1. Algorithms IV
Top-Down Design

2. Top-Down Design Also known as Top-Down Stepwise Refinement.
Big problem becomes a set of smaller problems
Smaller problems become even smaller problems
Finally a pile of simple problems, each of which is easy to solve.

3. Top-Down Design, Idealized Divide and Conquer
Problem P
Subproblem P1
Subproblem P2
P22
P11
P12
P21
P111
P112
P121
P122
P211
P212
P221
P222
P1111
P1112
P1121
P1122
P1211
P1212
P1221
P1222
P2111
P2112
P2121
P2122
P2211
P2212
P2221
P2222

4. Example Design Compute Income Tax
Goal: compute income tax
Steps
Read and verify income.
Read and verify filing status
Compute tax
Print income, filing status, and tax

5. Example Design Compute Income Tax
First high-level pseudocode
read and verify income.
read and verify filing status
compute tax
print income, filing status, and tax

6. Characteristics of a Good Decomposition
“Clean” --- Tasks don’t overlap.
All tax computations are in the “Compute Tax” section.
“Not all modules are equal”
Modules are divided according to function, not size.

7. Writing Pseudocode: Read and verify income
while entered income is incorrect ask the user to enter a correct income value
end_while

8. Read and verify income
set INCORRECT to -1 /* income must be non-negative */
set MININCOME to /* minimum income for this program */
set income to INCORRECT
while INCOME is INCORRECT ask the user to enter a correct income value
set INCOME to the value entered
ask the user to verify INCOME
if the user does not verify INCOME then
set INCOME to INCORRECT
else if INCOME is less than MININCOME then
end_if
end_while

9. Read and verify filing status
print the filing status menu
while entered filingStatus is incorrect ask the user to enter a correct filing status
end_while

10. Read and verify filing status (II)
set correctStatusInput to ‘n’ /* this is an indicator variable */
print filing status menu /* “n” means “no” or “bad” */
while correctStatusInput is equal to ‘n’
print “Enter filing status: should be between 1 and 4: “
read status
if status is greater than 0
if status is less than 5
set correctStatusInput to ‘y’
end_if end_if
end_while

11. Print filing status menu
print “Single ”
print “Married filing jointly ”
print “Married filing separately ”
print “Head of household ”

12. Compute tax (A) if status is 1
compute tax = x (income )
end_if
if status is 2
if income is less than or equal to 82,150
compute tax = x (income )
else
compute tax = x (income )

13. Compute tax (B) if status is 3
compute tax = x (income )
end_if
if status is 4
if income is less then or equal to
compute tax = x (income )
else
compute tax = x (income )

14. Print income, filing status, and tax
print verbal description of filing status
print tax

15. Print income, filing status, and tax (II)
if status is equal to 1
print “Single”
end_if
if status is equal to 2
print “Married filing jointly”

16. Print income, filing status, and tax (IIA)
if status is equal to 3
print “Married filing separately”
end_if
if status is equal to 4
print “Head of household”
print tax

17. 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.

18. Summary (II)
Combine all final refinements of subprograms according to the logic of the original program.