Symmetric difference
You are encouraged to solve this task according to the task description, using any language you may know.
- Task
Given two sets A and B, compute
That is, enumerate the items that are in A or B but not both. This set is called the symmetric difference of A and B.
In other words: (the set of items that are in at least one of A or B minus the set of items that are in both A and B).
Optionally, give the individual differences ( and ) as well.
- Test cases
A = {John, Bob, Mary, Serena}
B = {Jim, Mary, John, Bob}
- Notes
- If your code uses lists of items to represent sets then ensure duplicate items in lists are correctly handled. For example two lists representing sets of
a = ["John", "Serena", "Bob", "Mary", "Serena"]andb = ["Jim", "Mary", "John", "Jim", "Bob"]should produce the result of just two strings:["Serena", "Jim"], in any order. - In the mathematical notation above
A \ Bgives the set of items in A that are not in B;A ∪ Bgives the set of items in both A and B, (their union); andA ∩ Bgives the set of items that are in both A and B (their intersection).
Ada
Ada has the lattice operation xor predefined on Boolean, modular types, 1D arrays, set implementations from the standard library. The provided solution uses arrays: <lang Ada>with Ada.Text_IO; use Ada.Text_IO;
procedure Test_XOR is
type Person is (John, Bob, Mary, Serena, Jim);
type Group is array (Person) of Boolean;
procedure Put (Set : Group) is
First : Boolean := True;
begin
for I in Set'Range loop
if Set (I) then
if First then
First := False;
else
Put (',');
end if;
Put (Person'Image (I));
end if;
end loop;
end Put;
A : Group := (John | Bob | Mary | Serena => True, others => False); B : Group := (Jim | Mary | John | Bob => True, others => False);
begin
Put ("A xor B = "); Put (A xor B); New_Line;
Put ("A - B = "); Put (A and not B); New_Line;
Put ("B - A = "); Put (B and not A); New_Line;
end Test_XOR;</lang> Sample output:
A xor B = SERENA,JIM A - B = SERENA B - A = JIM
Aime
<lang aime>show_sdiff(record u, x) {
record r; text s;
r.copy(u);
for (s in x) {
if (r.key(s)) {
r.delete(s);
} else {
r.p_integer(s, 0);
}
}
r.vcall(o_, 0, "\n");
}
new_set(...) {
record r;
ucall(r_p_integer, 1, r, 0);
r;
}
main(void) {
show_sdiff(new_set("John", "Bob", "Mary", "Serena"),
new_set("Jim", "Mary", "John", "Bob"));
0;
}</lang>
- Output:
Jim Serena
Apex
<lang Java>Set<String> setA = new Set<String>{'John', 'Bob', 'Mary', 'Serena'}; Set<String> setB = new Set<String>{'Jim', 'Mary', 'John', 'Bob'};
// Option 1 Set<String> notInSetA = setB.clone(); notInSetA.removeAll(setA);
Set<String> notInSetB = setA.clone(); notInSetB.removeAll(setB);
Set<String> symmetricDifference = new Set<String>(); symmetricDifference.addAll(notInSetA); symmetricDifference.addAll(notInSetB);
// Option 2 Set<String> union = setA.clone(); union.addAll(setB);
Set<String> intersection = setA.clone(); intersection.retainAll(setB);
Set<String> symmetricDifference2 = union.clone(); symmetricDifference2.removeAll(intersection);
System.debug('Not in set A: ' + notInSetA); System.debug('Not in set B: ' + notInSetB); System.debug('Symmetric Difference: ' + symmetricDifference); System.debug('Symmetric Difference 2: ' + symmetricDifference2);</lang>
- Output:
Not in set A: {Jim}
Not in set B: {Serena}
Symmetric Difference: {Jim, Serena}
Symmetric Difference 2: {Jim, Serena}
AppleScript
(ES6 Functional JS)
<lang AppleScript>-- SYMMETRIC DIFFERENCE -------------------------------------------
-- symmetricDifference :: [a] -> [a] -> [a] on symmetricDifference(xs, ys)
union(difference(xs, ys), difference(ys, xs))
end symmetricDifference
-- TEST ----------------------------------------------------------- on run
set a to ["John", "Serena", "Bob", "Mary", "Serena"]
set b to ["Jim", "Mary", "John", "Jim", "Bob"]
symmetricDifference(a, b)
--> {"Serena", "Jim"}
end run
-- GENERIC FUNCTIONS ----------------------------------------------
-- delete :: Eq a => a -> [a] -> [a] on |delete|(x, xs)
set mbIndex to elemIndex(x, xs)
set lng to length of xs
if mbIndex is not missing value then
if lng > 1 then
if mbIndex = 1 then
items 2 thru -1 of xs
else if mbIndex = lng then
items 1 thru -2 of xs
else
tell xs to items 1 thru (mbIndex - 1) & ¬
items (mbIndex + 1) thru -1
end if
else
{}
end if
else
xs
end if
end |delete|
-- difference :: [a] -> [a] -> [a] on difference(xs, ys)
script
on |λ|(a, y)
if a contains y then
my |delete|(y, a)
else
a
end if
end |λ|
end script
foldl(result, xs, ys)
end difference
-- elemIndex :: a -> [a] -> Maybe Int on elemIndex(x, xs)
set lng to length of xs
repeat with i from 1 to lng
if x = (item i of xs) then return i
end repeat
return missing value
end elemIndex
-- foldl :: (a -> b -> a) -> a -> [b] -> a on foldl(f, startValue, xs)
tell mReturn(f)
set v to startValue
set lng to length of xs
repeat with i from 1 to lng
set v to |λ|(v, item i of xs, i, xs)
end repeat
return v
end tell
end foldl
-- Lift 2nd class handler function into 1st class script wrapper -- mReturn :: Handler -> Script on mReturn(f)
if class of f is script then
f
else
script
property |λ| : f
end script
end if
end mReturn
-- nub :: [a] -> [a] on nub(xs)
if (length of xs) > 1 then
set x to item 1 of xs
