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 If <condition (s)> Then <True instructions> Else <False instructions> T F 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 . 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.

Print “Alert: You must study hard” Flowchart Algorithm StudentAlert() Integer grade Enter grade If grade < 4 Print “Alert: You must study hard” end StudentAlert() Integer grade Enter grade F 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 Logic Positive Logic Negative 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 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 It is way we think If the condition is true  The easiest type to use. Why??!! It is way we think Positive logic works in the following manner: If the condition is true  the computer follows a set of instructions & continues processing. If 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 If the condition is true  Negative logic works in the following manner: If the condition is true  The computer process another decision until the resultant is false, or there are no more decisions to process. If 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

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