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Chapter 1 -- IntroductionChapter 2 -- Algorithms and Complexity

暨南大學資訊工程系黃光璿 (Guan-Shieng Huang)2005/02/21

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A Rock Game

Alice vs Bob 10+10 Bob can solve 2+2. How about 20+20? Or, 10+10+10?

The rule is: you can remove one rock from each pile or both of them.

The player who takes the last rock(s) wins the game.

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Alice

Move first. Had learned Algorithm CSIE210022.

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Answer

If you had learned Finite Automata…

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What is an Algorithm?

Assignment a:=1 b:=a

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Arithmetic a+b a-b (a+b)*c+a/d

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Conditional if statement1 then

statement2 else

statement3

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for loops for i=1 to 100 do statement

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while loops while statement1 dostatement2

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Array access a[100] a[a[i]]

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Biological Algorithms vs Computer Algorithms

DNA helicase

topoisomerase

single-strandbinding protein

DNA

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primase

DNA polymerase

5’ 3’

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DNA ligase

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Correct versus Incorrect Algorithms Soundness

所考慮到的情況都正確的處理 Completeness

考慮到所有可能的情況

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Recursive Algorithms

Tower of Hanoi Problem

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Iterative versus Recursive Algorithms

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Fast versus Slow Algorithms

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Big-O Notation

A function f(x) is O(g(x)) if there are positive real constants c and x0 such that f(x)≤g(x) for all values of x≧x0.

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Algorithm Design Techniques

Exhaustive Search Branch-and-Bound Algorithms Dynamic Programming Divide-and-Conquer Algorithms Machine Learning Randomized Algorithms

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Tractable versus Intractable Problems polynomial-time solvable problems nondeterministic polynomial-time solvable

problems beyond P P vs NP