1. ITP © Ron Poet Lecture 6 1 More on if

2. ITP © Ron Poet Lecture 6 2 Remembering Tests  We often want to remember the result of a test, so that we can use it later on.  We might work out if a year is a leap year or not.  The formula is quite complicated.  If we could remember the result of the test, we would not have to keep applying the complicated formula.

3. ITP © Ron Poet Lecture 6 3 boolean Data Type  The boolean data type has two possible values, true and false.  These are boolean literals.  Any test is a boolean expression, with possible values true and false.  We can store boolean values in boolean variables.

4. ITP © Ron Poet Lecture 6 4 Storing Test Results in Variables  We can store our previous test results in boolean variables. boolean nightFeast = startTotalMins < 0; boolean itsRon = name.equals(“Ron”);  They are either true or false.  There are just examples, it would not be good style to actually do this in these cases.

5. ITP © Ron Poet Lecture 6 5 Using boolean Variables in Tests  We can use these stored values in tests.  As part of an if statement. if (nightFeast) startTotalMins = startTotalMins + 1440; if (isRon) con.println(“Why, Hello Ron”);  Using the tests later is often useful.  But not in these simple examples.

6. ITP © Ron Poet Lecture 6 6 Leap Years  The rules for deciding if a year is a leap year are complicated.  Making it a useful example.  A year is a leap year if:  It is divisible by 4.  But if it is divisible by 100 it is not a leap year.  Unless it is also divisible by 400.

7. ITP © Ron Poet Lecture 6 7 Leap Year Calculation  Let us try and calculate if a year is leap, storing the result in the boolean variable isLeapYear.  We can use this stored value later on to calculate how many days there are in February of that year.

8. ITP © Ron Poet Lecture 6 8 Chaining if Statements  Remember, make the most restrictive test first. Boolean isLeapYear; if (year % 400 == 0)// divisible by 400 isLeapYear = true; else if (year % 100 == 0) // divisible by 100 isLeapYear = false; else if (year % 4 == 0) // divisible by 4 isLeapYear = true; else isLeapYear = false;

9. ITP © Ron Poet Lecture 6 9 Nested if Statements  We can go straight from the definition, leading to a less elegant solution. Boolean isLeaYear; if (year % 4 == 0) if (year % 100 == 0) if (year % 400 == 0) isLeapYear = true; else isLeapYear = false; else isLeapYear = true; else isLeapYear = false;

10. ITP © Ron Poet Lecture 6 10 Days in The Month  Whichever approach we take, we now have a variable called isLeapYear that is either true or false.  Now let us assume we have a String variable month which stores the 3 letter abbreviation of the month name.  We want to calculate int daysInMonth.

11. ITP © Ron Poet Lecture 6 11 Twelve Tests  The obvious solution is the rather long series of tests. if (month.equals(“Jan”)) daysInMonth = 31; else if (month.equals(“Feb”)) if (isLeapYear) daysInMonth = 29; else daysInMonth = 28; else if (month.equals(“Mar”)) daysInMonth = 31;...

12. ITP © Ron Poet Lecture 6 12 Reflection  Note how we have stored the result of a test in a boolean variable.  The boolean variable is then used in place of the test in an if statement.  Note that things can get complicated and we have to keep track of which if the else parts belong to.  Indentation is vital.

13. ITP © Ron Poet Lecture 6 13 Combining Tests  The previous two examples have used multiple tests to calculate whether a year is leap and the days in a month.  It would be convenient if we could combine tests to produce super-tests.  Rather than using lots of if statements with simple tests.

14. ITP © Ron Poet Lecture 6 14 Boolean Operators  Boolean operators combine tests to produce super-tests.  These super-tests still have possible values of true or false.  They can be used like any of the simpler tests.  We can combine super-tests to produce even bigger tests, as far as we want.

15. ITP © Ron Poet Lecture 6 15 Test AND Test  If we combine two tests with the AND operator then the result is only true if both the simple tests are true.  If one test is false then the result is false, no matter what the result of the other test is.  The Java notation for AND is &&.

