Problem Solving for Programming

1. Problem Solving for Programming Session 7 Data Types for Computer Programs

2. Data Types • So far we have looked at several basic data types in this module: • Integer • Decimal/fractional • String • Boolean • We also looked at how variables are created and initialized: • sugarsAdded  0 ; • parcelWeight  22.5 Kg ; • phoneNo ‘020 7631 6805’ ; • milkRequired true ; • We will now look at both of these topics in greater detail

3. Declaring Data Types • In programming, whenever a variable is declared, its data type must be declared integer: numberOfSugars ; boolean: milkRequired ; • Declaring variables as a particular data type helps in the allocation of computer memory: • Integer: 32 bits (Java) • Boolean: 1 bit (Java) • It also helps to avoid typing errors • integer: parcelWeight  ‘seven’ ;

4. Integer data types • Programming tasks require us to work with a multitude of number sizes in computer programming (e.g. sugarsRequired, stadiumCapacity, distanceBetweenStars). • Using one data type (e.g. integer) for all number ranges would therefore be inefficient. • To account for different numerical ranges, most programming languages have several sub-types of integer:

5. Integer data types • Which integer data types do you think would be applicable to the following variables? • populationOfCountry (geography) • squadNumber (football) • licenceEndorsements (driving) • employees (small/medium enterprise)

6. Declaring Variables • Most programming languages allow us to declare a variables data type individually: byte: sugarsAdded ; shortinteger: parcelWeight ; shortinteger: payload ; • Or to declare them collectively: byte: sugarsAdded ; shortinteger: parcelWeight, payload, capacity ;

7. Integer data types • They also allow us to assign a value to a variable at the point of declaration: shortinteger: parcelWeight  0, payload  0, capacity  750 ;

8. Real (fractional) data types • If the only numeric data types available to us were integer types, this would lead to some complex program code (e.g. How would we calculate 17÷9 using only integers?) • To account for this, all programming languages come with real data types. • Real data types allow us to represent any number that has a fractional element real: pi  3.147 ; (constant) real: sizeOfVirus  0.009347678 ;

9. Mathematical Operators for Integer and Real Data • Earlier we saw that a data type is defined not only by the values it can take, but also by the operations that can be performed on it: • Where numerical data types are concerned, the following operators apply:

10. Mathematical Operators for Integer and Real Data

11. Operator precedence • Mathematical operators can be combined to allow expressions such as: integer: result  3 + 4 x 6 ; • What would be the result of this expression be? • Obviously it depends on which way round we do it. • (3+4) * 6 = 42 • 3 + (4 * 6) = 27 • However, a computer program would always evaluate the expression as 27. Why?

12. Operator precedence • Because programming languages have an order of precedence when it comes to mathematical operations. • Given these rules what would be the result of the following pseudo code snippet: • boolean: result: • IF (3^3 ÷ 9 + 20 < 7 * (2 – 1)) • result  true ; • ELSE • result  false ; • ENDIF

13. Characters and Strings • String and character data types are used to represent data which is neither numeric nor boolean. • All strings are collections of characters. E.g. the name ‘David Smith’ is a collection of 11 characters: D + a + v + i + d + ‘ ’ + S + m + i + t + h • Because strings are collections of characters we have a way of performing some basic operations on them (e.g. sorting a list of names, or working out a customer’s initials) string: firstInitial firstName[0] ; string: lastInitial lastName[0] ; string: initials  firstInitial + lastInitial ; Character at position zero in the string

14. Characters and Strings • All characters belong to a particular characterset (e.g. English, Japanese or Arabic). • Each character in any character set is represented by a unique ASCIIcode (American Standard Code for Information Interchange)

15. Characters and Strings • The ASCII code is a numerical (decimal) representation of a character: • A (65) • a (97) • ! (33) • By giving a character a decimal code, the character can be transposed into a binary number and can therefore be stored in computer memory.

16. Boolean Data Types • We encountered Boolean data types earlier in this module (e.g. milkRequired) • We saw that a Boolean can only ever take a value of yes or no (true or false) • We also saw how Booleans could be used to form the conditions for conditional and repetition structures IF (milkRequired) Add milk ; ENDIF WHILE (NOT payNow)AND(productCount < 11) Scan Item ; itemsScanned  itemsScanned + 1 ; Display Pay Now button ; Get payNow ; ENDWHILE

17. Declaring and Assigning Values to Boolean Variables • As we have seen a boolean can be assigned a value of true or false: boolean: isAdult  false ; • A boolean can also be assigned the value of an expression: boolean: isAdult  (age <= 18) ; boolean: vanFull  (payload + parcelWeight > 750) ;

18. Using Booleans as Flags to Control Iterations • We can think of a Boolean as a flag: a raised flag corresponds to true and a lowered flag corresponds to false. • Boolean flags are often employed as sentinels to determine the point at which an iteration structure should be exited.