[x] & nub(|delete|(x, items 2 thru -1 of xs))
else
xs
end if
end nub
-- union :: [a] -> [a] -> [a] on union(xs, ys)
script flipDelete
on |λ|(xs, x)
my |delete|(x, xs)
end |λ|
end script
set sx to nub(xs)
sx & foldl(flipDelete, nub(ys), sx)
end union</lang>
- Output:
<lang AppleScript>{"Serena", "Jim"}</lang>
AutoHotkey
<lang autohotkey>setA = John, Bob, Mary, Serena setB = Jim, Mary, John, Bob MsgBox,, Singles, % SymmetricDifference(setA, setB)
setA = John, Serena, Bob, Mary, Serena setB = Jim, Mary, John, Jim, Bob MsgBox,, Duplicates, % SymmetricDifference(setA, setB)
- ---------------------------------------------------------------------------
SymmetricDifference(A, B) { ; returns the symmetric difference of A and B
- ---------------------------------------------------------------------------
StringSplit, A_, A, `,, %A_Space%
Loop, %A_0%
If Not InStr(B, A_%A_Index%)
And Not InStr(Result, A_%A_Index%)
Result .= A_%A_Index% ", "
StringSplit, B_, B, `,, %A_Space%
Loop, %B_0%
If Not InStr(A, B_%A_Index%)
And Not InStr(Result, B_%A_Index%)
Result .= B_%A_Index% ", "
Return, SubStr(Result, 1, -2)
}</lang> Message boxes show:
Singles --------------------------- Serena, Jim OK
Duplicates --------------------------- Serena, Jim OK
AWK
<lang AWK>
- syntax: GAWK -f SYMMETRIC_DIFFERENCE.AWK
BEGIN {
load("John,Bob,Mary,Serena",A)
load("Jim,Mary,John,Bob",B)
show("A \\ B",A,B)
show("B \\ A",B,A)
printf("symmetric difference: ")
for (i in C) {
if (!(i in A && i in B)) {
printf("%s ",i)
}
}
printf("\n")
exit(0)
} function load(str,arr, i,n,temp) {
n = split(str,temp,",")
for (i=1; i<=n; i++) {
arr[temp[i]]
C[temp[i]]
}
} function show(str,a,b, i) {
printf("%s: ",str)
for (i in a) {
if (!(i in b)) {
printf("%s ",i)
}
}
printf("\n")
} </lang>
output:
A \ B: Serena B \ A: Jim symmetric difference: Serena Jim
BBC BASIC
Here sets are represented as integers, hence there are a maximum of 32 elements in a set. <lang bbcbasic> DIM list$(4)
list$() = "Bob", "Jim", "John", "Mary", "Serena"
setA% = %11101
PRINT "Set A: " FNlistset(list$(), setA%)
setB% = %01111
PRINT "Set B: " FNlistset(list$(), setB%)
REM Compute symmetric difference:
setC% = setA% EOR setB%
PRINT '"Symmetric difference: " FNlistset(list$(), setC%)
REM Optional:
PRINT "Set A \ Set B: " FNlistset(list$(), setA% AND NOT setB%)
PRINT "Set B \ Set A: " FNlistset(list$(), setB% AND NOT setA%)
END
DEF FNlistset(list$(), set%)
LOCAL i%, o$
FOR i% = 0 TO 31
IF set% AND 1 << i% o$ += list$(i%) + ", "
NEXT
= LEFT$(LEFT$(o$))</lang>
Output:
Set A: Bob, John, Mary, Serena Set B: Bob, Jim, John, Mary Symmetric difference: Jim, Serena Set A \ Set B: Serena Set B \ Set A: Jim
Bracmat
Walk through the concatenation of the two lists, using backtracking (forced by the ~ operator).
If an element is in both lists, or if the element already is in the accumulated result symdiff, continue. Otherwise add the element to symdiff. When all elements are done and backtracking therefore finally fails, return the contents of symdiff. The flag % in the pattern %@?x ensures that only nontrivial elements (i.e. non-empty strings in this case) are matched. The @ flag ensures that at most one string is matched. Together these flags ensure that exactly one element is matched.
<lang bracmat>(SymmetricDifference=
A B x symdiff
. !arg:(?A.?B)
& :?symdiff
& ( !A !B
: ?
( %@?x
& ( !A:? !x ?&!B:? !x ?
| !symdiff:? !x ?
| !symdiff !x:?symdiff
)
& ~
)
?
| !symdiff
));</lang>
Run: <lang bracmat>SymmetricDifference$(john serena bob mary serena.jim mary john jim bob)</lang> Output: <lang bracmat>serena jim</lang>
C
Simple method: <lang c>#include <stdio.h>
- include <string.h>
const char *A[] = { "John", "Serena", "Bob", "Mary", "Serena" }; const char *B[] = { "Jim", "Mary", "John", "Jim", "Bob" };
- define LEN(x) sizeof(x)/sizeof(x[0])
/* null duplicate items */ void uniq(const char *x[], int len) { int i, j; for (i = 0; i < len; i++) for (j = i + 1; j < len; j++) if (x[j] && x[i] && !strcmp(x[i], x[j])) x[j] = 0; }
int in_set(const char *const x[], int len, const char *match) { int i; for (i = 0; i < len; i++) if (x[i] && !strcmp(x[i], match)) return 1; return 0; }
/* x - y */ void show_diff(const char *const x[], int lenx, const char *const y[], int leny) { int i; for (i = 0; i < lenx; i++) if (x[i] && !in_set(y, leny, x[i])) printf(" %s\n", x[i]); }
/* X ^ Y */ void show_sym_diff(const char *const x[], int lenx, const char *const y[], int leny) { show_diff(x, lenx, y, leny); show_diff(y, leny, x, lenx); }
int main() { uniq(A, LEN(A)); uniq(B, LEN(B)); printf("A \\ B:\n"); show_diff(A, LEN(A), B, LEN(B)); printf("\nB \\ A:\n"); show_diff(B, LEN(B), A, LEN(A)); printf("\nA ^ B:\n"); show_sym_diff(A, LEN(A), B, LEN(B));
return 0; }</lang>output
A \ B: Serena B \ A: Jim A ^ B: Serena Jim
If you prefer something elaborate: <lang c>#include <assert.h>
- include <stdio.h>
- include <string.h>
- include <stdlib.h>
const char *mary="Mary"; const char *bob="Bob"; const char *jim="Jim"; const char *john="John"; const char *serena="Serena";
const char *setA[] = {john,bob,mary,serena}; const char *setB[] = {jim,mary,john,bob};
- define XSET(j) j, (sizeof(j)/sizeof(*j))
- define TALLOC(n,typ) malloc(n*sizeof(typ))
typedef enum {
