6 problem solving with decisions

Data Structures and Algorithms

The Decision
Logic Structure

Some examples of conditional expressions are as
follows :

1. A < B (A and B are the same the data type)
2. X + 5 >=Z (X and Z are numeric data)
3. E < 5 or F > 10 (E and F are numeric data)
4. DATAOK (DATAOK is a logical datum)

Problem Solving with Decisions *Property of STI
Page 1 of 40


The Decision
Logic Structure

Multiple IF/THEN/ELSE
There are three types of decision logic you will use to
write algorithms for solutions consisting of more than
one decision. These types of decision logic include:

· Straight-through logic
· Positive logic
· Negative Logic
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The Decision
Logic Structure

@ Single Condition – Two Possible Actions or Sets of
Actions

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The Decision
Logic Structure

Straight-through logic
@ Means that all of the decisions are processed
sequentially, one after the other.
@ There is no ELSE part of the instruction; the FALSE
branch always goes to the next decision, and the
TRUE branch goes to the next decision after the
instructions for the TRUE branch have been
processed.

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The Decision
Logic Structure

Positive Logic
@ Allows the flow of the processing to continue
through the module instead of processing
succeeding decisions, once the resultant of a
decision is true.

@ Whenever the resultant is FALSE (the ELSE part of
the decision), another decision in the sequence is
processed until the resultant is TRUE, or there are
no more decisions to process.

@ At that time, the FALSE branch processes the
remaining instructions.

Page 5 of 40


The Decision
Logic Structure

Negative Logic
@ similar to positive logic except that the flow of the
processing continues through the module when the
resultant of a decision is FALSE

@ whenever the resultant is TRUE, another decision
is processed until the resultant is FALSE, or there
are no more decisions to process

@ at that time, the TRUE branch processes the
remaining instructions

@ the hardest to use and understand

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The Decision
Logic Structure

Using Straight-through logic
Problem: Find the amount to charge people of varying ages
for a food ticket. When the person is under 16, the charge is
P7; when the person is 65 or over, the charge is P5; all others
are charged P10. The conditions are the following :

AGE CHARGE
AGE < 16 7
AGE >=16 and AGE < 65 10
AGE >=65 5
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The Decision
Logic Structure

Solution :

Algorithm Flowchart
A

IF AGE < 16
THEN
T CHARGE = 7
IF T
AGE < 16
IF AGE >= 16 AND AGE <65
THEN
T CHARGE = 10 Charge = 7

IF AGE >= 65 F
THEN
T CHARGE = 5 IF
AGE >= 16 T
and
AGE < 65

Charge = 10

F

IF T
AGE >= 65

Charge = 10

F

B

Page 8 of 40


The Decision
Logic Structure

Problem: Change the value of X to 0 when X becomes
greater than 100, and to change the value of Y to 0
when Y becomes greater than 250

Algorithm Flowchart
A

IF X < 100
THEN IF T
T X = 10 X > 100

IF Y > 250 X=0

THEN
T F
Y=0

IF T
Y > 250

Y=0

F

B

Page 9 of 40


The Decision
Logic Structure

Using Positive Logic
Problem: Find the amount to charge people of varying
ages for a food ticket. When the person is under 16,
the charge is P7; when the person is 65 or over, the
charge is P5; all others are charged P10. The conditions
are the following :
Algorithm
IF AGE <16
THEN
CHARGE = 7

ELSE
IF AGE < 65
THEN
CHARGE = 10
ELSE
CHARGE = 5

Page 10 of 40


The Decision
Logic Structure

Flowchart

A

F IF T
AGE < 16

F IF T
AGE < 65 CHARGE = 7

CHARGE = 5 CHARGE = 10

B

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The Decision
Logic Structure

