PROBLEM SOLVING WITH
DECISIONS
Chapter 6
The decision logic structure




Uses the If/Then/Else instruction .
It tells the computer that If a condition is true , then
execute a set of instructions, or Else execute another
set of instructions.
The else part is optional
As there is not always a set of instruction if the
condition are false .
Common Forms of decision structure
T
F
•If <condition (s)>
•Then
•<True instructions>
•Else
•<False instructions>
A condition can be one of four things :
•Logical expression: (AND, OR NOT)
• relational expression(>, <=, <, >=,…..)
•Variable logic data type.
•Combination of Relational , logic and mathematical operators.
•Note: the condition part can combine more than one condition using the
logical operators.
Examples .
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


A < B ( a, b the same data type numeric or
character )
X + 5 > = Z ( X , Z are numeric )
E < 5 OR F < 10
DataOk ( is logical datum )
The decision logic structure

Single condition :
A
simple decision with only one condition and one
action or set of actions .

Multiple condition :
 Decisions
in which you have multiple conditions that
lead to one action or set of actions .
 You will use logical operators to connect the conditions .
Single condition
one possible action or set of action

write an algorithm and corresponding flowchart that
read a student grade on a test which is out of 10,
then alerts the student if his grade is under 4.
Algorithm
Flowchart
StudentAlert()
1.Integer grade
2.Enter
grade
3.If grade < 4
1. Print “Alert: You must study hard”
4.end
StudentAlert()
Integer grade
Enter
F
grade
If grade <
4
T
Print “Alert: You
must study hard”
End
Single Condition
one Possible Actions or Sets of Actions

assume you are calculating pay at an hourly rate ,
and overtime pay ( over 40 hours ) at 1.5 times the
hourly rate .
Single Condition
Two Possible Actions or Sets of Actions
The Multiple If/Then/Else

Three type of decision logic used to for solution
consisting for more than one decision:
 Straight-through
 Positive
Logic
 Negative Logic
Logic
The Multiple If/Then/Else
1. Straight-through logic :
 All
of the decisions are processed sequentially , one
after the other.
2. positive logic :
 Not
all of the instruction are processed
 the flow of the processing continues through the module
when the resultant of a decisions is true.
 If the resultant is false another decision is processed
until the resultant is true or there is no decision to be
processed .
The Multiple If/Then/Else
3. negative logic :
the flow of the processing continues through the module
when the resultant of a decisions is false .
 when the resultant is true , another decision is processed
until the resultant is false or there is no decision to be
processed .

The Nested Decision
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



In algorithms containing multiple decisions, you may
write nested If/Then/Else instructions.
Decisions using positive and negative logic use nested
If/Then/Else instructions.
Decisions using straight-through logic do not.
Nested If/Then/Else instructions in which each level
of a decision is embedded in a level before it.
Use the nested If/then/Else when one of several
possible actions or set of action are to be processed .
Nested If/Then/Else Instructions
1.Straight-through

All decisions (Conditions) are processed sequentially,
one after another.
There is no else part of the instructions .




is required when all the decisions have to be
processed , and thy are independent of each other .
The false branch always goes to the next decision.
The true branch goes to the next decision after the
instruction for the true have been processed .
Least efficient, why?
 Because
all the decisions must be processed .
1- Straight-Through Logic Example 1
Write an algorithm to change the value of X to 0 when X becomes
greater then 100, and to change the value of Y to 0 when Y
becomes greater then 250.
X > 100
X=0
Y > 250
Y=0
Straight-Through Logic – Example 2
1- Straight-Through Logic Example 2
Write an algorithm to find the amount to charge people of varying
ages for a concert ticket. When a person is under 16, the charge is
$7; when the person is 65 or over, the charge is $5; all others are
charged $10.
Age
Charge
Age < 16
7
Age >= 16 AND Age < 65
10
Age >= 65
5
Straight-Through
Logic
2. Positive Logic

The easiest type to use. Why??!!
 It

is way we think
Positive logic works in the following manner:
 If

 If

the condition is true 
the computer follows a set of instructions & continues processing.
the condition is false 
the computer process another decision until the resultant is true, or
there are no more decisions to process.
2. Positive Logic Example 1
Write an algorithm and corresponding flowchart to find the amount
to charge people of varying ages for a concert ticket. When a
person is under 16, the charge is $7; when the person is 65 or over,
the charge is $5; all others are charged $10.
Age
Charge
Age < 16
7
Age >= 16 AND Age < 65
10
Age >= 65
5
Positive Logic – Example 1
2. Positive Logic Example 2
Design an algorithm that Calculate the commission rate of a
sales person, given the amount of sales. When the salesperson
has sold less than or equal to $2000, the commission is 2%. When
the sales total is more than $2000, and less than or equal to
$4000, the commission is 4%. When the sales total is more than
$4000, and less than or equal to $6000, the commission is 7%.
When the person has sold more than $6000, the commission is
10%.
SALES
Commission
≤ 2000
.02
2001 - 4000
.04
4001 – 6000
.07
> 6000
.10
Positive Logic – Example 2
The Conditions in example-2
Set Up in a Different Way
3. Negative Logic

Negative logic works in the following manner:
 If

 If


the condition is true 
The computer process another decision until the resultant is false, or
there are no more decisions to process.
the condition is false 
The computer follows a set of instructions & continues processing.
It is often advantageous to use negative logic to decrease
the number of tests or to improve the readability of a
program .
3. Negative Logic Example 1
Write an algorithm and corresponding flowchart to find the amount
to charge people of varying ages for a concert ticket. When a
person is under 16, the charge is $7; when the person is 65 or over,
the charge is $5; all others are charged $10.
Age
Charge
Age < 16
7
Age >= 16 AND Age < 65
10
Age >= 65
5
Negative Logic – Example 1
age ˃= 16
age ˃= 65
age ˃= 16
age ˃= 65
2. Negative Logic Example 2
Design an algorithm that Calculate the commission rate of a
sales person, given the amount of sales. When the salesperson
has sold less than or equal to $2000, the commission is 2%. When
the sales total is more than $2000, and less than or equal to
$4000, the commission is 4%. When the sales total is more than
$4000, and less than or equal to $6000, the commission is 7%.
When the person has sold more than $6000, the commission is
10%.
SALES
Commission
≤ 2000
.02
2001 - 4000
.04
4001 – 6000
.07
> 6000
.10
Negative Logic – Example 2
The Conditions in example-2 Set Up
in a Different Way
Logic Conversion

If there are no instruction for the true section of decision
instruction , Then it is better to convert the logic type :
Change all < to >=
 Change all <= to >
 Change all > to <=
 Change all >= to <
 Change all = to <>
 Change all <> to =
 Interchange all of the Then set of instructions with the
corresponding Else set of instructions.

Conversion from Positive Logic to Negative Logic
Conversion from Positive Logic to Negative Logic