esdDIFFERENCE, esdSYMMETRIC } EsdFunction;
/** * * * * * * * * * * * * * * * * * * * *
* return value is difference or symmetric difference set * its size is returned in sym_size * f determinse whether it is a symmetric difference, or normal difference * * * * * * * * * * * * * * * * * * * * **/
const char ** symmdiff( int *sym_size, EsdFunction f, const char *setA[], int setAsize, const char *setB[], int setBsize) {
int union_size; int max_union_size; int diff_size; const char **union_set; const char **diff_set; int *union_xor; int ix, ixu;
max_union_size = setAsize + setBsize; union_set = TALLOC(max_union_size, const char *); union_xor = TALLOC(max_union_size, int);
/* I'm assuming here that setA has no duplicates,
* i.e. is a set in mathematical sense */
for (ix=0; ix<setAsize; ix++) {
union_set[ix] = setA[ix];
union_xor[ix] = 1;
}
diff_size = union_size = setAsize;
for (ix=0; ix<setBsize; ix++) {
for (ixu=0; ixu<union_size; ixu++) {
if (union_set[ixu] == setB[ix]) break;
}
if (ixu < union_size) { /* already in union */
union_xor[ixu] = 1-union_xor[ixu];
diff_size--;
}
else { /* not already in union -add */
if (f == esdSYMMETRIC) {
union_set[ixu] = setB[ix];
union_xor[ixu] = 1;
union_size++;
diff_size++;
}
}
}
/* Put results in symdiff set */
diff_set = TALLOC(diff_size, const char *);
ix = 0;
for (ixu=0; ixu<union_size; ixu++) {
if (union_xor[ixu]) {
if (ix == diff_size) {
printf("Short of space in diff_set\n");
exit(1);
}
diff_set[ix] = union_set[ixu];
ix++;
}
}
*sym_size = diff_size;
free(union_xor);
free(union_set);
return diff_set;
}
/* isSet tests that elements of list are unique, that is, that the list is a
* mathematical set. The uniqueness test implemented here is strcmp. */
int isSet(const char *list[], int lsize) {
int i, j;
const char *e;
if (lsize == 0) {
return 1;
}
for (i = lsize-1; i>0; i--) {
e = list[i];
for (j = i-1; j>=0; j--) {
if (strcmp(list[j], e) == 0) {
return 0;
}
}
}
return 1;
}
void printSet (const char *set[], int ssize) {
int ix;
printf(" = {");
for (ix=0;ix<ssize; ix++) {
printf( "%s ", set[ix]);
}
printf("}\n");
}
int main() {
const char **symset; int sysize;
/* Validate precondition stated by task, that inputs are sets. */ assert(isSet(XSET(setA))); assert(isSet(XSET(setB)));
printf ("A symmdiff B");
symset = symmdiff( &sysize, esdSYMMETRIC, XSET(setA), XSET(setB));
printSet(symset, sysize);
free(symset);
printf ("A - B");
symset = symmdiff( &sysize, esdDIFFERENCE, XSET(setA), XSET(setB));
printSet(symset, sysize);
printf ("B - A");
symset = symmdiff( &sysize, esdDIFFERENCE, XSET(setB), XSET(setA));
printSet(symset, sysize);
free(symset);
return 0;
}</lang> Output
A symmdiff B = {Serena Jim }
A - B = {Serena }
B - A = {Jim }
C#
<lang csharp>using System; using System.Collections.Generic; using System.Linq;
namespace RosettaCode.SymmetricDifference {
public static class IEnumerableExtension
{
public static IEnumerable<T> SymmetricDifference<T>(this IEnumerable<T> @this, IEnumerable<T> that)
{
return @this.Except(that).Concat(that.Except(@this));
}
}
class Program
{
static void Main()
{
var a = new[] { "John", "Bob", "Mary", "Serena" };
var b = new[] { "Jim", "Mary", "John", "Bob" };
foreach (var element in a.SymmetricDifference(b))
{
Console.WriteLine(element);
}
}
}
}</lang> Output:
Serena Jim
C++
<lang cpp>#include <iostream>
- include <set>
- include <algorithm>
- include <iterator>
- include <string>
using namespace std;
int main( ) {
string setA[] = { "John", "Bob" , "Mary", "Serena" };
string setB[] = { "Jim" , "Mary", "John", "Bob" };
set<string>
firstSet( setA , setA + 4 ),
secondSet( setB , setB + 4 ),
symdiff;
set_symmetric_difference( firstSet.begin(), firstSet.end(),
secondSet.begin(), secondSet.end(),
inserter( symdiff, symdiff.end() ) );
copy( symdiff.begin(), symdiff.end(), ostream_iterator<string>( cout , " " ) ); cout << endl; return 0;
}</lang>
Output: Jim Serena
Clojure
<lang clojure>(use '[clojure.set])
(defn symmetric-difference [s1 s2]
(union (difference s1 s2) (difference s2 s1)))
(symmetric-difference #{:john :bob :mary :serena} #{:jim :mary :john :bob})</lang>
Common Lisp
<lang lisp>(set-exclusive-or
(remove-duplicates '(John Serena Bob Mary Serena)) (remove-duplicates '(Jim Mary John Jim Bob)))</lang>
Output:
(JIM SERENA)
D
Generic version. <lang d>import std.stdio, std.algorithm, std.array;
struct Set(T) {
immutable T[] items;
Set opSub(in Set other) const pure nothrow {
return items.filter!(x => !other.items.canFind(x)).array.Set;
}
Set opAdd(in Set other) const pure nothrow {
return Set(this.items ~ (other - this).items);
}
}
Set!T symmetricDifference(T)(in Set!T left, in Set!T right) pure nothrow {
return (left - right) + (right - left);
}
void main() {
immutable A = ["John", "Bob", "Mary", "Serena"].Set!string; immutable B = ["Jim", "Mary", "John", "Bob"].Set!string;
writeln(" A\\B: ", (A - B).items);
writeln(" B\\A: ", (B - A).items);
writeln("A symdiff B: ", symmetricDifference(A, B).items);
}</lang>
- Output:
A\B: ["Serena"]
B\A: ["Jim"]
A symdiff B: ["Serena", "Jim"]
Déjà Vu
Déjà Vu has no real set type. Instead, it uses a dictionary whose keys are the set values. The set{ constructor uses true as a dummy value, and sets false as a dummy value.
