Java Building Programs
Chapter 5 Lecture 5-3: Boolean Logic reading: 5.2
self-check: #11 - 17 exercises: #12 videos: Ch. 5 #2
Copyright 2009 by Pearson Education
Midterm Logistics
Bring your UW Student ID card!!
Will check your ID while you're leaving Bring your stuff with you while you exit (don't go back to seat)
60 minute exam
-10 if you start early or try to write after time
Any paper notes allowed, but NO ELECTRONICS
Book OK, section handouts OK, past exams + solutions OK, etc. NO CALCULATORS! NO LAPTOPS!
Aiming for a median of 80
Will be a curve if the exam is too hard, will not have a hurtful
curve if exam is too easy
Copyright 2009 by Pearson Education
2
About the Exam
100 pts, 20% of course grade
Non-programming 61 pts
Expressions (10), parameter mystery (12), if/else simulation (12), while loop simulation (12), assertions (15)
Easy Programming 15 pts Medium Programming 15 pts Really Hard Programming 9 pts
Topics covered: Chapters 1-5
Topics not covered: see website!
Includes Graphics, printf, do/while, break
Copyright 2009 by Pearson Education
3
More Exam Info
Non-programming questions
You do not need to show your work You are not allowed to use calculators (e.g. on expressions)
Programming questions
Are not graded on style, only external correctness Must write valid Java code that would compile
Will not grade comments or pseudo-code Do NOT use abbreviations Do not have to write import statements Write as much as you can: even a method header and the beginnings of a while loop could earn you partial points!
Substantial partial credit is given for partially working solutions
More info on course website!
Copyright 2009 by Pearson Education
4
Logical assertions
reading: 5.5 self-checks: #26-28
Copyright 2009 by Pearson Education
Logical assertions
assertion: A statement that is either true or false.
Examples: Java was created in 1995. The sky is purple. 23 is a prime number. 10 is greater than 20. x divided by 2 equals 7. (depends on the value of x)
An assertion might be false ("The sky is purple" above), but it is still an assertion because it is a true/false statement.
Copyright 2009 by Pearson Education
6
Reasoning about assertions
Suppose you have the following code:
if (x > 3) { // Point A x--; } else { // Point B x++; } // Point C
What do you know about x's value at the three points?
Is x > 3? Always? Sometimes? Never?
Copyright 2009 by Pearson Education
7
Assertions in code
We can make assertions about our code and ask whether
they are true at various points in the code.
Valid answers are ALWAYS, NEVER, or SOMETIMES. System.out.print("Type a nonnegative number: "); double number = console.nextDouble(); (SOMETIMES) // Point A: is number < 0.0 here?
while (number < 0.0) { (ALWAYS) // Point B: is number < 0.0 here? System.out.print("Negative; try again: ");
number = console.nextDouble(); // Point C: is number < 0.0 here? } // Point D: is number < 0.0 here? (NEVER) (SOMETIMES)
Copyright 2009 by Pearson Education
8
Reasoning about assertions
Right after a variable is initialized, its value is known:
int x = 3; // is x > 0?
ALWAYS
In general you know nothing about parameters' values:
public static void mystery(int a, int b) { // is a == 10? SOMETIMES
But inside an if, while, etc., you may know something:
public static void mystery(int a, int b) { if (a < 0) { // is a == 10? NEVER ... } }
Copyright 2009 by Pearson Education
9
Assertions and loops
At the start of a loop's body, the loop's test must be true:
while (y < 10) { // is y < 10? ... }
ALWAYS
After a loop, the loop's test must be false:
while (y < 10) { ... } // is y < 10? NEVER
Inside a loop's body, the loop's test may become false:
while (y < 10) { y++; // is y < 10? } SOMETIMES
Copyright 2009 by Pearson Education
10
"Sometimes"
Things that cause a variable's value to be unknown (often leads to "sometimes" answers):
reading from a Scanner reading a number from a Random object a parameter's initial value to a method
If you can reach a part of the program both with the answer being "yes" and the answer being "no", then the correct answer is "sometimes".
