Sets exist in every day life. They are a way of classifying common
types into groups. In Pascal, we think of sets as containing a range of
limited values, from an initial value through to an ending value.
Consider the following set of integer values :
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
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This is a set of numbers (integers) whose set value ranges from 1 to 10.
To define this as a set type in Pascal, we would use the following syntax.
program SetsOne;
type numberset = set of 1..10;
var mynumbers : numberset;
begin
end.
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The statement
type numberset = set of 1..10;
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declares a new type called numberset, which represents a set of
integer values ranging from 1 as the lowest value, to 10 as the highest
value. The value 1..10 means the numbers 1 to 10 inclusive. We call
this the base set, that is, the set of values from which the set is
taken.
The base set is a range of limited values. For example, we can have a
set of char, but not a set of integers, because the set of
integers has too many possible values, whereas the set of characters is very
limited in possible values.
The statement
var mynumbers : numberset;
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makes a working variable in our program called mynumbers, which is
a set and can hold any value from the range defined in numberset.
The typical operations associated with sets are,
- assign values to a set
- determine if a value is in one or more sets
- set addition (UNION)
- set subtraction (DIFFERENCE)
- set commonality (INTERSECTION)
Assigning Values to a set: UNION
program SetsTWO;
type numberset = set of 1..10;
var mynumbers : numberset;
begin
mynumbers := [];
mynumbers := [2..6]
end.
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The statement
assigns an empty set to mynumbers. The statement
assigns a subset of values (integer 2 to 6 inclusive) from the
range given for the set type numberset. Please note that assigning
values outside the range of the set type from which mynumbers is
derived will generate an error, thus the statement
is illegal, because mynumbers is derived from the base type
numberset, which is a set of integer values ranging from 1 to 10. Any
values outside this range are considered illegal.
Determining if a value is in a set
Lets expand the above program example to demonstrate how we check to see
if a value resides in a set. Consider the following program, which reads an
integer from the keyboard and checks to see if its in the set.
program SetsTHREE( input, output );
type numberset = set of 1..10;
var mynumbers : numberset;
value : integer;
begin
mynumbers := [2..6];
value := 1;
while( value <> 0 ) do
begin
writeln('Please enter an integer value, (0 to exit)');
readln( value );
if value <> 0 then
begin
if value IN mynumbers then
writeln('Its in the set')
else
writeln('Its not in the set')
end
end
end.
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More on set UNION, combining sets
Lets now look at combining some sets together. Consider the following
program, which creates two sets, then joins the sets together to create
another.
program SetsUNION( input, output );
type numberset = set of 1..40;
var mynumbers, othernumbers, unionnumbers : numberset;
value : integer;
begin
mynumbers := [2..6];
othernumbers := [4..10];
unionnumbers := mynumbers + othernumbers + [14..20];
value := 1;
while( value <> 0 ) do
begin
writeln('Please enter an integer value, (0 to exit)');
readln( value );
if value <> 0 then
begin
if value IN unionnumbers then
writeln('Its in the set')
else
writeln('Its not in the set')
end
end
end.
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The statement
var mynumbers, othernumbers, unionnumbers : numberset;
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declares three sets of type numberset.
The statement
assigns a subset of values (integer 2 to 6 inclusive) from the
range given for the set type numberset.
The statement
assigns a subset of values (integer 4 to 10 inclusive) from the
range given for the set type numberset.
The statement
unionnumbers := mynumbers + othernumbers + [14..20];
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assigns the set of values in mynumbers, othernumbers and
the set of values of 14 to 20 to unionnumbers.
If a specific value occurs in more than one set (as is the case of 4, 5,
and 6, which are in mynumbers and othernumbers), then the
other duplicate value is ignored (ie, only one instance of the value is
copied to the new set.
This means that unionnumbers contains the values
Set Subtraction, DIFFERENCE
In this operation, the new set will contain the values of the first set
that are NOT also in the second set.
program SetsDIFFERENCE( input, output );
type numberset = set of 1..40;
var mynumbers, othernumbers, unionnumbers : numberset;
value : integer;
begin
mynumbers := [2..6];
othernumbers := [4..10];
unionnumbers := mynumbers - othernumbers;
value := 1;
while( value <> 0 ) do
begin
writeln('Please enter an integer value, (0 to exit)');
readln( value );
if value <> 0 then
begin
if value IN unionnumbers then
writeln('Its in the set')
else
writeln('Its not in the set')
end
end
end.
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unionnumbers contains the values
Set Commonality, INTERSECTION
In this operation, the new set will contain the values which are common
(appear as members) of the specified sets.
program SetsINTERSECTION( input, output );
type numberset = set of 1..40;
var mynumbers, othernumbers, unionnumbers : numberset;
value : integer;
begin
mynumbers := [2..6];
othernumbers := [4..10];
unionnumbers := mynumbers * othernumbers * [5..7];
value := 1;
while( value <> 0 ) do
begin
writeln('Please enter an integer value, (0 to exit)');
readln( value );
if value <> 0 then
begin
if value IN unionnumbers then
writeln('Its in the set')
else
writeln('Its not in the set')
end
end
end.
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unionnumbers contains the values