<lang dejavu>set :setA set{ :John :Bob :Mary :Serena }
set :setB set{ :Jim :Mary :John :Bob }
symmetric-difference A B: } for a in keys A: if not has B a: a for b in keys B: if not has A b: b set{
!. symmetric-difference setA setB</lang>
- Output:
set{ :Serena :Jim }
E
<lang e>? def symmDiff(a, b) { return (a &! b) | (b &! a) }
- value: <symmDiff>
? symmDiff(["John", "Bob", "Mary", "Serena"].asSet(), ["Jim", "Mary", "John", "Bob"].asSet())
- value: ["Jim", "Serena"].asSet()</lang>
Elixir
<lang elixir>iex(1)> a = ~w[John Bob Mary Serena] |> MapSet.new
- MapSet<["Bob", "John", "Mary", "Serena"]>
iex(2)> b = ~w[Jim Mary John Bob] |> MapSet.new
- MapSet<["Bob", "Jim", "John", "Mary"]>
iex(3)> sym_dif = fn(a,b) -> MapSet.difference(MapSet.union(a,b), MapSet.intersection(a,b)) end
- Function<12.54118792/2 in :erl_eval.expr/5>
iex(4)> sym_dif.(a,b)
- MapSet<["Jim", "Serena"]></lang>
Erlang
<lang erlang>%% Implemented by Arjun Sunel -module(symdiff). -export([main/0]).
main() -> SetA = sets:from_list(["John","Bob","Mary","Serena"]), SetB = sets:from_list(["Jim","Mary","John","Bob"]), AUnionB = sets:union(SetA,SetB), AIntersectionB = sets:intersection(SetA,SetB), SymmDiffAB = sets:subtract(AUnionB,AIntersectionB), sets:to_list(SymmDiffAB). </lang>
- Output:
["Serena","Jim"]
F#
<lang fsharp>> let a = set ["John"; "Bob"; "Mary"; "Serena"]
let b = set ["Jim"; "Mary"; "John"; "Bob"];;
val a : Set<string> = set ["Bob"; "John"; "Mary"; "Serena"] val b : Set<string> = set ["Bob"; "Jim"; "John"; "Mary"]
> (a-b) + (b-a);; val it : Set<string> = set ["Jim"; "Serena"]</lang> Or, if you don't like the infix operators: <lang fsharp>> Set.union (Set.difference a b) (Set.difference b a);; val it : Set<string> = set ["Jim"; "Serena"]</lang>
Eiffel
<lang Eiffel>note description: "Summary description for {SYMETRIC_DIFFERENCE_EXAMPLE}." URI: "http://rosettacode.org/wiki/Symmetric_difference"
class SYMETRIC_DIFFERENCE_EXAMPLE
create make
feature {NONE} -- Initialization
make local a,a1,b,b1: ARRAYED_SET [STRING] do create a.make (4) create b.make (4) a.compare_objects b.compare_objects a.put ("John") a.put ("Bob") a.put ("Mary") a.put ("Serena")
create a1.make (4) a1.copy (a)
b.put ("Jim") b.put ("Mary") b.put ("John") b.put ("Bob")
create b1.make (4) b1.copy (b)
a1.subtract (b1) b.subtract (a) a1.merge (b) across a1 as c loop print (" " + c.item) end end
end</lang>
Factor
<lang factor>: symmetric-diff ( a b -- c )
[ diff ] [ swap diff ] 2bi append ;
{ "John" "Bob" "Mary" "Serena" } { "Jim" "Mary" "John" "Bob" } symmetric-diff .</lang>
Forth
GForth 0.7.0 tested. <lang Forth>: elm ( n -- ; one cell per set ) [ cell 8 * 1- ] literal umin CREATE 1 swap lshift , DOES> ( -- 2^n ) @ ;
- universe ( u "name" -- )
dup 0 DO I elm latest swap LOOP CREATE dup , 0 DO , LOOP DOES> ( n a -- ) dup @ tuck cells + swap 0 DO ( n a' ) over I rshift 1 AND IF dup @ name>string space type THEN 1 cells - LOOP 2drop ;
5 universe john bob mary serena jim persons john bob mary serena or or or jim mary john bob or or or
2dup xor persons 2dup -1 xor and cr persons swap -1 xor and cr persons cr bye </lang> Output:
$ gforth wrk.fs serena jim serena jim $
Fortran
<lang fortran>program Symmetric_difference implicit none
character(6) :: a(4) = (/ "John ", "Bob ", "Mary ", "Serena" /) character(6) :: b(4) = (/ "Jim ", "Mary ", "John ", "Bob " /) integer :: i, j
outer1: do i = 1, size(a)
do j = 1, i-1
if(a(i) == a(j)) cycle outer1 ! Do not check duplicate items
end do
if(.not. any(b == a(i))) write(*,*) a(i)
end do outer1
outer2: do i = 1, size(b)
do j = 1, i-1
if(b(i) == b(j)) cycle outer2 ! Do not check duplicate items
end do
if(.not. any(a == b(i))) write(*,*) b(i)
end do outer2
end program</lang> Output
Serena Jim
GAP
<lang gap>SymmetricDifference := function(a, b)
return Union(Difference(a, b), Difference(b, a));
end;
a := ["John", "Serena", "Bob", "Mary", "Serena"]; b := ["Jim", "Mary", "John", "Jim", "Bob"]; SymmetricDifference(a,b); [ "Jim", "Serena" ]</lang>
Go
<lang go>package main
import "fmt"
var a = map[string]bool{"John": true, "Bob": true, "Mary": true, "Serena": true} var b = map[string]bool{"Jim": true, "Mary": true, "John": true, "Bob": true}
func main() {
sd := make(map[string]bool)
for e := range a {
if !b[e] {
sd[e] = true
}
}
for e := range b {
if !a[e] {
sd[e] = true
}
}
fmt.Println(sd)
}</lang> Output:
map[Jim:true Serena:true]
Alternatively, the following computes destructively on a. The result is the same. <lang go>func main() {
for e := range b {
delete(a, e)
}
fmt.Println(a)
}</lang>
Groovy
Solution: <lang groovy>def symDiff = { Set s1, Set s2 ->
assert s1 != null assert s2 != null (s1 + s2) - (s1.intersect(s2))
}</lang> Test: <lang groovy>Set a = ['John', 'Serena', 'Bob', 'Mary', 'Serena'] Set b = ['Jim', 'Mary', 'John', 'Jim', 'Bob']
assert a.size() == 4 assert a == (['Bob', 'John', 'Mary', 'Serena'] as Set) assert b.size() == 4 assert b == (['Bob', 'Jim', 'John', 'Mary'] as Set)
def aa = symDiff(a, a) def ab = symDiff(a, b) def ba = symDiff(b, a) def bb = symDiff(b, b)
assert aa.empty assert bb.empty assert ab == ba assert ab == (['Jim', 'Serena'] as Set) assert ab == (['Serena', 'Jim'] as Set)
println """ a: ${a} b: ${b}
Symmetric Differences
=========
a <> a: ${aa} a <> b: ${ab} b <> a: ${ba} b <> b: ${bb}
"""