16. ITP © Ron Poet Lecture 6 16 Test OR Test  If we combine two tests with the OR operator then the result is true if only one of the simple tests is true.  It is only false if both the simple tests are false.  The Java notation for OR is ||.  It has the lowest precedence of the boolean operators.

17. ITP © Ron Poet Lecture 6 17 NOT Test  The NOT operator switches the value of the test.  If the test were true then NOT test is false.  If the test were false then NOT test is true.  The Java notation for NOT is !  It has the highest precedence of the boolean operators.

18. ITP © Ron Poet Lecture 6 18 Days in the Month Again  This makes the days in the month code easier.  It fits on one page.  Note that we combine the month test with OR. Only one test will ever be true!

19. ITP © Ron Poet Lecture 6 19 Days in the Month Code if (month.equals(“Jan”) || month.equals(“Mar”) || month.equals(“May”) || month.equals(“Jul”) || month.equals(“Aug”) || month.equals(“Oct”) || month.equals(“Dec”)) daysInMonth = 31; else if (month.equals(“Apr”) || month.equals(“Jun”) || month.equals(“Sep”) || month.equals(“Nov”)) daysInMonth = 30; else// must be Feb if (isLeapYear) daysInMonth = 29; else daysInMonth = 28;

20. ITP © Ron Poet Lecture 6 20 Leap Years Again  The leap year code is also complicated.  We must make sure we have the right combinations of AND and OR.  Use test data. Year = 3, 4, 100, 400 covers all the possibilities.

21. ITP © Ron Poet Lecture 6 21 Leap Year Code if ((year % 4 == 0 && year % 100 != 0) || year % 400 == 0) isLeapYear = true; else isLeapYear = false;

22. ITP © Ron Poet Lecture 6 22 Testing in a Range  Suppose we want a test that is true if an integer x is between 37 and 39.  We must make two tests.  x >= 37, bigger than the lower value.  x <= 39, smaller than the higher value.  Join them with AND, both tests must be true.  if (x >= 37 && x <= 39).

23. ITP © Ron Poet Lecture 6 23 Alphabetical Order  We might want to test two strings to see which one comes first in the alphabet.  Use compareTo rather than equals.  a.compareTo(b) returns an int.  If the value < 0 then a comes before b.  If the value > 0 then a comes after b.  If the value == 0 then a and b are equal.

24. ITP © Ron Poet Lecture 6 24 Dangling else  If we have two if s but only one else.  The else belongs to the nearest if. if (test1) if (test2) // else belongs to this one statement; else statement;  Unless that is not possible because of {}.

25. ITP © Ron Poet Lecture 6 25 Dangling else and {} if (test1) // else belongs to this if { if (test2) // statement; } else statement;

26. ITP © Ron Poet Lecture 6 26 doubles Are Not Stored Exactly  Real numbers ( double ) are not normally stored exactly.  They are stored very accurately, to around 17 significant figures.  A variable that we expect to hold the value 3.0 might actually hold 2.99999999999999.  This is good enough for most purposes.  int s are stored exactly.

27. ITP © Ron Poet Lecture 6 27 Comparing doubles  If we compare a variable x with the value 3.0 then the result might be false because x actually contained 2.99999999999.  We should not write  if (x == 3.0)  We should instead subtract 3.0 from x and see if the number is very small.

28. ITP © Ron Poet Lecture 6 28 Close Enough  If x is close enough to 3.0, then x – 3.0 will be a small number, either positive or negative.  We should take the absolute value of x – 3.0  which is always positive. if (x > 3.0) absxmin3 = x – 3.0; else absxmin3 = 3.0 - x;  It is better to use java.lang.Math.abs(x – 3.0).

29. ITP © Ron Poet Lecture 6 29 Close Enough (2)  A typical small value is 1.0e-10.  So the test to see if x is close enough to 3.0 would be if (java.lang.Math.abs(x – 3.0) < 1.0e-10)