IB Computer Science Topic B2.1.1: Constructing and Tracing Programs Using Global and Local Variables of Various Data Types Notes

Variables: Named Storage the Program Reads and Rewrites

1. A variable is a named storage location in memory that holds one value at a time.
2. Assigning a new value overwrites the old one, so the value behind a name depends on which line of the program you have reached.
3. Java is statically typed, so you state the data type when you declare the variable and that type cannot change.
4. Python is dynamically typed, so the type is taken from the value you assign and changes if you assign a different kind of value.

The Five Data Types on the Syllabus

1. Boolean
   1. Holds one of two values, true or false, and is what every condition in a program evaluates to.
   2. Java writes these as true and false, Python capitalises them as True and False.
2. Integer
   1. Holds a whole number with no fractional part, so it suits counters, index positions and quantities.
   2. Dividing one integer by another in Java gives an integer, which is the trap traced later on this page.
3. Decimal
   1. Holds a number with a fractional part, declared as double or float in Java and as float in Python.
   2. A decimal value is stored as an approximation, so two decimals that look equal can differ in the last few bits.
4. Char
   1. Holds exactly one character, written in single quotes in Java as char grade = 'A';.
   2. Python has no separate char type, so a single character is stored as a string of length one.
5. String
   1. Holds a sequence of characters and comes with methods for searching and slicing it.
   2. Strings are immutable in both languages, which is why every string method returns a new string rather than editing the old one.

Scope: A Global Variable Is Visible Everywhere, a Local One Is Not

1. Global variables
   1. Declared outside every function or method, so any part of the program can read them.
   2. They keep their value for as long as the program runs.
2. Local variables
   1. Declared inside a function or method, so only the code in that function can see them.
   2. They are created when the function is called and destroyed when it returns, so the same name in two functions refers to two different variables.
3. Assigning to a global from inside a function
   1. Python treats any name you assign to inside a function as local, so you must write global total first to change the global instead of shadowing it.
   2. Java has no true globals, so the nearest equivalent is a static class variable, which any method of the class can assign to directly.

Tracing: Record Every Variable After Each Line That Changes It

1. To trace a program is to execute it by hand and write down what each variable holds as you go.
2. A trace table has one column per variable you are tracking, plus a column for any condition being tested and a column for output.
3. Each row records the state after one line or one pass of a loop, and a variable that did not change keeps its previous value.
4. Write the value after the line has run, which is why a loop counter in the last row is already past the value that failed the test.

Why the Same Trace Ends With Two Different Answers

1. Python's / operator always produces a decimal, so 10 / 4 gives 2.5.
2. Java's / operator between two integers produces an integer, so 10 / 4 gives 2 and the remainder is discarded before it is ever stored in the double.
3. Casting one operand fixes it, so (double) total / 4 gives 2.5 and the trace then matches Python.

Producing a Trace That Earns the Marks

1. Draw the columns before you start, one per variable named in the question, so you are not adding columns halfway through.
2. Complete every row rather than only the rows where something changed, because an examiner marks the state of the table, not your reasoning.
3. Check the final row against the printed output, since a trace that ends on a different value than the program prints has an error in it.
4. Trace tables also work as a way of finding a bug rather than describing one, which is covered in B2.1.4 Constructing and Using Common Debugging Techniques.