the best immediate, or local solution while finding an answer
• Greedy algorithms may find the overall or globally optimal solution for some optimization problems, but may find less-than-optimal solutions for some instances of other problems
• KEY ADVANTAGE: Greedy algorithms are usually faster, since they don't consider the details of possible alternatives
Deterministic Algorithm
• An algorithm whose behavior can be completely predicted from the inputs
• That is, each time a certain set of input is presented, the algorithm gives the same results as any other time the set of input is presented
Randomized Algorithm
• Any algorithm whose behavior is not only determined by the input, but also values produced by a random number generator
• These algorithms are often simpler and more efficient than deterministic algorithms for the same problem
• Simpler algorithms have the advantages of being easier to analyze and implement
Syntax & SemanticsAn algo. is “correct” if its:
– Semantics are correct– Syntax is correct
Semantics:The concept embedded in an algorithm (the soul!)
Syntax:The actual representation of an algorithm (the body!)
WARNINGS:
1. An algo. can be syntactically correct, yet semantically incorrect – very dangerous situation!
2. Syntactic correctness is easier to check as compared with semantic