Decisions, decisions, decisions

1. Decisions, decisions, decisions Chapter 3 Spring 2007 CS 101 Aaron Bloomfield

2. Background • Our problem-solving solutions so far have the straight-line property • They execute the same statements for every run of the program public class DisplayForecast // main(): application entry point public static void main(String[] args) { System.out.print("I think there is a world"); System.out.print(" market for maybe five "); System.out.println("computers. “); System.out.print(" Thomas Watson, IBM, “); System.out.println("1943.“); } }

3. Background • For general problem solving we need more capabilities • The ability to control which statements are executed • The ability to control how often a statement is executed • We will concentrate first on controlling which statements are executed • Java provides the if and switch conditional constructs to control whether a statement list is executed • The if constructs use logical expressions to determine their course of action • We will start with logical expressions

4. Logical expressions

5. Logical expressions • The branch of mathematics dealing with logical expressions is Boolean algebra • Developed by the British mathematician George Boole

6. Logical expressions • A logical expression has either the value logical true or logical false • Some expressions whose values are logical true • The year 2004 is a leap year • A meter equals 100 centimeters • Some expressions whose values are logical false • A triangle has four sides • The area of square is always equal to twice its perimeter

7. Logical expressions • There are three primary logical operators for manipulating logical values • Logical and • Logical or • Logical not • The operators work as most of us would expect

8. p q p and q False False False False True False True False False True True True Truth tables • We use truth tables to give formal specifications of the operators • “It works as most of us would expect” allows for ambiguity of interpretation • Jim is smiling or Patty is smiling • Can both Jim and Patty both be smiling? • Truth tables • Lists all combinations of operand values and the result of the operation for each combination

9. p q p or q False False False False True True True False True True True True p not p False True True False Or and not truth tables

10. p q p and q not (p and q) False False False True False True False True True False False True True True True False Boolean algebra • Can create complex logical expressions by combining simple logical expressions • not (p and q)

11. (not p) orp q p and q not (p and q) ( not p) (not q) (not q) False False False True True True True False True False True True False True True False False True False True True True True True False False False False DeMorgan’s laws • not (p and q) equals (not p) or (not q)

12. (not p) andp q p or q not (p or q) ( not p) (not q) (not q) False False False True True True True False True True False True False False True False True False False True False True True True False False False False DeMorgan’s laws • not (p or q) equals (not p) and (not q)

13. DeMorgan’s laws • If you remember nothing else about the Boolean operators, remember that: • not (a and b) == (not a) or (not b) • not (a or b) == (not a) and (not b)

14. Sidewalk chalk guy • Source: http://www.gprime.net/images/sidewalkchalkguy/

15. Boolean expressions

16. A boolean type • Java has the logical type boolean • Type boolean has two literal constants • true • false • Operators • The and operator is && • Don’t use & • The or operator is || • Don’t use | • The not operator is !

17. Defining boolean variables • Local boolean variables are uninitialized by default boolean isWhitespace; boolean receivedAcknowledgement; boolean haveFoundMissingLink;

18. Defining boolean variables • Local boolean variables with initialization boolean canProceed = true; boolean preferCyan = false; boolean completedSecretMission = true;

19. Assignment vs. comparison • = is the assignment operator • It copies the value on the right to the location on the left • Consider: int x; x = 5; • The value 5 is copied to the spot x in memory • == is the comparison operator • Returns a boolean (true or false) if the two sides are equal • Consider: int x = 5; System.out.println (x == 5); System.out.println (x == 6); • Prints out true, false

20. Other operators • Equality operators == and != • Operator == • Returns true if the operands have the same value; otherwise, returns false • This is not the assignment operator! • Operator != • Returns true if the operands have different values; otherwise, returns false • The operators work with all types of values

21. Evaluating boolean expressions • Suppose boolean p = true; boolean q = false; boolean r = true; boolean s = false; • What is the value of p p && s !s p == q q q != r p && r r == s q || s q != s

22. Evaluating boolean expressions • Suppose int i = 1; int j = 2; int k = 2; char c = '#'; char d = '%'; char e = '#'; • What is the value of j == ki != k i == jj != k c == ed != e c == d c != e

23. These images are not animated…

24. Translating English to logical expressions

25. p q p or q not (p or q) p nor q False False False True True False True True False False True False True FalseFalse True True True FalseFalse Translating English to logical expressions • English doesn’t always translate cleanly into logical expressions • To see this, we need to examine the NOR operator • It doesn’t exist in Java, but we can fake it • p NOR q == NOT (p OR q) • NOR is represented by a downward arrow:  • In Java, given variables p and q • NOR is done by: !(p||q)

26. Translation Example • “I have neither given nor received help on this exam” • Rephrased: “I have not given nor received …” • Let p = “I have given help on this exam” • Let q = “I have received help on this exam” • Translation is: pq • Remember the precedence: NOT is done first!

