1. ALGORITHMS - PART 3 REPETITION/LOOP CONTROL STRUCTURE
CSI 1301
ALGORITHMS - PART 3
REPETITION/LOOP
CONTROL STRUCTURE

2. Need for Repetition
An algorithm with get/give, assignment and conditional branch instructions processes one set of data (givens) each time it is executed
What would we do if we needed to process multiple sets of data?
To calculate the grades for 150 students (instead of a grade for one student)
To determine the payroll for all employees
We could execute the algorithm multiple times or once, as in the following example…..

3. Algorithm 3.1 Write an algorithm to find the sum of 100 numbers.
Name: SUM100
Givens:N1, N2, N3, … N99, N100
Change:None
Results: Total
Intermediates: None
Definition: Total := SUM100(N1, N2, N3… N100)
Method
Get N1
Get N2 …
Get N100
Let Total = N1 + N2 + N3 + … + N99 + N100
Give Total
What would we do for 1,000,000 numbers?

4. Loop Block Clearly, we need a better way We need an instruction that
Executes a block of instructions multiple times, and
After each execution, tests to see if the block of instructions should be executed again
This instruction is called a loop (repetition) control instruction

5. Parts of a Loop There are four parts to a loop Setup
The conditions to be set before we enter the loop
Test (included in the loop control instruction)
The Boolean test to determine if the loop should be executed again (the same type of test used in a conditional branch instruction)
Instruction Block
The instructions that are to be executed repeatedly
Change
A change to one of the variables in the test so that we can exit the loop

6. Two Styles of Loops
Usually we place the test before the instructions that are to be executed
However, occasionally, we need to execute the instructions before we test; in this case, we place the test after the instructions that are to be executed repeatedly

7. Loop Block Set Up Set Up TEST Loop Block ----------------
Instruction 1
Instruction 2
Loop Block
Instruction 1
Instruction 2
Change
Change
TEST

8. Setting up a Loop in an Algorithm (1)
Syntax
Set Up
Loop When (Test)
Instruction 1
Instruction 2
……….
Change
Finish Loop
Semantic
After the Set Up, the Test is evaluated, if its value is true, instruction1, instruction2,… are executed, and Test is evaluated again. Instruction1, Instruction2 are repeated as long as the Test is true.
When the value of Test becomes false, the Loop ends and the instruction following the Loop is executed.

9. Setting up a Loop in an Algorithm (2)
Syntax
Set Up
Loop
Instruction 1
Instruction 2
……….
Change
Finish Loop When (Test)
Semantic
After the Set Up, instruction1, instruction2, … are executed and then Test is evaluated, if its value is true, instruction1, instruction2,… are executed and the Test is evaluated again.
When the value of Test becomes false, the Loop ends and the instruction following the Loop is executed.

10. Loop Instructions
Since a loop works on a block of instructions, any set of instructions can be repeated, not just assignment and conditional branch instructions
For example, multiple Gets
Loop
Get X
Finish Loop
Or multiple Gives
Give Answer

11. Algorithm 3.1 (a)
Write an algorithm to find the sum of 100 numbers. Place the test at the beginning of the loop.
Loop Set Up
Let Total = 0
Let Count = 0
Loop Test
Continue until 100 numbers have been read (Count <100)
Change
Let Count = Count + 1
Instructions
Get N
Let Total = Total + N

12. Algorithm 3.1 (a)
Write an algorithm to find the sum of 100 numbers. Place the test at the beginning of the loop.
Method
Let Total = 0
Let Count = 0
Loop When (Count < 100)
Get N
Let Total = Total + N
Let Count = Count + 1
Finish Loop
Give Total
Name: SUM100
Givens: N
Change: None
Results: Total
Intermediates: Count
Definition: Total := SUM100(N)

13. Algorithm 3.1 (b)
Write an algorithm to find the sum of 100 numbers. Place the test at the end of the loop.
Method
Let Total = 0
Let Count = 0
Loop
Get N
Let Total = Total + N
Let Count = Count + 1
Finish Loop When (Count = 100)
Give Total
Name: SUM100
Givens: N
Change: None
Results: Total
Intermediates: Count
Definition: Total := SUM100(N)

14. Algorithm 3.2
Write an algorithm to calculate the sum from 1 to N. ie. ( …N)
Setup
Let Sum = 0
Let Value = 1
Test
Value <= N
Change
Let Value = Value + 1

15. Algorithm 3.2
Write an algorithm to calculate the sum from 1 to N. ie. ( …N)
Name: SUMN
Givens: N
Change: None
Results: Sum
Intermediates: Value
Definition: Sum := SUMN(N)
Method
Get N
Let Value = 1
Let Sum = 0
Loop When (Value <= N)
Let Sum = Sum + Value
Let Value = Value + 1
Finish Loop
Give Sum

16. Trace 3.1 Trace algorithm 3.2 when N is 4 (1) Get N (2) Let Value = 1
LN N Value Sum Test
1 4
(1<=4)
(2<=4)
(3<=4)
(4<=4)
(5<=4)
8 Output 10
Trace algorithm 3.2 when N is 4
(1) Get N
(2) Let Value = 1
(3) Let Sum = 0
(4) Loop When (Value <= N)
(5) Let Sum = Sum + Value
(6) Let Value = Value + 1
(7) Finish Loop
(8) Give Sum

