Neal Stublen

Human Decisions  Think about a decision you've made today?  How did you arrive at that decision?  Was it a black-and-white decision for you?  Our decisions can be complex?

Computer "Decisions"  Computer decisions always reduce down to simple logic comparisons  Something is true or something is false  It has a boolean value of true or false  The decision block in a flow diagram requires a yes/no decision Is the light red? Is the light yellow? Is the light green?

Boolean Decisions  We use boolean expressions to determine a true or false condition  We implement a selection structure  Dual-alternative selection (if-then-else)  Single-alternative selection (if-then)

If-Then  If the condition is true, then perform an action or a sequence of actions if condition then action endif if time is 6pm then begin class endif

If-Then-Else  If the condition is true, then perform an action or a sequence of actions  Else perform a different action or sequence of actions if condition then action else another action endif if time is 6pm then begin class else wait endif

Boolean Expressions  An expression is just a statement the computer will evaluate x / 4  A boolean expression will be evaluated as either true or false  Relational operators are used in boolean expressions

Relational Operators  Equivalence, = or ==  Greater than, >  Less than, <  Greater than or equal to, >=  Less than or equal to, <=  Not equal to, <> or !=  Also called comparison operators

Relational Operators if customerAge >= 65 then discount = 0.10 else discount= 0.0 endif if customerAge <65 then discount = 0.0 else discount = 0.10 endif

Negation Operator  A negation operator reverses the logic of a true or false expression (NOT or !) if age >= 21 then allow purchase endif if NOT age >= 21 then refuse purchase endif

Example  What logic can we use to implement the following discount table: PurchaseDiscount $0.00 to $25.005% $25.01 to $ % $50.01 to $ % Over $ %

Implementing Minimal Conditions  Selecting from a group of ranges, the last check is never necessary  If the table is complete, we rule out one possibility with each check  If total is not > 100 and total is not > 50 and total is not > 25, then total must be <= 25.

Compound Conditions  Sometimes we need more complex logic to make a decision if I’m speeding then if I see a police car then slow down immediately endif

Nested Decisions if condition1 then if condition2 then take action endif if condition1 AND condition2 then take action endif

AND Operator if x AND y then do something endif “x AND y” is a boolean expression that can be evaluated as true or false xyx AND y True False TrueFalse

Short-Circuit Evaluation if x AND y then do something endif If we know x is false, we know x AND y is also false. There’s no need to evaluate y.

Short-Circuit Example if age > 12 AND age < 65 then movieDiscount = 0.0 endif If age is less than or equal to twelve, the computer will not need to determine if age is greater than 65.

Example  How would we implement the following discount table:  On Sundays, senior citizens receive an additional 5% discount. PurchaseDiscount $0.00 to $25.005% $25.01 to $ % $50.01 to $ % Over $ %

OR Operator if x OR y then do something endif “x OR y” is a boolean expression that can be evaluated as true or false xyx OR y True FalseTrue FalseTrue False

Short-Circuit Evaluation? if x OR y then do something endif Is there a short-circuit evaluation for the OR operator? If we know x is true, we know x OR y is also true. There’s no need to evaluate y.

OR Efficiency if age < 12 then movieDiscount = 0.10 endif if age > 65 then movieDiscount = 0.10 endif if age 65 then movieDiscount = 0.10 endif

AND/OR Precedence  AND operator is always evaluated before the OR operator  c1 OR c2 AND c3 OR c4  c1 OR (c2 AND c3) OR c4

Precedence Example if age = 65 AND not Friday then discount = 0.10 endif A twelve year old still gets the discount on Friday. if (age = 65) AND not Friday then discount = 0.10 endif Parentheses always clarify intention.

Summary  Boolean expressions  Relational operators  AND Logic  OR Logic  Selection within ranges  AND/OR precedence

Date Validation  What logic would we need to validate a user’s date input?  The user enters separate values for the month, day, and year.