Problem: Calculate the commission rate for a
salesperson, given the amount of sales. When the
salesperson has sold less than or equal to 2,000 worth
of goods, the commission is 2%. When the sales total is
more than 2,000 and less than or equal to 4,000, the
commission is 4%. When sales total is more than 4,000
and less than or equal to 6,000, the commission is 7%.
When the person has sold more than 6,000 the
commission is 10%. The conditions are the following:

SALES COMMISSION

<=2000 .02
2001 – 4000 .04
4001 – 6000 .07
> 6000 .10

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The Decision
Logic Structure

Solution 1: Algorithm
IF SALES <= 2000
THEN
COMMISSION = .02
T ELSE
IF SALES <= 4000
THEN
COMMISSION = .04
T
ELSE
IF SALES <= 6000
THEN
F T
COMMISSION = .07
F ELSE
F COMMISSION = .1

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The Decision
Logic Structure

Solution 1: Flowchart

A

F T
IF
SALES <=2000

F T COMMISSION =
IF .02
SALES <=4000

COMMISSION
F IF T = .04
SALES <=6000

COMMISSION COMMISSION
= .1 = .07

B

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The Decision
Logic Structure

Solution 1: Test

1. TEST FOR 3. TEST FOR
SALES = 1500 SALES = 5500
IS SALES <= 2000 IS SALES <= 2000
TRUE FALSE
COMMISSION = .02 IS SALES <= 4000
FALSE
2. TEST FOR IS SALES <= 6000
SALES = 3500 TRUE
IS SALES <= 2000 COMMISSION = .07
FALSE
IS SALES <= 4000 4. TEST FOR
TRUE SALES = 7500
COMMISSION = .04 IS SALES <= 2000
FALSE
IS SALES <= 4000
FALSE
IS SALES <= 6000
TRUE
COMMISSION = .1

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The Decision
Logic Structure

Solution 2: Algorithm
IF SALES > 6000
THEN
COMMISSION = .1
T ELSE
IF SALES > 4000
THEN
COMMISSION = .07
T
ELSE
IF SALES > 2000
THEN
F T
COMMISSION = .04
F ELSE
F COMMISSION = .02

Page 16 of 40


The Decision
Logic Structure

Solution 2: Flowchart
A

F T
IF
SALES > 6000

F T COMMISSION =
IF .1
SALES > 4000

COMMISSION
F IF T = .07
SALES > 2000

COMMISSION COMMISSION
= .02 = .04

B

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The Decision
Logic Structure

Solution 2: Test

1. SALES = 1500 3. SALES = 5500
IS SALES > 6000 IS SALES > 6000
FALSE FALSE
FALSE TRUE
IS SALES > 2000 COMMISSION = .07
FALSE
COMMISSION = .02

2. SALES = 3500 4. SALES = 7500
FALSE TRUE
IS SALES > 4000 COMMISSION = .1
FALSE
IS SALES > 2000
TRUE
COMMISSION = .04

Page 18 of 40


The Decision
Logic Structure

Using Negative Logic
@ Negative Logic is the hardest for most people to
comprehend because they do not think in negative
terms.

@ In general when you use negative logic you are
telling the computer to process another decision
when the resultant condition is TRUE;

@ If the resultant is FALSE, then the computer
processes a consequent set of instructions and then
continues processing the module.

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The Decision
Logic Structure

Negative Logic Solution 1: Algorithm

IF AGE >= 16
THEN
IF AGE >= 65
THEN
CHARGE = 5
ELSE
CHARGE = 10

ELSE
CHARGE = 7

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The Decision
Logic Structure

Negative Logic Solution 1: Flowchart

A

F T
IF
AGE >= 16

F T
CHARGE = 7 IF
AGE >= 16

CHARGE = 10 CHARGE = 5

B

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The Decision
Logic Structure

Negative Logic Solution 2: Algorithm

IF SALES > 2000
THEN
IF SALES > 4000
THEN
IF SALES > 6000
THEN
COMMISSION = .1
ELSE
COMMISSION = .07

ELSE
COMMISSION = .04

ELSE
COMMISSION = .02

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The Decision
Logic Structure