17. Complex Tests
Sometimes, a simple test is not adequate for either a conditional branch (If) or repetition (loop) control structure.
For more complicated tests, we use the Boolean operators
AND OR
NOT
XOR

18. Boolean Operators AND will return a TRUE only when both are TRUE
X | Y | X AND Y
F | F | F
F | T | F
T | F | F
T | T | T
OR will return a TRUE when either is TRUE
X | Y | X OR Y
F | F | F
F | T | T
T | F | T
T | T | T

19. Boolean Operators
NOT will change a TRUE to a FALSE or a FALSE to a TRUE
X | NOT(X)
F | T
T | F
XOR will return a TRUE when either is TRUE, but NOT BOTH
X | Y | X XOR Y
F | F | F
F | T | T
T | F | T
T | T | F

20. Algorithm 3.3
Write an algorithm to find the average of up to 10 numbers entered by the user.
Execution of the algorithm stops whenever one of the following conditions occurs
10 numbers have been entered
The user decides to stop entering numbers
Setup
Let Count = 0, Let Total = 0, Let Again = True
Test
Again = True AND Count <= 10
Change
Let Count = Count + 1, Get Again

21. Algorithm 3.3
Write an algorithm to find the average of up to 10 numbers entered by the user.
Name: AVERAGE10
Givens: N
Change: None
Results: AVG
Intermediates: Count, Sum
Again
Definition:
AVG = AVERAGE10(N)
Method
Let Count = 0
Let Sum = 0
Let Again = True
Loop When (Count < 10) AND
(Again)
Get N
Let Sum = Sum + N
Let Count = Count + 1
Get Again
Finish Loop
Let AVG = Sum/Count
Give AVG

22. LN N Count Sum Again AVG Test
Yes
(0<10)AND YES
5 1
Yes
(1<10)AND YES
5 3
(2<10)AND YES
5 5
(3<10)AND YES No
(4<10) AND NO
11 Output 3
Trace 3.2
Trace algorithm 3.3 when the user enters only the numbers 1, 3, 5 and 3
(1) Let Count = 0
(2) Let Sum = 0
(3) Let Again = True
(4) Loop When
(Count < 10) AND
(Again)
(5) Get N
(6) Let Sum = Sum + N
(7) Let Count = Count + 1
(8) Get Again
(9) Finish Loop
(10) Let AVG = Sum/Count
(11) Give AVG

23. Base Algorithm 1 Write an algorithm to perform a COUNT. Let COUNT = 0
Loop
……….
Let COUNT = COUNT + 1
Finish Loop
Give COUNT

24. Base Algorithm 2 Write an algorithm to perform a SUM. Let SUM = 0 Loop
Get N
……….
Let SUM = SUM + N
Finish Loop
Give SUM

25. Base Algorithm 3 Write an algorithm to perform an AVERAGE. Let SUM = 0
Let COUNT = 0
Loop
Get N
……….
Let SUM = SUM + N
Let COUNT = COUNT + 1
Finish Loop
Let Average = SUM/COUNT
Give Average

26. Base Algorithms 4 and 5 Write algorithms to perform a MAX and MIN.
Let MAX = - infinity
Loop
Get N
If (N > MAX)
Let MAX = N
Finish Loop
Give MAX
Let MIN = infinity
Loop
Get N
If (N < MIN)
Let MIN = N
Finish Loop
Give MIN

27. Base Algorithm 6 Write an algorithm to perform a SEARCH. Get Search
Let FOUND = False
LOOP Until (FOUND Or No_More_Values)
Get Value
If (Value = Search)
Let FOUND = True
Finish Loop
If FOUND
Give Value
Else
Give “Not Found”

28. Algorithm 3.4
Write an algorithm to find the average of all positive numbers given by the user.
Name: AVGPOS
Givens: N
Change: None
Results: Avg
Intermediates:
Again, Sum, Count
Definition:
Avg := AVGPOS(N)
Method
Let Sum = 0
Let Count = 0
Loop
Get N
If (N > 0)
Let Sum = Sum + N
Let Count = Count + 1
Get Again
Finish Loop When Not(Again)
Let Avg = Sum/Count
Give Avg

29. Trace 3.3
LN Sum Count N Avg Again Test 1,
(1>0)
6 1
Yes
Not(Yes)
(-5>0)
(5>0)
6 6
(3>0)
6 9 No
Not(No)
11 Output 3
Trace algorithm 3.4 when the user enters only the numbers 1, -5, 5 and 3
(1) Let Sum = 0
(2) Let Count = 0
(3) Loop
(4) Get N
(5) If (N > 0)
(6) Let Sum = Sum + N
(7) Let Count = Count + 1
(8) Get Again
(9) Finish Loop When Not(Again)
(10) Let Avg = Sum/Count
(11) Give Avg