Set apostles = ['Matthew', 'Mark', 'Luke', 'John', 'Peter', 'Paul', 'Silas'] Set beatles = ['John', 'Paul', 'George', 'Ringo', 'Peter', 'Stuart'] Set csny = ['Crosby', 'Stills', 'Nash', 'Young'] Set ppm = ['Peter', 'Paul', 'Mary']
def AA = symDiff(apostles, apostles) def AB = symDiff(apostles, beatles) def AC = symDiff(apostles, csny) def AP = symDiff(apostles, ppm)
def BA = symDiff(beatles, apostles) def BB = symDiff(beatles, beatles) def BC = symDiff(beatles, csny) def BP = symDiff(beatles, ppm)
def CA = symDiff(csny, apostles) def CB = symDiff(csny, beatles) def CC = symDiff(csny, csny) def CP = symDiff(csny, ppm)
def PA = symDiff(ppm, apostles) def PB = symDiff(ppm, beatles) def PC = symDiff(ppm, csny) def PP = symDiff(ppm, ppm)
assert AB == BA assert AC == CA assert AP == PA assert BC == CB assert BP == PB assert CP == PC
println """ apostles: ${apostles}
beatles: ${beatles}
csny: ${csny}
ppm: ${ppm}
Symmetric Differences
=========
apostles <> apostles: ${AA} apostles <> beatles: ${AB} apostles <> csny: ${AC} apostles <> ppm: ${AP}
beatles <> apostles: ${BA} beatles <> beatles: ${BB} beatles <> csny: ${BC} beatles <> ppm: ${BP}
csny <> apostles: ${CA} csny <> beatles: ${CB} csny <> csny: ${CC} csny <> ppm: ${CP}
ppm <> apostles: ${PA} ppm <> beatles: ${PB} ppm <> csny: ${PC} ppm <> ppm: ${PP} """</lang>
Output:
a: [Mary, Bob, Serena, John]
b: [Mary, Bob, Jim, John]
Symmetric Differences
=====================
a <> a: []
a <> b: [Jim, Serena]
b <> a: [Jim, Serena]
b <> b: []
apostles: [Paul, Mark, Silas, Peter, Luke, John, Matthew]
beatles: [Paul, Stuart, Ringo, Peter, John, George]
csny: [Crosby, Young, Nash, Stills]
ppm: [Paul, Mary, Peter]
Symmetric Differences
=====================
apostles <> apostles: []
apostles <> beatles: [Mark, Silas, Stuart, Ringo, Luke, Matthew, George]
apostles <> csny: [Paul, Crosby, Mark, Silas, Young, Peter, Luke, John, Matthew, Nash, Stills]
apostles <> ppm: [Mark, Mary, Silas, Luke, John, Matthew]
beatles <> apostles: [Mark, Stuart, Ringo, Silas, Luke, Matthew, George]
beatles <> beatles: []
beatles <> csny: [Paul, Crosby, Stuart, Ringo, Young, Peter, John, Nash, Stills, George]
beatles <> ppm: [Mary, Stuart, Ringo, John, George]
csny <> apostles: [Paul, Crosby, Mark, Silas, Young, Peter, Luke, John, Nash, Stills, Matthew]
csny <> beatles: [Paul, Crosby, Stuart, Ringo, Young, Peter, John, Nash, Stills, George]
csny <> csny: []
csny <> ppm: [Paul, Crosby, Mary, Young, Peter, Nash, Stills]
ppm <> apostles: [Mark, Mary, Silas, Luke, John, Matthew]
ppm <> beatles: [Mary, Stuart, Ringo, John, George]
ppm <> csny: [Paul, Crosby, Mary, Young, Peter, Nash, Stills]
ppm <> ppm: []
Haskell
<lang haskell>import Data.Set
a = fromList ["John", "Bob", "Mary", "Serena"] b = fromList ["Jim", "Mary", "John", "Bob"]
(-|-) :: Ord a => Set a -> Set a -> Set a x -|- y = (x \\ y) `union` (y \\ x)
-- Equivalently: (x `union` y) \\ (x `intersect` y)</lang>
Symmetric difference: <lang haskell>*Main> a -|- b fromList ["Jim","Serena"]</lang> Individual differences: <lang haskell>*Main> a \\ b fromList ["Serena"]
- Main> b \\ a
fromList ["Jim"]</lang>
HicEst
<lang HicEst>CALL SymmDiff("John,Serena,Bob,Mary,Serena,", "Jim,Mary,John,Jim,Bob,") CALL SymmDiff("John,Bob,Mary,Serena,", "Jim,Mary,John,Bob,")
SUBROUTINE SymmDiff(set1, set2)
CHARACTER set1, set2, answer*50 answer = " " CALL setA_setB( set1, set2, answer ) CALL setA_setB( set2, set1, answer ) WRITE(Messagebox,Name) answer ! answer = "Serena,Jim," in both cases
END
SUBROUTINE setA_setB( set1, set2, differences )
CHARACTER set1, set2, differences, a*100 a = set1 EDIT(Text=a, $inLeXicon=set2) ! eg a <= $John,Serena,$Bob,$Mary,Serena, EDIT(Text=a, Right="$", Mark1, Right=",", Mark2, Delete, DO) ! Serena,Serena, EDIT(Text=a, Option=1, SortDelDbls=a) ! Option=1: keep case; Serena, differences = TRIM( differences ) // a
END</lang>
Icon and Unicon
Set operations are built into Icon/Unicon. <lang Icon>procedure main()
a := set(["John", "Serena", "Bob", "Mary", "Serena"]) b := set(["Jim", "Mary", "John", "Jim", "Bob"])
showset("a",a) showset("b",b) showset("(a\\b) \xef (b\\a)",(a -- b) ++ (b -- a)) showset("(a\\b)",a -- b) showset("(b\\a)",b -- a) end
procedure showset(n,x)
writes(n," = { ")
every writes(!x," ")
write("}")
return
end</lang>
Sample output:
a = { Serena Mary Bob John }
b = { Mary Bob Jim John }
(a\b) ∩ (b\a) = { Serena Jim }
(a\b) = { Serena }
(b\a) = { Jim }
J
<lang j> A=: ~.;:'John Serena Bob Mary Serena'
B=: ~. ;:'Jim Mary John Jim Bob'
(A-.B) , (B-.A) NB. Symmetric Difference
┌──────┬───┐ │Serena│Jim│ └──────┴───┘
A (-. , -.~) B NB. Tacit equivalent
┌──────┬───┐ │Serena│Jim│ └──────┴───┘</lang> To illustrate some of the underlying mechanics used here: <lang j> A -. B NB. items in A but not in B ┌──────┐ │Serena│ └──────┘
A -.~ B NB. items in B but not in A
┌───┐ │Jim│ └───┘
A NB. A is a sequence without duplicates
┌────┬──────┬───┬────┐
│John│Serena│Bob│Mary│
└────┴──────┴───┴────┘</lang>
Here's an alternative implementation:
<lang j> A (, -. [ -. -.) B
┌──────┬───┐
│Serena│Jim│
└──────┴───┘</lang>
Here, (,) contains all items from A and B and ([ -. -.) is the idiom for set intersection, and their difference is the symmetric difference. (Note: an individual word in a J sentence may be placed inside a parenthesis with no change in evaluation, and this can also be used for emphasis when a word might get lost.)