Negative Logic Solution 2: Flowchart
A

IF
SALES > 2000

COMMISSION =
.02 IF
SALES > 4000

COMMISSION =
.04 IF
SALES > 6000

COMMISSION = COMMISSION =
.07 .01

B

Page 23 of 40


The Decision
Logic Structure

Negative Logic Solution 2: TEST

1. SALES = 1500 3. SALES = 5500
FALSE TRUE
COMMISSION = .02 IS SALES > 4000
TRUE
2. SALES = 3500 IS SALES > 6000
IS SALES > 2000 FALSE
TRUE COMMISSION = .1
IS SALES > 4000
FALSE 4. SALES = 7500
COMMISSION = .04 IS SALES > 2000
TRUE
IS SALES > 4000
TRUE
IS SALES > 6000
TRUE
COMMISSION = .1

Page 24 of 40


The Decision
Logic Structure

Another Set-Up: Algorithm

IF SALES <= 6000
THEN
IF SALES <= 4000
THEN
IF SALES <= 2000
THEN
COMMISSION = .02
ELSE
COMMISSION = .04
ELSE
COMMISION = .07
ELSE
COMMISSION = .1

Page 25 of 40


The Decision
Logic Structure

Another Set-Up: Flowchart
A

F T
IF
SALES <= 6000

CHARGE = .1 F T
IF
SALES <= 4000

COMMISSION =
.07
F IF T
SALES <= 2000

COMMISSION = COMMISSION =
.04 .02

B

Page 26 of 40


The Decision
Logic Structure

Another Set-Up: Test
1. SALES = 1500 3. SALES = 5500
TRUE TRUE
TRUE FALSE
TRUE
COMMISSION = .02

2. SALES = 3500 4. SALES = 7500
TRUE FALSE
TRUE
IS SALES <= 2000
FALSE
COMMISSION = .04

Page 27 of 40


The Decision
Logic Structure

Logic Conversion

To convert from positive logic to negative logic or vice
versa, do the following :

1. Change all < to >=
2. Change all <= to >
3. Change all > to <=
4. Change all >= to <
5. Change all = to <>
6. Change all <> to =
7. Interchange all of the THEN set of instructions
with the corresponding ELSE set of instructions.

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The Decision
Logic Structure

Conversion from Positive to Negative Logic

Page 29 of 40


The Decision
Logic Structure

Which Decision Logic?
To analyze which type of decision logic would be most
efficient for a particular solution, answer the following
questions:

1. Which type would make the solution most readable?
2. Which type would make the solution the easiest
to maintain or change?
3. Which would require the fewest test when you
don’t know anything about the data?
4. Which would require the fewest test when you’re
given some data?

Page 30 of 40


The Decision
Logic Structure

Four ways to Design a Set of Conditions

Page 31 of 40


The Decision
Logic Structure

Decision Tables
A decision table consists of four parts:
@ The conditions.
@ The actions.
@ The combinations of TRUE and FALSE for the conditions.
@ The action to be taken or the consequences for each
combination of conditions.

The four steps to develop a flowchart from the decision table
are :

@ Draw all decisions in flowchart form.
@ Compare the true and false sides of each decision, starting
with the first one.
@ Eliminate any decisions that have the same instructions
on both the true and false sides, keeping the true
consequence or action.
@ Redraw the flowchart.

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The Decision
Logic Structure

Decision Table Format

Page 33 of 40


The Decision
Logic Structure

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The Decision
Logic Structure

Elimination of Conditions

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The Decision
Logic Structure

Final Flowchart

Page 36 of 40


The Decision
Logic Structure

Decision Table

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The Decision
Logic Structure
Starting Flowchart

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The Decision
Logic Structure
Elimination of Condition

Page 39 of 40


The Decision
Logic Structure

Final Flowchart

Page 40 of 40

6 problem solving with decisions

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6 problem solving with decisions