Neal Stublen [email protected]. Human Decisions Think about a decision you've made today? How did you arrive at that decision? Was it a black-and-white.
Apr 01, 2015
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MAKING DECISIONS
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 decisionIs 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 evaluate4 + 3x / 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:
Purchase Discount
$0.00 to $25.00 5%
$25.01 to $50.00 10%
$50.01 to $100.00 15%
Over $100.00 20%
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
endif
Nested Decisions
if condition1 then
if condition2 then
take action
endif
endif
if condition1 AND condition2 then
take action
endif
AND Operatorif x AND y then
do something
endif
“x AND y” is a boolean expression that can be evaluated as true or false
x y x AND y
True True True
True False False
False True False
False False False
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.
Purchase Discount
$0.00 to $25.00 5%
$25.01 to $50.00 10%
$50.01 to $100.00 15%
Over $100.00 20%
OR Operatorif x OR y then
do something
endif
“x OR y” is a boolean expression that can be evaluated as true or false
x y x OR y
True True True
True False True
False True True
False False 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 < 12 OR 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 <=12 OR age >= 65 AND not Friday then
discount = 0.10
endif
A twelve year old still gets the discount on Friday.
if (age <=12 OR 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.
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