Java
<lang java>import java.util.Arrays; import java.util.HashSet; import java.util.Set;
public class SymmetricDifference {
public static void main(String[] args) {
Set<String> setA = new HashSet<String>(Arrays.asList("John", "Serena", "Bob", "Mary", "Serena"));
Set<String> setB = new HashSet<String>(Arrays.asList("Jim", "Mary", "John", "Jim", "Bob"));
// Present our initial data set
System.out.println("In set A: " + setA);
System.out.println("In set B: " + setB);
// Option 1: union of differences
// Get our individual differences.
Set<String> notInSetA = new HashSet<String>(setB);
notInSetA.removeAll(setA);
Set<String> notInSetB = new HashSet<String>(setA);
notInSetB.removeAll(setB);
// The symmetric difference is the concatenation of the two individual differences
Set<String> symmetricDifference = new HashSet<String>(notInSetA);
symmetricDifference.addAll(notInSetB);
// Option 2: union minus intersection
// Combine both sets
Set<String> union = new HashSet<String>(setA);
union.addAll(setB);
// Get the intersection
Set<String> intersection = new HashSet<String>(setA);
intersection.retainAll(setB);
// The symmetric difference is the union of the 2 sets minus the intersection
Set<String> symmetricDifference2 = new HashSet<String>(union);
symmetricDifference2.removeAll(intersection);
// Present our results
System.out.println("Not in set A: " + notInSetA);
System.out.println("Not in set B: " + notInSetB);
System.out.println("Symmetric Difference: " + symmetricDifference);
System.out.println("Symmetric Difference 2: " + symmetricDifference2);
}
}</lang> Output:
In set A: [Mary, Bob, Serena, John] In set B: [Mary, Bob, Jim, John] Not in set A: [Jim] Not in set B: [Serena] Symmetric Difference: [Jim, Serena] Symmetric Difference 2: [Jim, Serena]
JavaScript
ES5
Iterative
for the print() function.
Uses the Array function unique() defined here.
<lang javascript>// in A but not in B
function relative_complement(A, B) {
return A.filter(function(elem) {return B.indexOf(elem) == -1});
}
// in A or in B but not in both function symmetric_difference(A,B) {
return relative_complement(A,B).concat(relative_complement(B,A));
}
var a = ["John", "Serena", "Bob", "Mary", "Serena"].unique(); var b = ["Jim", "Mary", "John", "Jim", "Bob"].unique();
print(a); print(b); print(symmetric_difference(a,b));</lang> outputs
Bob,John,Mary,Serena Bob,Jim,John,Mary Serena,Jim
Clear JavaScript
<lang javascript>function Difference(A,B) {
var a = A.length, b = B.length, c = 0, C = [];
for (var i = 0; i < a; i++)
{ var j = 0, k = 0;
while (j < b && B[j] !== A[i]) j++;
while (k < c && C[k] !== A[i]) k++;
if (j == b && k == c) C[c++] = A[i];
}
return C;
}
function SymmetricDifference(A,B) {
var D1 = Difference(A,B), D2 = Difference(B,A),
a = D1.length, b = D2.length;
for (var i = 0; i < b; i++) D1[a++] = D2[i];
return D1;
}
/* Example
A = ['John', 'Serena', 'Bob', 'Mary', 'Serena']; B = ['Jim', 'Mary', 'John', 'Jim', 'Bob']; Difference(A,B); // 'Serena' Difference(B,A); // 'Jim' SymmetricDifference(A,B); // 'Serena','Jim'
- /</lang>
ES6
Functional
By composition of generic functions; <lang JavaScript>(() => {
'use strict';
const symmetricDifference = (xs, ys) =>
union(difference(xs, ys), difference(ys, xs));
// GENERIC FUNCTIONS ------------------------------------------------------
// First instance of x (if any) removed from xs
// delete_ :: Eq a => a -> [a] -> [a]
const delete_ = (x, xs) => {
const i = xs.indexOf(x);
return i !== -1 ? (xs.slice(0, i)
.concat(xs.slice(i, -1))) : xs;
};
// (\\) :: (Eq a) => [a] -> [a] -> [a]
const difference = (xs, ys) =>
ys.reduce((a, x) => filter(z => z !== x, a), xs);
// filter :: (a -> Bool) -> [a] -> [a] const filter = (f, xs) => xs.filter(f);
// flip :: (a -> b -> c) -> b -> a -> c const flip = f => (a, b) => f.apply(null, [b, a]);
// foldl :: (b -> a -> b) -> b -> [a] -> b const foldl = (f, a, xs) => xs.reduce(f, a);
// nub :: [a] -> [a]
const nub = xs => {
const mht = unconsMay(xs);
return mht.nothing ? xs : (
([h, t]) => [h].concat(nub(t.filter(s => s !== h)))
)(mht.just);
};
// show :: a -> String const show = x => JSON.stringify(x, null, 2);
// unconsMay :: [a] -> Maybe (a, [a])
const unconsMay = xs => xs.length > 0 ? {
just: [xs[0], xs.slice(1)],
nothing: false
} : {
nothing: true
};
// union :: [a] -> [a] -> [a]
const union = (xs, ys) => {
const sx = nub(xs);
return sx.concat(foldl(flip(delete_), nub(ys), sx));
};
// TEST -------------------------------------------------------------------
