1. ALGORITHMS - PART 2 CONDITIONAL BRANCH CONTROL STRUCTURE
CSI 1301
ALGORITHMS - PART 2
CONDITIONAL BRANCH
CONTROL STRUCTURE

2. Conditional Branch
So far, in the method part of our algorithms, the instructions have been executed sequentially
However, sometimes we need to vary the order of execution of the instructions. The order will be determined by the value of a condition
We will test to determine whether the condition is true or false
If the condition is true, we will execute certain instructions
If the condition is false, we will execute other instructions

3. Definition of a Block
But first, let us define a block as group of related instructions
A block can contain one or as many instructions as we want
BLOCK 1
Get X
Get Y
Let Z = X + Y
Give Z
BLOCK 2
Let X = A + B * C /D

4. Block
The key feature of a block is that it has only one entrance (one way to come in)
By executing the first instruction in the block
and only one exit (one way out)
By executing the last instruction in the block
You cannot execute any other instruction in the block without starting with the first and ending with the last instructions

5. Simple Sequence of Blocks
Input Block
Get X
Get Y
Process Block
Let X = X + Y
Let Y = 2 * Y
Let Z = X + Y
Output Block
Give Z

6. Test Blocks
By adding a test at the beginning of a block, we let the results of the test determine which block of instructions will be executed
TEST
True Block
Do these Instructions if Test is True
False Block
Do these Instructions if the Test is False

7. What is a Test?
The test used in a conditional branching control structure contains a variable or expression that evaluates to either True or False

8. Logical Operators in a Test Expression

9. Examples of Tests

10. Logical Tests
In practice, tests contain variables and expressions, not numbers
Suppose that X, Y and Z are 3, 5, 8 respectively

11. Test Block
Indentation is used to show different blocks in an algorithm
To write a test block, use an IF statement, and indent the instructions to be executed
If (Test)
Do this statement
Do this statement as well
Do this statement after the If statement

12. Test Block (syntax and interpretation)
if (Test)
Block1
Interpretation
If Test is evaluated to true Block1 is executed, else Block2 is executed. The else is optionnal. Note that the indentation is important. It determines the beginning and the end of each block.
if (Test)
Block1
else
Block2

13. Algorithm 2.1
Write an algorithm to compute the absolute value of a number.
Name: ABSOLUTE
Givens: Number
Change: None
Results: Value
Intermediates: None
Definition: Value := ABSOLUTE (Number)
Method
Get Number
If (Number >= 0)
Let Value = Number
If (Number < 0)
Let Value = (-1) * Number
Give Value

14. Else It is redundant to do the test twice as in
IF (X > 0)
Do this
IF (X <= 0)
Do that
The test should be written as
If (X > 0)
Else (or Otherwise)

15. Algorithm 2.1 (b)
Write an algorithm to compute the absolute value of a number using only one test
Name: ABSOLUTE
Givens: Number
Change:None
Results: Value
Intermediates: None
Definition: Value := ABSOLUTE (Number)
Method
Get Number
If (Number >= 0)
Let Value = Number
Else
Let Value = (-1) * Number
Give Value

16. Algorithm 2.2
Write an algorithm which finds the largest of three given numbers
General Concept
Keep track of “Biggest so Far”
Look at the first two numbers
Store the larger of the two numbers in “Biggest so Far”
Compare “Biggest so Far” with the third number
If the third number is larger, then store it in “Biggest so Far”

17. Algorithm 2.2
Write an algorithm which finds the largest of three given numbers
Name: BIG3
Givens: N1, N2, N3
Change:None
Results:Largest
Intermediates: None
Definition:
Largest := BIG3(N1,N2,N3)
Method
Get N1
Get N2
Get N3
If (N1 > N2)
Let Largest = N1
Else
Let Largest = N2
If (N3 > Largest)
Let Largest = N3
Give Largest

18. Trace 2.1 Trace Algorithm 2.2 with the values 8, 12, 7 (1) Get N1
(4) If (N1 > N2)
(5) Let Largest = N1
(6) Else
(7) Let Largest = N2
(8) If (N3 > Largest)
(9) Let Largest = N3
(10) Give Largest
LN N1 N2 N3 Largest Test
1 8
(8>12)
(7>12)
10 Output 12

