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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:
• Problem Solving
• Algorithm
• Matlab Environment
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

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

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)

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.

Algorithm
• A good algorithm implemented on a slow computer may perform much better than a bad algorithm implemented on a fast computer.
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.

Algorithm
• Brute Force attack: enumerate all possible spanning trees and select the best one among them.
• Given n points, there are nn-2possibilities !!!
Algorithm
• Prim’s algorithm for MST is: n2
• Kruskal’s algorithm for MST is : |E| log |E| + n
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)
MATLAB
• Matlab’s windows:
• File: list files in the current directory
MATLAB
• Workspace: show the variables you have declared
MATLAB
• Command History: show all commands you have typed so far.
MATLAB
• Command Window: where to enter your command.
MATLAB
• Help Browser: will appear when you click to Help in Help Menu (F1)
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
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

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