If you're unsure, "Sometimes" is a good guess.
Often around 1/2 of the correct answers are "sometimes."
Copyright 2009 by Pearson Education
11
Assertion example 1
public static void mystery(int x, int y) { int z = 0; // Point A while (x >= y) { // Point B x = x - y; // Point C z++; } // Point D
Point A Point B Point C Point D Point E
Which of the following assertions are true at which point(s) in the code? Choose ALWAYS, NEVER, or SOMETIMES.
x < y
SOMETIMES NEVER SOMETIMES SOMETIMES ALWAYS
x == y
SOMETIMES SOMETIMES SOMETIMES SOMETIMES NEVER
z == 0
ALWAYS SOMETIMES SOMETIMES NEVER SOMETIMES
}
// Point E System.out.println(z);
Copyright 2009 by Pearson Education
12
Assertion example 2
public static int mystery(Scanner console) { int prev = 0; int count = 0; int next = console.nextInt(); // Point A while (next != 0) { // Point B if (next == prev) { Which of the following assertions are // Point C true at which point(s) in the code? count++; Choose ALWAYS, NEVER, or SOMETIMES. } prev = next; next = console.nextInt(); next == 0 prev == 0 next == prev // Point D } SOMETIMES Point A SOMETIMES ALWAYS // Point E return count; SOMETIMES SOMETIMES Point B NEVER } NEVER ALWAYS Point C NEVER Point D Point E
SOMETIMES ALWAYS NEVER SOMETIMES SOMETIMES SOMETIMES
Copyright 2009 by Pearson Education
13
Assertion example 3
// Assumes y >= 0, and returns x^y public static int pow(int x, int y) { int prod = 1; // Point A Which of the following assertions are while (y > 0) { true at which point(s) in the code? // Point B Choose ALWAYS, NEVER, or SOMETIMES. if (y % 2 == 0) { // Point C y > 0 y % 2 == 0 x = x * x; y = y / 2; Point A SOMETIMES SOMETIMES // Point D } else { SOMETIMES Point B ALWAYS // Point E ALWAYS = prod prod * x; Point C ALWAYS y--; SOMETIMES Point D ALWAYS // Point F } NEVER Point E ALWAYS } // Point G Point F SOMETIMES ALWAYS return prod; ALWAYS Point G NEVER
}
Copyright 2009 by Pearson Education
14
Boolean logic
reading: 5.2 self-check: #11 - 17 exercises: #12
Copyright 2009 by Pearson Education
Recap: Type boolean
boolean: A logical type whose values are true and false.
A test in an if, for, or while is a boolean expression.
boolean minor = (age < 21); if (minor) { System.out.println("Can't purchase alcohol!"); }
boolean expressions can be combined using logical operators:
Operator
&& || !
Description and or
Example
(2 == 3) && (-1 < 5) (2 == 3) || (-1 < 5) !(2 == 3)
Result
false true true
16
not
Copyright 2009 by Pearson Education
De Morgan's Law
De Morgan's Law: Rules used to negate or reverse boolean expressions.
Useful when you want the opposite of a known boolean test.
Original Expression
a && b a || b
Negated Expression
!a || !b !a && !b
Alternative
!(a && b) !(a || b)
Example:
Original Code
if (x == 7 && y > 3) { ... }
Copyright 2009 by Pearson Education
Negated Code
if (x != 7 || y <= 3) { ... }
17
"Boolean Zen", part 1
Students new to boolean often test if a result is true:
if (bothOdd(7, 13) == true) { ... } // bad
But this is unnecessary and redundant. Preferred:
if (bothOdd(7, 13)) { ... } // good
A similar pattern can be used for a false test:
if (bothOdd(7, 13) == false) { if (!bothOdd(7, 13)) {
Copyright 2009 by Pearson Education
// bad // good
18
"Boolean Zen", part 2
Methods that return boolean often have an if/else that returns true or false:
public static boolean bothOdd(int n1, int n2) { if (n1 % 2 != 0 && n2 % 2 != 0) { return true; } else { return false; } }
But the code above is unnecessarily verbose.