const
a = ["John", "Serena", "Bob", "Mary", "Serena"],
b = ["Jim", "Mary", "John", "Jim", "Bob"];
return show(
symmetricDifference(a, b)
);
})();</lang>
- Output:
<lang JavaScript>["Serena", "Jim"]</lang>
Procedural
<lang JavaScript> const symmetricDifference = (...args) => {
let result = new Set();
for (const x of args)
for (const e of new Set(x))
if (result.has(e)) result.delete(e)
else result.add(e);
return [...result];
}
// TEST -------------------------------------------------------------------
console.log(symmetricDifference(["Jim", "Mary", "John", "Jim", "Bob"],["John", "Serena", "Bob", "Mary", "Serena"])); console.log(symmetricDifference([1, 2, 5], [2, 3, 5], [3, 4, 5]));
</lang>
- Output:
<lang JavaScript>["Jim", "Serena"] [1, 4, 5] </lang>
jq
The following implementation of symmetric_difference(a;b) makes no assumptions about the input lists except that neither contains null; given these assumptions, it is quite efficient. To workaround the no-null requirement would be tedious but straightforward. <lang jq># The following implementation of intersection (but not symmetric_difference) assumes that the
- elements of a (and of b) are unique and do not include null:
def intersection(a; b):
reduce ((a + b) | sort)[] as $i ([null, []]; if .[0] == $i then [null, .[1] + [$i]] else [$i, .[1]] end) | .[1] ;
def symmetric_difference(a;b):
(a|unique) as $a | (b|unique) as $b | (($a + $b) | unique) - (intersection($a;$b));
</lang>
Example:<lang jq>symmetric_difference( [1,2,1,2]; [2,3] ) [1,3]</lang>
Julia
Built-in function. <lang julia>A = ["John", "Bob", "Mary", "Serena"] B = ["Jim", "Mary", "John", "Bob"] @show A B symdiff(A, B)</lang>
- Output:
A = String["John", "Bob", "Mary", "Serena"] B = String["Jim", "Mary", "John", "Bob"] symdiff(A, B) = String["Serena", "Jim"]
K
<lang k> A: ?("John";"Bob";"Mary";"Serena")
B: ?("Jim";"Mary";"John";"Bob")
A _dvl B / in A but not in B
"Serena"
B _dvl A / in B but not in A
"Jim"
(A _dvl B;B _dvl A) / Symmetric difference
("Serena"
"Jim")</lang>
Kotlin
<lang scala>// version 1.1.2
fun main(args: Array<String>) {
val a = setOf("John", "Bob", "Mary", "Serena")
val b = setOf("Jim", "Mary", "John", "Bob")
println("A = $a")
println("B = $b")
val c = a - b
println("A \\ B = $c")
val d = b - a
println("B \\ A = $d")
val e = c.union(d)
println("A Δ B = $e")
}</lang>
- Output:
A = [John, Bob, Mary, Serena] B = [Jim, Mary, John, Bob] A \ B = [Serena] B \ A = [Jim] A Δ B = [Serena, Jim]
Lasso
<lang lasso> [ var(
'a' = array(
'John'
,'Bob'
,'Mary'
,'Serena'
)
,'b' = array
);
$b->insert( 'Jim' ); // Alternate method of populating array $b->insert( 'Mary' ); $b->insert( 'John' ); $b->insert( 'Bob' );
$a->sort( true ); // arrays must be sorted (true = ascending) for difference to work $b->sort( true );
$a->difference( $b )->union( $b->difference( $a ) );
] </lang>
Logo
<lang logo>to diff :a :b [:acc []]
if empty? :a [output sentence :acc :b] ifelse member? first :a :b ~ [output (diff butfirst :a remove first :a :b :acc)] ~ [output (diff butfirst :a :b lput first :a :acc)]
end
make "a [John Bob Mary Serena] make "b [Jim Mary John Bob]
show diff :a :b ; [Serena Jim]</lang>
Lua
<lang lua>A = { ["John"] = true, ["Bob"] = true, ["Mary"] = true, ["Serena"] = true } B = { ["Jim"] = true, ["Mary"] = true, ["John"] = true, ["Bob"] = true }
A_B = {} for a in pairs(A) do
if not B[a] then A_B[a] = true end
end
B_A = {} for b in pairs(B) do
if not A[b] then B_A[b] = true end
end
for a_b in pairs(A_B) do
print( a_b )
end for b_a in pairs(B_A) do
print( b_a )
end</lang>
Object-oriented approach:
<lang lua>SetPrototype = {
__index = {
union = function(self, other)
local res = Set{}
for k in pairs(self) do res[k] = true end
for k in pairs(other) do res[k] = true end
return res
end,
intersection = function(self, other)
local res = Set{}
for k in pairs(self) do res[k] = other[k] end
return res
end,
difference = function(self, other)
local res = Set{}
for k in pairs(self) do
if not other[k] then res[k] = true end
end
return res
end,
symmetric_difference = function(self, other)
return self:difference(other):union(other:difference(self))
end
},
-- return string representation of set
__tostring = function(self)
-- list to collect all elements from the set
local l = {}
for k in pairs(self) do l[#l+1] = k end
return "{" .. table.concat(l, ", ") .. "}"
end,
-- allow concatenation with other types to yield string
__concat = function(a, b)
return (type(a) == 'string' and a or tostring(a)) ..
