S.K.H. Kei Hau Secondary School 2003-2004
Set Data type
S.K.H. Kei Hau Secondary School
Department of Computer
AL Computer Studies
Set Data Type
Content
1. Set Data Type
2. Set Operator
3. Set Union, Intersection, and Difference
1. Set Data Type
Sets are structured variables that contain lists of integers, characters, or enumerated
type values.
Type
DigitSet = Set of 0..9;
Var Odds Evens, Middle, Mixed : DigitSet; (* four sets *)
Set assignment and set literals
Set literal is a list of values from the set base type enclosed in brackers.
Odds := [1, 3, 5, 7, 9];
Evens := [0, 2, 4, 6, 8];
The empty set
It has zero elements and is denoted by a pair of brackets. (different from undefined
set)
Middle := [];
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S.K.H. Kei Hau Secondary School 2003-2004
Set Data type
Sets with enumerated type value
You can define sets with values chosen from your own enumerated data type.
Type
Cars = (Dodge, Ford, Lincoln, Cadillac, Fiesta, Pointiac, Corvette, Buick,
Chevrolet, Mercury, Mustang);
CarSet = set of cars;
Var
Avis, Hertz, Merger : CarSet;
Avis := [Dodge, Lincoln, Fiesta];
Hertz := [Dodge..Cadillac, Mercury];
Merger := [Dodge..Mustang];
Avis consists of three elements.
Hertz consists of five elements.
Merger, which is the universal set for type CarSet, consists of all elements.
So, the following assignment is valid:
Merger := Hertz
Note that:
Valid set: [1, 3, 1..5]
Invalid set: [1, 3, ‘1’ .. ‘5’]
2. Set Operator
Pascal provides a set membership operator, in, to determine whether a particular value
is a set element.
Consider:
Statement 1:
(ch = ‘.’) or (ch = ‘?’) or (ch = ‘;’) or (ch = ‘!’)
Statement 2:
Ch in [‘.’, ‘?’, ‘;’, ‘!’]
Both conditions are true if ch is one of the characters in the set.
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Set Data type
Example
Type CharSet = set of Char;
Var
Vowels, Uppercase, Lowercase : CharSet; (* 3 sets *)
NextChar : Char;
Begin
Vowels := [‘A’, ‘a’, ‘E’, ‘e’, ‘I’, ‘i’, ‘O’, ‘o’, ‘U’, ‘u’];
Uppercase := [‘A’ .. ‘Z’];
Lowercase := [‘a’ .. ‘z’];
…
…
repeat
write(‘Enter a letter>’);
Readln(NextChar);
If NextChar in Vowels then
Writeln(NextChar, ‘ is a vowel’)
Else if NextChar in Uppercase then
Writeln(NextChar, ‘ is an uppercase consonant’)
Else if NextChar in Lowercase then
Writeln(NextChar, ‘ is a lowercase consonant’)
Else
Writeln(NextChar, ‘ is not a letter’)
Until NextChar in [‘A’ .. ‘Z’, ‘a’ .. ‘z’]
…
…
Note that, if you want to use the complement of the condition statement,
Valid statement: Not NextChar in [‘A’ .. ‘Z’, ‘a’ .. ‘z’]
Invalid statement: NextChar Not in [‘A’ .. ‘Z’, ‘a’ .. ‘z’]
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Set Data type
3. Set Union, Intersection, and Difference
Union
Intersection
Difference
Operation
Condition
Operator
Union
Or
+
Intersection
And
*
Difference
---
-
Note that,
 The difference of set A and set B is the set of elements that are in set A but not in
set B.
 The set operator ‘-’ is not commutative, that is A-B is different to B-A
 The set operator ‘+’ and ‘*’ are commutative.
 The precedence rules of the set operator in Pascal is +, * and –.
Example
[1, 3, 4] + [1, 2, 4] is [1, 2, 3, 4]
[‘A’, ‘C’, ‘F’] + [‘A’, ‘C’, ‘D’, ‘F’] is [‘A’, ‘C’, ‘D’, ‘F’]
[1, 3, 4, 5] + [2] is [1, 2, 3, 4, 5] (unit set)
[1, 3, 4] * [1, 2, 4] is [1, 4]
[‘A’, ‘C’, ‘F’] + [‘A’, ‘C’, ‘D’, ‘F’] is [‘A’, ‘C’, ‘F’]
[1, 3, 4] – [1, 2, 4] is [3]
[1, 3] – [2, 4] is [1,3]
[‘A’, ‘C’, ‘F’] – [‘B’, ‘C’, ‘D’, ‘F’] is [‘A’]
[‘A’, ‘C’, ‘F’] – [[‘A’, ‘C’, ‘D’, ‘F’] is [] (empty set)
Common errors
[1, 3, 4, 5] + 2 (2nd operand is not a set)
Avis + Cadillac (2nd operand is not a set)
[Avis] + [Cadillac] (1st operand is not a set)
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Set Data type
Set relational operators
= , <>, <= and >=
Operator
Meaning
=
Set equality
<>
Set inequality
<=
Subset
>=
Superset
Example
[1, 3] = [1, 3] is true
[1, 3] = [2, 4] is false
[1, 3] = [3, 1] is true
[] = [1] is false
[1, 3] <> [1, 3] is false
[1, 3] <> [2, 4] is true
[1, 3] <> [3, 1] is false
[] <> [1] is true
Set A is a subset of set B (A<= B) If every element of A is also an element of B:
[1, 3] < [1, 2, 3, 4] is true
[1, 3] <= [1, 3] is true
[] <= [1, 3] is true
Set A is a superset of set B (A>=B) if every element of B is also an element of A:
[1, 3] >= [1, 2, 3, 4] is false
[1, 3] <= [1, 3] is true
[] >= [1, 3] is false
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Set Data type
Read and write set
Example
Read set
Procedure ReadSet (var Letters : CharSet);
Const
Sentine1 = ‘.’;
Var
NextChar : Char;
Begin
Letters :[];
Writeln(‘enter a sentence ending with symbol’, Sentine1);
Read(NextChar);
While NextChar <> Sentine1 do
Begin
NextChar := UpCase(NextChar);
If NextChar in [‘A’ .. ‘Z’] then
Letters := Letters + [NextChar];
Read(NextChar)
End
End;
Write Set
Procedure PrintSet(Letters : CharSet);
Var
NextLetter : Char;
Begin
Write(‘{’);
For NextLetter := ‘A’ to ‘Z’ fo
If NextLetter in Letters then
Write(NextLetter, ‘, ’);
Writeln(‘}’)
End;
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