1 Chapter 1-- Introduction Chapter 2-- Algorithms and Complexity 暨南大學資訊工程系 黃光璿 (Guan-Shieng Huang) 2005/02/21

2 A Rock Game Alice vs Bob   Bob can solve 2+2.  How about 20+20? Or, ? 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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4 Alice Move first. Had learned Algorithm CSIE

5 Answer If you had learned Finite Automata…

6 What is an Algorithm? Assignment  a:=1  b:=a

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

8 Conditional  if statement1 then statement2 else statement3

9 for loops  for i =1 to 100 do statement

10 while loops  while statement1 do statement2

11 Array access  a[100]  a[a[ i ]]

12 Biological Algorithms vs Computer Algorithms DNA helicase topoisomerase single-strandbinding protein DNA

13 primase DNA polymerase 5’  3’

14 DNA ligase

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16 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

17 Recursive Algorithms Tower of Hanoi Problem

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20 Iterative versus Recursive Algorithms

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24 Fast versus Slow Algorithms

25 Big-O Notation A function f(x) is O(g(x)) if there are positive real constants c and x 0 such that f(x)≤g(x) for all values of x ≧ x 0.

26 Algorithm Design Techniques Exhaustive Search Branch-and-Bound Algorithms Dynamic Programming Divide-and-Conquer Algorithms Machine Learning Randomized Algorithms

27 Tractable versus Intractable Problems polynomial-time solvable problems nondeterministic polynomial-time solvable problems beyond P P vs NP