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Lecture 2:. Problem Solving Algorithm Matlab Environment. Algorithm. Algorithm: a sequence of instructions that allows us to accomplish some goals.

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lecture 2
Lecture 2:
  • Problem Solving
  • Algorithm
  • Matlab Environment
algorithm
Algorithm
  • Algorithm: a sequence of instructions that allows us to accomplish some goals.
  • The word ”algorithm” comes from the name of a Persian author, Abu Ja’far Mohammed ibn Musa al Khowarizmi (c. 825 A.D.), who wrote a textbook on mathematics.
  • Examples:

- Directions to a party

- Recipe

- Computer programs

algorithm3
Algorithm
  • Characteristics of an algorithm

1. Finiteness

- terminates after a finite number of steps

2. Input & Output

3. Definiteness

- rigorously and umambiguously specified

4. Effectiveness

- steps are sufficiently simple and basic

algorithm4
Algorithm
  • Example: Find the greatest common divisor of a and b:

GCD(a,b):

1. Input a and b

2. If b=0 then output GCD(a,b) = a and stop!

3. Assign t=b , b= a mod b , a = t

Go to step 2.

Notes: GCD(a,b)=GCD(b, a mod b)

algorithm5
Algorithm
  • GCD(10,6)

1. a=10, b=6

2. _

3. t=6, b= 4, a=6

2. _

3. t=4, b=2, a=4

2. _

3. t=2, b=0, a=2

2. GCD(10,6)=2.

GCD(a,b):

1. Input a and b

  • If b=0 then output GCD(a,b) = a and stop!

3. Assign t=b , b= a mod b , a = t

Go to step 2.

algorithm6
Algorithm
  • A good algorithm implemented on a slow computer may perform much better than a bad algorithm implemented on a fast computer.
algorithm7
Algorithm
  • Minimal spanning tree problem

- Spanning tree: given a connected graph, a spanning tree is sub-graph (a tree) that connects all the vertices together.

- MST: is a spanning tree with the shortest total length.

algorithm9
Algorithm
  • Brute Force attack: enumerate all possible spanning trees and select the best one among them.
    • Given n points, there are nn-2possibilities !!!
algorithm12
Algorithm
  • Prim’s algorithm for MST is: n2
  • Kruskal’s algorithm for MST is : |E| log |E| + n
matlab
MATLAB
  • MATLAB® is a high-level language and interactive environment that enables you to perform computationally intensive tasks faster than with traditional programming languages such as C, C++, and Fortran.
  • Latest version is R2008a, 7.6 (2008)
matlab14
MATLAB
  • Matlab’s windows:
    • File: list files in the current directory
matlab15
MATLAB
  • Workspace: show the variables you have declared
matlab16
MATLAB
  • Command History: show all commands you have typed so far.
matlab17
MATLAB
  • Command Window: where to enter your command.
matlab18
MATLAB
  • Help Browser: will appear when you click to Help in Help Menu (F1)
matlab19
MATLAB
  • Getting Help !
    • Help command
    • Lookfor command
    • Examples: Lookfor sine
    • Google is your friend
  • Variables
    • Is a tag that you assign to a value while that value remains in memory
    • Variables are defined with the assignment operator
    • Variable names must begin with a letter, which may be followed by any combination of letters, digits, and underscores.
    • Variables names are case-sensitive
    • Examples: x1,x2, m_weight, X1,X2, M_Weight are different variables
matlab20
MATLAB
  • Some examples:

1) Calculate BMI

m_weight=input(‘input your weight (kg): ’);

m_height=input(‘input your height (m):’);

bmi=weight/height^2

2) Calculate area of a doughnut

matlab21
MATLAB

m_radius_large=input(‘input larger radius: ’);

m_radius_small=input(‘input smaller radius: ’);

m_area=(m_radius_large^2 m_radius_small^2)*pi