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A set is a collection of elements of same type. Pascal allows defining the set data type. The elements in a set are called its members. In mathematics, sets are represented by enclosing the members within braces{}. However, in Pascal, set elements are enclosed within square brackets [], which are referred as set constructor.
Defining Set Types and Variables
Pascal Set types are defined as
type set-identifier = set of base type;
Variables of set type are defined as
var s1, s2, ...: set-identifier;
or,
s1, s2...: set of base type;
Examples of some valid set type declaration are −
type Days = (mon, tue, wed, thu, fri, sat, sun); Letters = set of char; DaySet = set of days; Alphabets = set of ''A'' .. ''Z''; studentAge = set of 13..20;
Set Operators
You can perform the following set operations on Pascal sets.
| Sr.No | Operations & Descriptions |
|---|---|
| 1 |
Union This joins two sets and gives a new set with members from both sets. |
| 2 |
Difference Gets the difference of two sets and gives a new set with elements not common to either set. |
| 3 |
Intersection Gets the intersection of two sets and gives a new set with elements common to both sets. |
| 4 |
Inclusion A set P is included in set Q, if all items in P are also in Q but not vice versa. |
| 5 |
Symmetric difference Gets the symmetric difference of two sets and gives a set of elements, which are in either of the sets and not in their intersection. |
| 6 |
In It checks membership. |
Following table shows all the set operators supported by Free Pascal. Assume that S1 and S2 are two character sets, such that −
S1 := [”a”, ”b”, ”c”];
S2 := [”c”, ”d”, ”e”];
| Operator | Description | Example |
|---|---|---|
| + | Union of two sets |
S1 + S2 will give a set [”a”, ”b”, ”c”, ”d”, ”e”] |
| – | Difference of two sets |
S1 – S2 will give a set [”a”, ”b”] |
| * | Intersection of two sets |
S1 * S2 will give a set [”c”] |
| >< | Symmetric difference of two sets | S1 >< S2 will give a set [”a”, ”b”, ”d”, ”e”] |
| = | Checks equality of two sets | S1 = S2 will give the boolean value False |
| <> | Checks non-equality of two sets | S1 <> S2 will give the boolean value True |
| <= | Contains (Checks if one set is a subset of the other) | S1 <= S2 will give the boolean value False |
| Include | Includes an element in the set; basically it is the Union of a set and an element of same base type |
Include (S1, [”d”]) will give a set [”a”, ”b”, ”c”, ”d”] |
| Exclude | Excludes an element from a set; basically it is the Difference of a set and an element of same base type |
Exclude (S2, [”d”]) will give a set [”c”, ”e”] |
| In | Checks set membership of an element in a set | [”e”] in S2 gives the boolean value True |
Example
The following example illustrates the use of some of these operators −
program setColors;
type
color = (red, blue, yellow, green, white, black, orange);
colors = set of color;
procedure displayColors(c : colors);
const
names : array [color] of String[7]
= (''red'', ''blue'', ''yellow'', ''green'', ''white'', ''black'', ''orange'');
var
cl : color;
s : String;
begin
s:= '' '';
for cl:=red to orange do
if cl in c then
begin
if (s<>'' '') then s :=s +'' , '';
s:=s+names[cl];
end;
writeln(''['',s,'']'');
end;
var
c : colors;
begin
c:= [red, blue, yellow, green, white, black, orange];
displayColors(c);
c:=[red, blue]+[yellow, green];
displayColors(c);
c:=[red, blue, yellow, green, white, black, orange] - [green, white];
displayColors(c);
c:= [red, blue, yellow, green, white, black, orange]*[green, white];
displayColors(c);
c:= [red, blue, yellow, green]><[yellow, green, white, black];
displayColors(c);
end.
When the above code is compiled and executed, it produces the following result −
[ red , blue , yellow , green , white , black , orange] [ red , blue , yellow , green] [ red , blue , yellow , black , orange] [ green , white] [ red , blue , white , black]
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