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139 lines
4.4 KiB
Markdown
139 lines
4.4 KiB
Markdown
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# Lecture for February 6th
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## If Statements -- Cont.
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Inside the parenthesis of the `if` statement must be a boolean expression. This is an expression that evaluates to either `true` or `false`. We can do more complex boolean expressions through logical operators.
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## Logical Operators
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NOT `!a` this is true when `a` is false
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AND `a && b ` this is true when both operands are true
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OR `a || b` this is true when either a is true OR b is true
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## Truth Tables
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- Show all possible outcomes
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- It breaks the expression down into parts
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### Not
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Let's look at the most simplest case. Not.
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| a | !a |
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| ----- | ----- |
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| true | false |
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| false | true |
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### AND
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| a | b | a && b |
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| ----- | ----- | ------ |
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| true | true | true |
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| true | false | false |
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| false | true | false |
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| false | false | false |
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Notice here that `a && b` is only true when both `a` and `b` are true.
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### OR
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| a | b | a \|\| b |
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| ----- | ----- | -------- |
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| true | true | true |
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| true | false | true |
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| false | true | true |
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| false | false | false |
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Notice here that `a || b` is only false when both `a` and `b` are false.
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## Precedence (Order of Operations)
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| | |
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| --------------------------------- | ------------------- |
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| Parenthesis | `()` |
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| Logical Not | `!` |
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| Arithmetic Operators | `*` `/` `%` `+` `-` |
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| Relational Operators | `<` `<=` `>` `>=` |
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| Equality and Inequality operators | `==` `!=` |
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| Logical AND | `&&` |
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| Logical OR | `||` |
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## Playing with Truth Tables Example
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### a && !b
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| a | b | !b | a && !b |
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| ----- | ----- | ----- | ------- |
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| true | true | false | false |
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| true | false | true | true |
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| false | true | false | false |
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| false | false | true | false |
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### !a || b
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| a | b | !a | !a \|\| b |
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| ----- | ----- | ----- | --------- |
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| true | true | false | true |
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| true | false | false | false |
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| false | true | true | true |
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| false | false | true | true |
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### !(a || b && c)
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| a | b | c | b && c | a \|\| (b && c) | !(a \|\| b && c) |
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| ----- | ----- | ----- | ------ | --------------- | ---------------- |
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| true | true | true | true | true | false |
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| true | true | false | false | true | false |
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| true | false | true | false | true | false |
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| false | true | true | true | true | false |
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| true | true | false | false | true | false |
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| true | false | true | false | true | false |
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| false | true | true | true | true | false |
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| false | false | false | false | false | true |
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### !a || b && c
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| a | b | c | !a | b && c | !a \|\| b && c |
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| ----- | ----- | ----- | ----- | ------ | -------------- |
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| true | true | true | false | true | true |
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| true | true | false | false | false | false |
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| true | false | true | false | false | false |
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| false | true | true | true | true | true |
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| true | false | false | false | false | false |
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| false | true | false | true | false | true |
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| false | false | true | true | false | true |
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| false | false | false | true | false | true |
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## Distributive Property of Logical Operators
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The following statements are equivalent
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`!(a && b)` is equivalent to `!a || !b`
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Notice how when you distribute the `!` you have to flip the operand as well. `&&` becomes `||`
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Same is true for the following example
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`!(a || b)` is equivalent to `!a && !b`
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`!(a || b && c)` is equivalent to `!a && (!b || !c)`
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## Short Circuit Evaluation
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In an `&&` (AND) statement, if the left side is `false`, there is no need to evaluate the right side. Since it's going to be false anyways!!
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```java
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false && true; // FALSE no matter what the right side is
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```
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In an `||` (OR) statement, if the left side is `true, there is no need to evaluate the right side. Since it's going to be true by default!!
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```java
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true || false; // TRUE no matter what the right side is
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```
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Java takes this shortcut by default for efficiency reasons
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