19. Algorithm 2.3
Write an algorithm which, when given an ordered list X1, X2, & X3, modifies the list so that the values are in ascending order
General Concept
Look at the first two numbers, X1 and X2. If X1 is larger than X2, swap them (remember the swap algorithm?)
Look at X2 and X3. If X2 is larger than X3, swap them
This will put the largest number in the X3 position
X2 may have changed, so we have to look at X1 again
Look again at X1 and X2. If X1 is larger than X2, swap them
Now the list is in non-decreasing order

20. Algorithm 2.3
Write an algorithm which, given an ordered list X1, X2 & X3, modifies it so that the values are in ascending order
Method
Get X1, X2, X3
If (X1 > X2)
Let Temp = X1
Let X1 = X2
Let X2 = Temp
If (X2 > X3)
Let Temp = X2
Let X2 = X3
Let X3 = Temp
Give X1, X2, X3
Name: SORT3
Givens: X1,X2,X3
Change: X1,X2,X3
Results: None
Intermediates: Temp
Definition: SORT3(X1,X2,X3)

21. Trace 2.2
Trace algorithm 2.3 with list X having values 3, 8 and 2 respectively
(1) Get X
(2) If (X1 > X2)
(3) Let Temp = X1
(4) Let X1 = X2
(5) Let X2 = Temp
(6) If (X2 > X3)
(7) Let Temp = X2
(8) Let X2 = X3
(9) Let X3 = Temp
(10) If (X1 > X2)
(11) Let Temp = X1
(12) Let X1 = X2
(13) Let X2 = Temp
(14) Give X
LN X TEMP TEST
1 (3,8,2)
(3 > 8)
(8 > 2)
8 (3,2,2)
9 (3,2,8)
(3 > 2)
12 (2,2,8)
13 (2,3,8)
14 Output (2,3,8)

22. Multiple Tests Sometimes we need to perform multiple related tests
For example, in assigning grades, a student can receive A+, A, A-….E, F
We can add an ELSE IF clause for multiple test results
IF (Test 1)
Execute block for Test 1
Else IF (Test 2)
Execute block for Test 2
Else
Execute block for Else

23. Algorithm 2.4
Write an algorithm which calculates the amount of money to charge for a ticket. The amount varies with the age of the individual. The charge for a person less than 16 is $7. The charge for a person over age 65 is $5 The charge is $10 for everyone else
Name: FARE
Givens: Age
Change: None
Results: Price
Intermediates: None
Definition: Price := FARE(Age)
Method
Get Age
If (Age < 16)
Let Price = $7
Else If (Age > 65)
Let Price = $5
Else
Let Price = $10
Give Price

24. Trace 2.3 Trace algorithm 2.4 with the given age 35 (1) Get Age
(2) If (Age < 16)
(3) Let Price = $7
(4) Else If (Age > 65)
(5) Let Price = $5
(6) Else
(7) Let Price = $10
(8) Give Price
LN Age Price Test
(35<16)
(35>65)
$10
8 Output $10

25. Algorithm 2.5
Given an employee’s eligible medical expenses for a calendar year, write an algorithm which computes the amount of reimbursement from group medical insurance. The insurance does not cover the first $100 of medical expenses. It pays 90% of the remaining amount in the first $2000 of expenses and 100% of any additional expenses.

26. Algorithm 2.5 Name: MEDICAL Givens: Expense Change: None
Results: Refund
Intermediates:
LL (Constant 100)
UL (Constant 2000)
Definition:
Refund := MEDICAL(Expense)
Method
Set LL = 100
Set UL = 2,000
Get Expense
If (Expense < LL)
Let Refund = 0
Else If (Expense < UL)
Let Refund = 90% (Expense-LL)
Else
Let Refund = 90% (UL-LL) +
100% (Expense - UL)
Give Refund