30. Algorithm 3.5
Write an algorithm to find the largest of 5 numbers (range ).
Name: MAX5
Givens: N
Change: None
Results: Max
Intermediates:
Count
LastCount (Constant)
Definition:
Max := Max5(N)
Method
Set LastCount = 5
Let Max = -1
Let Count = 1
Loop When (Count <= LastCount)
Get N
If (N > Max)
Let Max = N
Let Count = Count + 1
Finish Loop
Give Max

31. LN Max Count LC N Test
1,2,
(1<=5)
(1>-1)
(2<=5)
(5>1)
(3<=5)
(8>5)
(4<=5)
(3>8)
(5<=5)
(2>8)
(6<=5)
10 Output 8
Trace 3.4
Trace algorithm 3.5 when the user enters only the numbers 1,5,8,3 and 2
(1) Set LastCount = 5
(2) Let Max = -1
(3) Let Count = 1
(4) Loop When (Count <= 5)
(5) Get N
(6) If (N > Max)
(7) Let Max = N
(8) Let Count = Count + 1
(9) Finish Loop
(10) Give Max

32. Additional Materials

33. Flow Charts

34. Flow Charts The Diamond symbol is reused, to test the condition.
At the end of the block, the flow will reverse itself back to the top of the loop
Note the Test can be at the bottom or the top as stated previously

35. Algorithm 3.1(a) Name: SUM100 Givens: N Change: None Results: Total
Intermediates: Count
Definition: Total := SUM100(N)

36. Algorithm 3.1(b) Name: SUM100 Givens: N Change: None Results: Total
Intermediates: Count
Definition: Total := SUM100(N)

37. Algorithm 3.2 Name: SUMN Givens: N Change: None Results: Sum
Intermediates: Value
Definition: Sum := SUMN(N)

38. Algorithm 3.3 Name: AVERAGE10 Givens: N Change: None Results: AVG
Intermediates: Count, Sum
Again
Definition:
AVG = AVERAGE10(N)

39. Algorithm 3.4 Name: AVGPOS Givens: N Change: None Results: Avg
Intermediates:
Again, Sum, Count
Definition:
Avg := AVGPOS(N)

40. Algorithm 3.5 Name: MAX5 Givens: N Change: None Results: Max
Intermediates:
Count
LastCount (Constant)
Definition:
Max := Max5(N)

41. NSD

42. NSD Create an L or Γ The test, while or until, goes in the row part
The column controls what block is to be repeated
NB this is done with two cells (1 row, 1 column) with no boarder between the two

43. Algorithm 3.1(a) Name: SUM100 Givens: N Change: None Results: Total
Intermediates: Count
Definition: Total := SUM100(N)

44. Algorithm 3.1(b) Name: SUM100 Givens: N Change: None Results: Total
Intermediates: Count
Definition: Total := SUM100(N)

45. Algorithm 3.2 Name: SUMN Givens: N Change: None Results: Sum
Intermediates: Value
Definition: Sum := SUMN(N)

46. Algorithm 3.3 Name: AVERAGE10 Givens: N Change: None Results: AVG
Intermediates: Count, Sum
Again
Definition:
AVG = AVERAGE10(N)

47. Algorithm 3.4 Name: AVGPOS Givens: N Change: None Results: Avg
Intermediates:
Again, Sum, Count
Definition:
Avg := AVGPOS(N)

48. Algorithm 3.5 Name: MAX5 Givens: N Change: None Results: Max
Intermediates:
Count
LastCount (Constant)
Definition:
Max := Max5(N)

49. Homework

50. In your homework (Lecture 9), you developed algorithms, and traces
reversing the digits in a three digit number and adding that number to 500
determining the eldest of 2 people
calculating a sales commission For each of these questions, revise the algorithm to:
Run the reversing algorithm multiple times until the user enters the value 999
Run the eldest algorithm until the user indicates “no” to the question “Do you want to continue?”
Run the sales commission algorithm for exactly 10 sales representatives

51. Develop an algorithm to assist a clerk in determining some statistics about students. For each student, she enters the name, gender (M or F), age and marital status (M or S). She wants to determine the number of married men, married women, single women and eligible bachelors (single men over 25). Each time she has completed entry of data for a student, the algorithm should give her a chance to indicate whether she has entered the data for all of the students.

52. Write an algorithm to determine the closing balance for a teller
Write an algorithm to determine the closing balance for a teller. The teller enters his opening balance and then a number of transactions. Deposits are entered as positive numbers and withdrawals are entered as negative numbers. He also needs to calculate the number of deposits and the number of withdrawals. The teller indicates that all transactions have been entered by entering a transaction with a value of 0.

53. Write an algorithm to calculate and display the total gross earnings, tax payable, medical deduction and net earnings for all employees.
The user will input the hours worked and the hourly rate of pay for each employee. The gross earnings for each employee can be calculated from this information.
The net earnings are calculated by subtracting the tax payable and medical deductions from the gross earnings. Tax payable is 20% of gross pay for the first $300, 30% for the next $200 and 40% thereafter. The medical deduction is calculated as 1% of gross pay.
The user will indicate that all employee information has been entered by entering hours worked as 999.