19. Using Booleans as Flags to Control Iterations 1. integer: number, 2. square ; 3. character: response ; 4. boolean: finished ; 5. DO 5.1 Display ‘Enter a number :’ ; 5.2 get value of number; 5.3 square  number * number ; 5.4 Display ‘Your number squared is ‘ ; 5.5 Display square ; 5.6 Display ‘Do you want another go? Y/N’ 5.7 Get value of response ; 5.8 finished  (response = ‘N’) OR (response = ‘n’) ; WHILE (NOT finished)

20. Boolean Operators • Like numeric data types, Boolean data types are defined by the operations available to them. • There are three (basic) Boolean operators, two of which we have already encountered: • AND • OR • NOT • The outcome of logical operators is always a Boolean true or false value

21. Combining Operands with AND or OR • Where two or more operands (expressions) are connected by an AND operator, both conditions must be true in order for the outcome of the statement to be true: boolean: grantVisa false ; integer: age ; boolean: isEUCitizen ; Get age ; Get isEUCitizen ; IF (age >= 16) AND (isEUCitizen) grantVisa true ; ENDIF • What would be the outcome if: • age 13 and Colombian • age  16 and Jamaican • age  16 and Italian

22. Combining Operands with AND or OR • Where two or more operands are connected by an OR operator, if either of the conditions is true, the outcome of the statement is true: boolean: grantVisa false ; integer: age ; boolean: isEUCitizen ; Get age ; Get isEUCitizen ; IF (age <= 16) OR (isEUCitizen) grantVisa true ; ENDIF • What would be the outcome if: • age 13 and Canadian • age  17 and Indian • age  16 and Danish

23. Negating a Boolean value with the NOT Operator • NOT inverts or negates the value of its associated operand: WHILE NOT(conveyorIsEmpty) Process parcels . . . ENDWHILE WHILE NOT (payNow) Scan Items ; ENDWHILE

24. Boolean Logic • The following truth table illustrates the results the results that the three operators (AND, OR, and NOT) give for all permutations of their operands (p & q).

25. Boolean Logic • Consider the following problem: An algorithm has been devised to calculate the average marks of a class. A teacher enters the mark for each student along with each student’s name. Entering ‘ZZZZZ’ and a mark of zero signals the end of the data and at this point the average mark for the class is calculated.

26. Boolean Logic • The algorithm may look something like the following: 1. string: name ; 2. integer mark , 3. total , 4. numberOfMarks ; 5. total  0 ; 6. numberOfMarks  0 ; 7. Get name and mark ; 8. WHILE (name ≠ ‘ZZZZZ’) AND (mark ≠ 0) 8.1 total  total + mark ; 8.2 numberOfMarks  numberOfMarks + 1 ; 8.3 Get next name and mark END WHILE //code to calculate average mark

27. Boolean Logic • At first glance the solution looks good, • Unfortunately, though, it will not suffice. • This is because the condition at #8 means that the loop will terminate as soon as a mark of zero is entered, even if name is different than ‘ZZZZZ’. The following truth table shows this clearly WHILE (name ≠ ‘ZZZZZ’) AND (mark ≠ 0)

28. Boolean Logic • The correct solution for this problem replaces the AND with an OR 1. string: name ; 2. integer mark , 3. total , 4. numberOfMarks ; 5. total  0 ; 6. numberOfMarks  0 ; 7. Get name and mark ; 8. WHILE (name ≠ ‘ZZZZZ’) OR (mark ≠ 0) 8.1 total  total + mark ; 8.2 numberOfMarks  numberOfMarks + 1 ; 8.3 Get next name and mark END WHILE //code to calculate average mark

29. Boolean Logic • A truth table demonstrates why this is correct WHILE (name ≠ ‘ZZZZZ’) OR (mark ≠ 0)

30. Boolean Logic • In both example algorithms, we have started with a condition that will be true each time the loop iterates: WHILE (name ≠ ‘ZZZZZ’) AND (mark ≠ 0) WHILE (name ≠ ‘ZZZZZ’) OR (mark ≠ 0) • An alternative approach, and one that dispenses with the OR, would be to start instead with condition that would be true when the loop terminates: WHILE (name=‘ZZZZZ’) AND (mark=0) • If we negate this condition, then any values apart from ‘ZZZZZ’ and 0 will cause the loop to continue. But we must negate the condition as a whole. WHILE NOT((name=‘ZZZZZ’) AND (mark=0)) • Again, a truth table demonstrates why this is correct

31. Boolean Logic WHILE NOT((name=‘ZZZZZ’) AND (mark=0))