27. Trace 2.4 Trace Algorithm 2.5 for $3,000 worth of expenses
LN UL LL Exp Refund Test
1, K
(3K<100)
(3K<2K)
,710
10 Output 2,710
( 1) Set LL = 100
( 2) Set UL = 2,000
( 3) Get Expense
( 4) If (Expense < 100)
( 5) Let Refund = 0
( 6) Else If (Expense < 2,000)
( 7) Let Refund = 90% (Expense-100)
( 8) Else
( 9) Let Refund = 90% (1,900) +
100% (Expense - 2,000)
(10) Give Refund

28. Additional Material

29. Flow Charts

30. Flow Charts Logic is implemented with a Diamond Symbol
There are two exits, which should be labeled Y/N or T/F
The two paths need to join before the end of the flowchart

31. Algorithm 2.1(a) Name: ABSOLUTE Givens: Number Change: None
Results: Value
Intermediates: None
Definition: Value := ABSOLUTE (Number)

32. Algorithm 2.1(b) Name: ABSOLUTE Givens: Number Change: None
Results: Value
Intermediates: None
Definition: Value := ABSOLUTE (Number)

33. Algorithm 2.2 Name: BIG3 Givens: N1, N2, N3 Change:None
Results:Largest
Intermediates: None
Definition:
Largest := BIG3(N1,N2,N3)

34. Algorithm 2.3 Name: SORT3 Givens: X1,X2,X3 Change: X1,X2,X3
Results: None
Intermediates: Temp
Definition: SORT3(X1,X2,X3)

35. Algorithm 2.4 Name: FARE Givens: Age Change: None Results: Price
Intermediates: None
Definition: Price := FARE(Age)

36. Algorithm 2.5 Name: MEDICAL Givens: Expense Change: None
Start
MEDICAL
Get Expense If (
Expense
< LL ) UL
Let Refund = 90 %( –
UL-LL )+
100
Give
Refund
Finish N Y
Set LL
Set UL 2 ,
000
Name: MEDICAL
Givens: Expense
Change: None
Results: Refund
Intermediates:
LL (Constant 100)
UL (Constant 2,000)
Definition:
Refund := MEDICAL(Expense)

37. NSD

38. NSD Tricky to do in Excel Use 2 columns
Merge the 2 cells to form question
Format Cells/Borders Diagonal lines can be put in
Add Y/N cells

39. Algorithm 2.1(a) Name: ABSOLUTE Givens: Number Change: None
Results: Value
Intermediates: None
Definition: Value := ABSOLUTE (Number)

40. Algorithm 2.1(b) Name: ABSOLUTE Givens: Number Change: None
Results: Value
Intermediates: None
Definition: Value := ABSOLUTE (Number)

41. Algorithm 2.2 Name: BIG3 Givens: N1, N2, N3 Change:None
Results:Largest
Intermediates: None
Definition:
Largest := BIG3(N1,N2,N3)

42. Algorithm 2.3 Name: SORT3 Givens: X1,X2,X3 Change: X1,X2,X3
Results: None
Intermediates: Temp
Definition: SORT3(X1,X2,X3)

43. Algorithm 2.4 Name: FARE Givens: Age Change: None Results: Price
Intermediates: None
Definition: Price := FARE(Age)

44. Algorithm 2.5 Name: MEDICAL Givens: Expense Change: None
Results: Refund
Intermediates:
Definition:
Refund := MEDICAL(Expense)

45. Homework

46. For each of the following questions: Develop an algorithm
Trace the algorithm with suitable data
Write an algorithm to reverse the digits in a three digit number and then add that number to For example, 468 becomes When added to 500, the result is 1364.
Write an algorithm to get the names and ages of two people. Return the name of the person who is older (in the format “x is older than y”, where x and y are the names of the two people), unless the two people are the same age, in which case, return the message “x is the same age as y”.

47. An automotive sales representative’s commission is calculated as a percentage of the sale:
8% of the first $5, of the sale price
10% on the remainder of the sale price, if the remainder is less than or equal to $80, or
12.5% on the remainder, if the remainder is more than $80,000.00
Develop an algorithm that will accept the sale price of the automobile and calculate and display the sales representative’s commission.