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# lecture 2: - PowerPoint PPT Presentation

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

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Presentation Transcript

• Problem Solving

• Algorithm

• Matlab Environment

• 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

• 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

• 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)

• 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.

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

• 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.

• Brute Force attack: enumerate all possible spanning trees and select the best one among them.

• Given n points, there are nn-2possibilities !!!

• Prim’s algorithm for MST is: n2

• Kruskal’s algorithm for MST is : |E| log |E| + n

• 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.

• Matlab’s windows:

• File: list files in the current directory

• Workspace: show the variables you have declared

• Command History: show all commands you have typed so far.

• Command Window: where to enter your command.

• Help Browser: will appear when you click to Help in Help Menu (F1)

• Getting Help !

• Help command

• Lookfor command

• Examples: Lookfor sine

• 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

• Some examples:

1) Calculate BMI