算法与设计算法分析基础-整体框架讲解材料

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How to describe an algorithm?
Natural language
• Step1 Input m and n.
• Step2 Divide m by n and assign the value of the remainder to r.
• Step3 If r=0, return the value of n as the answer and stop; otherwise, proceed to Step 4.
Goals of this lecture
At the end of this lecture, you should be able to • Describe how to analyze an algorithm • Understand what is a best-case, worse-case and
The notion of algorithm
• Input output finiteness effectiveness definiteness
Algorithm design pattern
2007-2008-01《Design and Analysis of Algorithms》SCUEC
Definition:
Algorithm analysis means to evaluate the two computer resources, time and space, which needed by an algorithm. Less resources an algorithm needs, more efficiency it is.
Issues:
• time efficiency
– Determines the amount of time that algorithm needs to be executed.
• space efficiency
– Determines the amount of space that algorithm needs to be executed.
2007-2008-01《Design and Analysis of Algorithms》SCUEC
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Chapter 2
Fundamentals of the Analysis of Algorithm Efficiency (I)
1、The framework to analyze algorithms 2、Best, worst, average-case analysis 3、Three asymptotic notations
average-case analysis • Master the three asymptotic notations , , O,
rate of growth
2007-2008-01《Design and Analysis of Algorithms》SCUEC
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Analysis of algorithms
Approaches:
• theoretical analysis • empirical analysis
2007-2008-01《Design and Analysis of Algorithms》SCUEC
Review of last class
How to solve a problem by computer
• Actual problem • Mathematics model • Algorithm design and analysis • Programming • Result analysis
Start
Input m and n
r=mБайду номын сангаасn
r= 0
m=n n=r
Advantages: intuitive
output n
Disadvantages: lack flexibility
Stop
2007-2008-01《Design and Analysis of Algorithms》SCUEC
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How to describe an algorithm? (II)
Flow chart
A flowchart is a method of expressing an algorithm by a collection of connected geometric shapes containing descriptions of the algorithm’s steps.
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How to describe an algorithm? (IV)
Pseudocode
A pseudocode is a mixture of a natural language and programming language. It uses the basic grammar of programming language, but the operation instructions can designed with natural language.
• Step4 Assign the value of n to m and the value of r to n.
• Step5 Go to Step2.
Advantages: easy understand
Disadvantages: exist inherent ambiguity
2007-2008-01《Design and Analysis of Algorithms》SCUEC
1 r=m%n; 2 While r≠0
2.1 m=n; 2.2 n=r; 2.3 r=m%n; 3 return n;
Advantages: more precise than natural language
Disadvantages: not exist a single form of pseudocode