Top-Down Design in Algorithms: Stepwise Refinement

1. Algorithms, Part 3 of 3 Topics • Top down-design • Structure charts Reading • Sections 1.4 - 1.5 , 3.3

2. Pseudocode and Then Some • We can write an algorithm for finding the average of two integers: Read integer <num1>, from the user Read integer <num2> from the user <sum> = <num1> + <num2> <average> = <sum> / 2 Display “The average of <num1> “and” <num2 > “is” <average>. • Steps 1, 2 & 5 will make use of code found in the run-time library. 1 2 3 4 5

3. Investigating Steps 1 & 5 Read integer <num1>, from the user Display “The average =” <average>. • Are these really single steps? • Each of them is really a sequence of steps, a subprogram. Two kinds of subprograms: • Functions - an answer is returned to the main program. • Procedures - no answer returned to the main program

4. Functions and Procedures • In our example, the function that gets a value from the user and the procedure that prints out the answer were already written. • Many times it is necessary for us to write our own procedures or functions.

5. Top-Down Design • If we look at a problem as a whole, it may seem impossible to solve because it is so complex. Examples: • writing a tax computation program • writing a word processor • Complex problems can be solved using top-down design, also known as stepwise refinement. • We break the problem into parts • Then break the parts into parts • Soon, each of the parts will be easy to do

6. Advantages of Top-Down Design • Breaking the problem into parts helps us to clarify what needs to be done. • At each step of refinement, the new parts become less complicated and, therefore, easier to figure out. • Parts of the solution may turn out to be reusable. • Breaking the problem into parts allows more than one person to work on the solution.

7. An Example of Top-Down Design • Scenario: • We own a home improvement company. • We do painting, roofing, and basement waterproofing. • A section of town has recently flooded (zip code 21222). • We want to send out pamphlets to our customers in that area.

8. The Top Level • Get the customer list from a file. • Sort the list according to zip code. • Make a new file of only the customers with the zip code 21222 from the sorted customer list. • Print an envelope for each of these customers. Main Read Sort Select Print

9. Pseudocode for our Main Program • Start • Call Read Customer List • Call Sort on customer list by zipcode • Call Select Target List from Customer List using only zipcode 21222 • Call Print Envelopes using target list • Stop

10. Another Level? • Should any of these steps be broken down further? Possibly. • How do I know? Ask yourself whether or not you could easily write the algorithm for the step. If not, break it down again. • When you are comfortable with the breakdown, write pseudocode for each of the steps (modules) in the hierarchy.

11. Structured Programs • We will use top-down design for all of our programming projects. • This is the standard way of writing programs. • Programs produced using this method and using only the three kinds of control structures, sequential, selection and repetition, are called structured programs. • Structured programs are easier to test, modify, and are also easier for other programmers to understand.

12. Another Example • Problem: Write a program that draws this picture of a house.

13. The Top Level • Draw the outline of the house • Draw the chimney • Draw the door • Draw the windows Main Draw Outline Draw Chimney Draw Door Draw Windows

14. Observation • The door has both a frame and knob. We could break this into two steps. Main Draw Outline Draw Chimney Draw Door Draw Windows Draw Door Frame Draw Knob

15. Another Observation • There are three windows to be drawn. Main Draw Outline Draw Windows . . . Draw Window 1 Draw Window 2 Draw Window 3 (x1,y1) (x2,y2) (x3,y3)

16. Code Reuse • But don’t the windows look the same? They just have different locations. • So, we can reuse the code that draws a window. • Simply copy the code three times and edit it to place the window in the correct location, or • Use the code three times, “sending it” the correct location each time (we will see how to do this later). • This is an example of code reuse.

17. The Pseudocode • Start • Call DrawHouseOutline giving a position • Call DrawChimney giving position • Call DrawDoor giving position • Call DrawWindow giving (x,y) position #1 • Call DrawWindow giving (x,y) position #2 • Call DrawWindow giving (x,y) position #3 • Stop

18. Summary • Use the divide-and conquer strategy to split the original problem into a series of sub-problems. • Consider each sub-problem separately and split them further into smaller sub-problems, progressively refining the previous versions in a top-to-bottom manner, until no further refinement is possible. Stop the process when you have the pseudocode that can be directly translated in a C program.

19. Exam 1 • All material before this page is “fair game” for the midterm. • Exam 1 will be on Wednesday October 10th • If you know that you can not make the exam, tell me today after class, so that we can schedule a possible makeup. • Only very SERIOUS conflicts will be honored.