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					            TA C252 :Computer Programming II                                Top-down Design
                                                            • Design Approach
                          Lec-2                             • Principle
                                                                  – Divide and Conquer
                  Today’s Agenda                            • Steps
                  • Top-Down Design                               – Divide the problem into sub-problems
                  • Top-Down Design Examples                      – Solve the sub-problems
                  • The Function Concept                          – Combine the (sub-)solutions



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                  Top-down Design                                                           Task


•       How do you solve the sub-problem?
•       Divide-and-conquer again!
•       Steps                                                              Subtask1        Subtask2        Subtask3
      1. Divide the problem into sub-problems
      2. Repeat step 1 for each sub-problem
         until the problem is small enough to have an
         atomic solution.
                                                              Subtask1.1                 Subtask1.2
      3. Combine the solutions.


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                  Top-Down Design                                Advantages of Top-Down Design
• If we look at a problem as a whole, it may seem           • Breaking the problem into parts helps us to clarify
  impossible to solve because it is so complex.               what needs to be done.
  Examples:
                                                            • At each step of refinement, the new parts become
   – writing a tax computation program                        less complicated and, therefore, easier to figure
   – writing a word processor                                 out.
• Complex problems can be solved using top-down             • Parts of the solution may turn out to be reusable.
  design, also known as stepwise refinement, where
                                                            • Breaking the problem into parts allows more than
   – We break the problem into parts                          one person to work on the solution.
   – Then break the parts into parts
   – Soon, each of the parts will be easy to do




                                                                                                                          1
  An Example of Top-Down Design                                        The Top Level
                                                    • Get the customer list from a file.
 • Problem:
                                                    • Sort the list according to zip code.
    – We own a home improvement company.
                                                    • Make a new file of only the customers with the zip
    – We do painting, roofing, and basement           code 21222 from the sorted customer list.
      waterproofing.
                                                    • Print an envelope for each of these customers.
    – A section of town has recently flooded (zip
      code 21222).
    – We want to send out pamphlets to our                                     Main
      customers in that area.

                                                          Read         Sort           Select     Print




               Another Level?                                      Structured Programs
• Should any of these steps be broken down              • We will use top-down design for all remaining
  further? Possibly.                                      programming problems.
• How do I know? Ask yourself whether or not            • This is the standard way of writing programs.
  you could easily write the algorithm for the          • Programs produced using this method and using
  step. If not, break it down again.                      only the three kinds of control structures,
                                                          sequential, selection and repetition, are called
• When you are comfortable with the
                                                          structured programs.
  breakdown, write the pseudocode for each of
                                                        • Structured programs are easier to test, modify,
  the steps (modules) in the hierarchy.                   and are also easier for other programmers to
• Typically, each module will be coded as a               understand.
  separate function.




              Another Example                                          The Top Level
• Problem: Write a program that draws this          •    Draw the outline of the house
  picture of a house.                               •    Draw the chimney
                                                    •    Draw the door
                                                    •    Draw the windows

                                                                               Main


                                                         Draw         Draw            Draw         Draw
                                                         Outline     Chimney          Door        Windows




                                                                                                             2
          Pseudocode for Main                                                 Observation
                                                             • The door has both a frame and knob. We could
Call Draw Outline                                              break this into two steps.
Call Draw Chimney
                                                                                    Main
Call Draw Door
Call Draw Windows                                              Draw        Draw             Draw           Draw
                                                               Outline    Chimney           Door          Windows


                                                                               Draw                Draw
                                                                             Door Frame            Knob




      Pseudocode for Draw Door                                           Another Observation
Call Draw Door Frame                                         • There are three windows to be drawn.
Call Draw Knob
                                                                                    Main


                                                               Draw                                        Draw
                                                               Outline              . . .                 Windows


                                                                              Draw             Draw             Draw
                                                                             Window 1         Window 2         Window 3




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




                                                                                                                          3
       Pseudocode for Draw Windows                                  Top-Down Design – Example 1
 Call Draw a Window, sending in Location 1                    • Problem: Compute a solution to a quadratic
 Call Draw a Window, sending in Location 2                      equation.
 Call Draw a Window, sending in Location 3                          – Input: Real Numbers a,b,c
                                                                    – Output: x such that ax^2 + bx + c = 0
                                                              • Fact:
                                                                    – x = (-b + sqrt(b^2 – 4ac)) / (2a) is a solution.




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         Top-Down Design – Example 1                                Top-Down Design – Example 2
               Compute x      s.t.   ax^2+bx+c=0
                                                              • Problem: Compute the sum of n natural
                                                                numbers
               Compute (-b + sqrt(b^2 – 4ac)) / (2a)                – Input: n
                                                                    – Output: sum(n) = 1 + 2 + ……+n-1 + n

Compute (-b + d) / (2a)         Compute d = sqrt(b^2 – 4ac)




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                                                              12-Aug-11                                                  22




                     Example2:
               Sum(n) =1+2+ ….(n-1)+n                                Top-Down Design – Example 3
                                                              • Compute xy where y is a power of 2.
             Sum(n-1)           +              n              • Input: x and y
                                                              • Output: xy
       +
Sum(n-2)               n-1
                    ……………….

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                                                                                                                              4
                   Example 3 – xy

   • Consider xy, where y=2k
                                 xy

                   xy/2           *   xy/2

                   *                   *
            xy/4   …      xy/4        …
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