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Chapter 1-- Introduction Chapter 2-- Algorithms and Complexity

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Chapter 1 -- Introduction Chapter 2 -- Algorithms and Complexity (Guan-Shieng Huang) 2007/02/26 A Rock Game Alice vs Bob 10+10 ... – PowerPoint PPT presentation

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Title: Chapter 1-- Introduction Chapter 2-- Algorithms and Complexity


1
Chapter 1 -- IntroductionChapter 2 -- Algorithms
and Complexity
  • ?????????
  • ??? (Guan-Shieng Huang)
  • 2007/02/26

2
A Rock Game
  • Alice vs Bob
  • 1010
  • Bob can solve 22.
  • How about 2020? Or, 101010?
  • 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.

3
(No Transcript)
4
Alice
  • Move first.
  • Had learned Algorithm CSIE210022.

5
Answer
  • If you had learned Finite Automata

6
What is an Algorithm?
  • Assignment
  • a1
  • ba

7
  • Arithmetic
  • ab
  • a-b
  • (ab)ca/d

8
  • Conditional
  • if statement1 then statement2 else statement3

9
  • for loops
  • for i1 to 100 do statement

10
  • while loops
  • while statement1 dostatement2

11
  • Array access
  • a100
  • aai

12
  • The concept of algorithms can be modeled formally
    by Turing machines
  • ????

13
Biological Algorithms vs Computer Algorithms
DNA
DNA helicase
topoisomerase single-strand binding protein
14
primase
DNA polymerase
5 ? 3
15
DNA ligase
16
(No Transcript)
17
Correct versus Incorrect Algorithms
  • Soundness
  • ?????????????
  • Completeness
  • ??????????

18
Recursive Algorithms
  • Tower of Hanoi Problem

19
(No Transcript)
20
(No Transcript)
21
Iterative versus Recursive Algorithms
22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
Fast versus Slow Algorithms
26
Big-O Notation
  • A positive integer function f(n) is O(g(n)) if
    there are positive real constants c and n0 such
    that f(n) c g(n) for all values of n?n0.

27
Algorithm Design Techniques
  • Exhaustive Search
  • Branch-and-Bound Algorithms
  • Dynamic Programming
  • Divide-and-Conquer Algorithms
  • Machine Learning (?)
  • Randomized Algorithms

28
Tractable versus Intractable Problems
  • polynomial-time solvable problems
  • nondeterministic polynomial-time solvable
    problems
  • beyond P
  • P vs NP
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