27. Translation example, take 2 • “I have neither given nor received help on this exam” • Rephrased: “I have not (given nor received …)” • Let p = “I have given help on this exam” • Let q = “I have received help on this exam” • Another translation is: (pq) = p || q

28. Translation example, rephrased • What is meant is “I have not given and I have not received help on this exam” • Or “I have not (given or received) help on this exam” • This is a DeMorgaization of the one above it • The problem:  has a higher precedence than  in Boolean logic, but not always in English • Also, “neither” is vague

29. Disclaimer • The preceding example was showing that when English can be clear, it does not always translate clearly into Boolean logic • The English meaning is exact • The Boolean translation is not • This does not mean that you can cheat, and say that I said it was allowed by the honor code

30. Floating point comparison

31. Floating point precission • What gets printed? class FloatTest { public static void main (String args[]) { double y = 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1; System.out.println (y); } } There are 10 0.1’s

32. Program demo • FloatTest.java

33. Take care with floating-point values • Consider double a = 1; double b = 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1 + 0.1; double c = .9999999999999999; • Two true expressions! c == b b != a • Two false expressions! a == b b != c • Problem lies with the finite precision of the floating-point types • Instead with the ordering operators for closeness

34. How to solve this • Don’t compare floating-point values if you can help it! • Both doubles and floats • Need to test if the two doubles are “close” in value final double EPSILON = 0.000001; boolean foo = Math.abs (a-b) < EPSILON;

35. Sand Castles

36. More on evaluating expressions

37. Ordering operators • Java provides ordering operators for the primitive types • Four ordering operators, <, >, <=, and >= • They correspond to mathematical operators of <, >, ≤, and ≥ • Together the equality and ordering operators are known as the relational operators • False is less than true

38. Evaluation boolean expressions • Suppose int i = 1; int j = 2; int k = 2; • What is the value of i < j j < k i <= k j >= k i >= k

39. Unicode values • Character comparisons are based on their Unicode values • Characters ‘0’, ‘1’, … ‘9’ have expected order • Character ‘0’ has the encoding 48 • Character ‘1’ has the encoding 49, and so on. • Upper case Latin letters ‘A’, ‘B’, … ‘Z’ have expected order • Character ‘A’ has the encoding 65, character ‘B’ has the encoding 66, and so on. • Lower case Latin letters ‘a’, ‘b’, … ‘z’ have expected order • Character ‘a’ has the encoding 97 • Character ‘b’ has the encoding 98, and so on.

40. Evaluation boolean expressions • Suppose char c = '2'; char d = '3'; char e = '2'; • What is the value of c < d c < e c <= e d >= e c >= e

41. Operator precedence revisited • Highest to lowest • Parentheses • Unary operators • Multiplicative operators • Additive operators • Relational ordering • Relational equality • Logical and • Logical or • Assignment

42. Expressions vs. statements • A statement is a single command for Java to do, and always ends in a semi-colon (for now, at least) • System.out.println (“hello world”); • int x = 4; • ++x; • An expression returns a value, and does not have a semi-colon • 5 • circle.getRadius() • x • Note the difference between the following: • ++i is an expression • ++i; is a statement

43. New 2005 demotivatiors!

44. if statement

45. Conditional constructs • Provide • Ability to control whether a statement list is executed • Two constructs • If statement • if • if-else • if-else-if • Switch statement

46. Expression true false Action Basic if statement • Syntax if (Expression) Action • If the Expression is true then execute Action • Action is either a single statement or a group of statements within braces • For us, it will always be a group of statements within braces

47. Is our number negative? If Value is less than Value < 0 zero then we need to update its value true false to that of its additive If Value is not inverse less than zero then our number Value = -Value is fine as is Our number is now definitely nonnegative Example if (value < 0) { value = -value; }

48. Sorting two values System.out.print("Enter an integer number: "); int value1 = stdin.nextInt(); System.out.print("Enter another integer number: "); int value2 = stdin.nextInt(); // rearrange numbers if necessary if (value2 < value1) { // values are not in sorted order int rememberValue1 = value1; value1 = value2; value2 = rememberValue1; } // display values System.out.println("The numbers in sorted order are " + value1 + " and then " + value2); What happens if the user enters 11 and 28? What happens if the user enters 11 and 4?

49. Are the numbers out of order Rearrange value1 and value2 < value1 value2 to put their values in the proper order false true int rememberValue1 = value1 value1 = value2 value2 = rememberValue1 The numbers were rearranged into the proper order The numbers were initially in order The numbers are in order If semantics

50. What an if statement executes • An if statement executes the next block of code • A block is either: • A single statement without curly brackets: if (a == b) System.out.println (“a==b!!!”); • A number of statements enclosed by curly brackets: if (a == b) { System.out.print (“a”); System.out.print (“==”); System.out.print (“b”); System.out.println (“!!!”); }