Copyright 2009 by Pearson Education
19
Solution w/ boolean variable
We could store the result of the logical test.
public static boolean bothOdd(int n1, int n2) { boolean test = (n1 % 2 != 0 && n2 % 2 != 0); if (test) { // test == true return true; } else { // test == false return false; } }
Notice: Whatever test is, we want to return that.
If test is true , we want to return true. If test is false, we want to return false.
Copyright 2009 by Pearson Education
20
Solution w/ "Boolean Zen"
Observation: The if/else is unnecessary.
The variable test stores a boolean value;
its value is exactly what you want to return. So return that!
public static boolean bothOdd(int n1, int n2) { boolean test = (n1 % 2 != 0 && n2 % 2 != 0); return test; }
An even shorter version:
We don't even need the variable test.
We can just perform the test and return its result in one step.
public static boolean bothOdd(int n1, int n2) { return (n1 % 2 != 0 && n2 % 2 != 0); }
Copyright 2009 by Pearson Education
21
"Boolean Zen" template
Replace
public static boolean name(parameters) { if (test) { return true; } else { return false; } }
with
public static boolean name(parameters) { return test; }
Copyright 2009 by Pearson Education
22
When to return?
In methods that involve a loop and a boolean return:
How do you figure out whether to return true or false? When should the method return its result?
Example problem:
Write a method seven that accepts a Random parameter and
uses it to pick up to 10 lotto numbers between 1 and 30. The method should print each number as it is drawn.
Example output from 2 calls: 15 29 18 29 11 3 30 17 19 22 29 5 29 16 4 7
If any of the numbers is a lucky 7, the method should return
true. Otherwise, it should return false.
Copyright 2009 by Pearson Education
23
Flawed solution
Common incorrect solution:
// Draws 10 random lotto numbers. // Returns true if one of them is a lucky 7. public static boolean seven(Random rand) { for (int i = 1; i <= 10; i++) { int num = rand.nextInt(30) + 1; System.out.print(num + " "); if (num == 7) { return true; } else { return false; } } }
The method tries to return immediately after the first roll. This is bad, if that roll isn't a 7; we need to roll all 10 times to see
if any of them is a 7.
Copyright 2009 by Pearson Education
24
Returning at the right time
Corrected code:
// Draws 10 random lotto numbers. // Returns true if one of them is a lucky 7. public static boolean seven(Random rand) { for (int i = 1; i <= 10; i++) { int num = rand.nextInt(); System.out.print(num + " "); if (num == 7) { // found lucky 7; can exit now return true; } } } // if we get here, we know there was no 7 return false;
Returns immediately if 7 is found, because the answer must be
true. If 7 isn't found, we draw the next lotto number. If all 10 aren't 7, the loop ends and we return false.
Copyright 2009 by Pearson Education
25
Boolean return questions
Write a method named hasAnOddDigit that returns whether any digit of a positive integer is odd.
hasAnOddDigit(4822116) returns true hasAnOddDigit(2448) returns false
Write a method named allDigitsOdd that returns
whether every digit of a positive integer is odd.
allDigitsOdd(135319) returns true allDigitsOdd(9175293) returns false
Write a method named isAllVowels that returns true if every character in a String is a vowel, else false.
isAllVowels("eIeIo") returns true isAllVowels("oink") returns false
Copyright 2009 by Pearson Education
26
Boolean return answers
public static boolean hasAnOddDigit(int n) { while (n > 0) { if (n % 2 != 0) { // check whether last digit is odd return true; } n = n / 10; } return false; } public static boolean allDigitsOdd(int n) { while (n > 0) { if (n % 2 == 0) { // check whether last digit is even return false; } n = n / 10; } return true; } public static boolean isAllVowels(String s) { for (int i = 0; i < s.length(); i++) { String letter = s.substring(i, i + 1); if (!isVowel(letter)) { return false; } } return true; }
Copyright 2009 by Pearson Education
27