The Origins of “Algorithm”

The Origins of the Term “Algorithm”

Developing Algorithm Using Stepwise Refinement Read the problem statement carefully Rewrite it in your own words if it is not clear Highlight the nouns and look for data items Highlight the verbs to determine the work that needs to be done Write the initial algorithm that just describes the inputs, outputs and work to be done

Stepwise Refinement Now go back to each step in the initial algorithm and refine it to describe how it will be implemented The Key steps are: Rewrite the statement if not clear Nouns==>Data, Verbs==>Action Initial Algorithm(WHAT) Final Algorithm(HOW)

Algorithm Development Exercise Problem 1 A Sunoco gas station offers 5 cents per gallon discount each Sunday. If a person fills up 20 gallons every week, how much money will that person save in X weeks?

Algorithm Development Exercise Problem 2 Given the radius of a circle, develop an algorithm that computes the area and circumference

Algorithm Development Exercise Problem 3 Write a cash register algorithm that will compute 7 percent sales tax at the price of an item and then add the tax to the price to obtain the final price

Properties of Algorithms Simplicity Precision Various Levels of Abstraction

Algorithms Algorithms specify the “behavior” Programs in specific languages just express the algorithm in one particular form

Information Information means knowledge about something Data is a specific representation of information

Components of An Algorithm Data Structures Data Manipulation Instructions Conditional Expressions (if price greater than my_limit then don’t buy) Control Structures (while (condition) do statement Modules

Levels of Abstraction Details are HIDDEN if we use TOP DOWN approach to describe algorithms Example: Counting names that begin with ‘A’ in a list of names

Recap What is the advantage of hiding details at the initial level of algorithm development? What properties of an object must be known to us before we can use it? How can we make software reusable? How many types of statements can be part of an algorithm?