(type(b) == 'string' and b or tostring(b))
end
}
function Set(items)
local _set = {}
setmetatable(_set, SetPrototype)
for _, item in ipairs(items) do _set[item] = true end
return _set
end
A = Set{"John", "Serena", "Bob", "Mary", "Serena"} B = Set{"Jim", "Mary", "John", "Jim", "Bob"}
print("Set A: " .. A) print("Set B: " .. B)
print("\nSymm. difference (A\\B)∪(B\\A): " .. A:symmetric_difference(B)) print("Union A∪B : " .. A:union(B)) print("Intersection A∩B : " .. A:intersection(B)) print("Difference A\\B : " .. A:difference(B)) print("Difference B\\A : " .. B:difference(A))</lang>
Output:
Set A: {Serena, Mary, John, Bob}
Set B: {Mary, Jim, John, Bob}
Symm. difference (A\B)∪(B\A): {Serena, Jim}
Union A∪B : {John, Serena, Jim, Mary, Bob}
Intersection A∩B : {Mary, John, Bob}
Difference A\B : {Serena}
Difference B\A : {Jim}
Maple
Maple has built-in support for set operations. Assign the sets A and B: <lang Maple>A := {John, Bob, Mary, Serena}; B := {Jim, Mary, John, Bob};</lang> Now compute the symmetric difference with the symmdiff command: <lang Maple>symmdiff(A, B);</lang>
- Output:
{Jim, Serena}
Mathematica
Mathematica has built-in support for operations on sets, using its generic symbolic lists. This function finds the entries in each list that are not present in the intersection of the two lists. <lang Mathematica>SymmetricDifference[x_List,y_List] := Join[Complement[x,Intersection[x,y]],Complement[y,Intersection[x,y]]]</lang> For large lists, some performance improvement could be made by caching the intersection of the two lists to avoid computing it twice: <lang Mathematica>CachedSymmetricDifference[x_List,y_List] := Module[{intersect=Intersection[x,y]},Join[Complement[x,intersect],Complement[y,intersect]]]</lang> Also, due to Mathematica's symbolic nature, these functions are automatically applicable to lists of any content, such as strings, integers, reals, graphics, or undefined generic symbols (e.g. unassigned variables).
MATLAB
If you are using a vector of numbers as the sets of which you like to find the symmetric difference, then there are already utilities that operate on these types of sets built into MATLAB. This code will take the symmetric difference of two vectors: <lang MATLAB>>> [setdiff([1 2 3],[2 3 4]) setdiff([2 3 4],[1 2 3])]
ans =
1 4</lang>
On the other hand, if you are using cell-arrays as sets, there are no built-in set utilities to operate on those data structures, so you will have to program them yourself. Also, the only way to have a set of strings is to put each string in a cell of a cell array, trying to put them into a vector will cause all of the strings to concatenate.
This code will return the symmetric difference of two sets and will take both cell arrays and vectors (as in the above example) as inputs.
<lang MATLAB>function resultantSet = symmetricDifference(set1,set2)
assert( ~xor(iscell(set1),iscell(set2)), 'Both sets must be of the same type, either cells or matricies, but not a combination of the two' );
%% Helper function definitions
%Define what set equality means for cell arrays
function trueFalse = equality(set1,set2)
if xor(iscell(set1),iscell(set2)) %set1 or set2 is a set and the other isn't
trueFalse = false;
return
elseif ~(iscell(set1) || iscell(set2)) %set1 and set2 are not sets
if ischar(set1) && ischar(set2) %set1 and set2 are chars or strings
trueFalse = strcmp(set1,set2);
elseif xor(ischar(set1),ischar(set2)) %set1 or set2 is a string but the other isn't
trueFalse = false;
else %set1 and set2 are not strings
if numel(set1) == numel(set2) %Since they must be matricies if the are of equal cardinality then they can be compaired
trueFalse = all((set1 == set2));
else %If they aren't of equal cardinality then they can't be equal
trueFalse = false;
end
end
return
else %set1 and set2 are both sets
for x = (1:numel(set1))
trueFalse = false;
for y = (1:numel(set2))
%Compair the current element of set1 with every element
%in set2
trueFalse = equality(set1{x},set2{y});
%If the element of set1 is equal to the current element
%of set2 remove that element from set2 and break out of
%this inner loop
if trueFalse
set2(y) = [];
break
end
end
%If the loop completes without breaking then the current
%element of set1 is not contained in set2 therefore the two
%sets are not equal and we can return an equality of false
if (~trueFalse)
return
end
end
%If, after checking every element in both sets, there are still
%elements in set2 then the two sets are not equivalent
if ~isempty(set2)
trueFalse = false;
end
%If the executation makes it here without the previous if
%statement evaluating to true, then this function will return
%true.
end
end %equality
%Define the relative complement for cell arrays
function set1 = relativeComplement(set1,set2)
for k = (1:numel(set2))
if numel(set1) == 0
return
end
j = 1;
while j <= numel(set1)
if equality(set1{j},set2{k})
set1(j) = [];
j = j-1;
end
j = j+1;
end
end
end %relativeComplement
%% The Symmetric Difference Algorithm
if iscell(set1) && iscell(set2)
resultantSet = [relativeComplement(set1,set2) relativeComplement(set2,set1)];
else
resultantSet = [setdiff(set1,set2) setdiff(set2,set1)];
end
resultantSet = unique(resultantSet); %Make sure there are not duplicates
end %symmetricDifference</lang> Solution Test: <lang MATLAB>>> A = {'John','Bob','Mary','Serena'}
A =
'John' 'Bob' 'Mary' 'Serena'
>> B = {'Jim','Mary','John','Bob'}
B =
'Jim' 'Mary' 'John' 'Bob'
>> symmetricDifference(A,B)
ans =
'Serena' 'Jim' %Correct
>> symmetricDifference([1 2 3],[2 3 4])
ans =
1 4 %Correct</lang>
Maxima
<lang maxima>/* builtin */ symmdifference({"John", "Bob", "Mary", "Serena"},
{"Jim", "Mary", "John", "Bob"});
{"Jim", "Serena"}</lang>
Mercury
<lang mercury>:- module symdiff.
- - interface.
- - import_module io.
- - pred main(io::di, io::uo) is det.
- - implementation.
- - import_module list, set, string.
main(!IO) :-
A = set(["John", "Bob", "Mary", "Serena"]),
B = set(["Jim", "Mary", "John", "Bob"]),
print_set("A\\B", DiffAB @ (A `difference` B), !IO),
print_set("B\\A", DiffBA @ (B `difference` A), !IO),
print_set("A symdiff B", DiffAB `union` DiffBA, !IO).
- - pred print_set(string::in, set(T)::in, io::di, io::uo) is det.
print_set(Desc, Set, !IO) :-
to_sorted_list(Set, Elems),
io.format("%11s: %s\n", [s(Desc), s(string(Elems))], !IO).</lang>
Nim
<lang nim>import sets
var setA = ["John", "Bob", "Mary", "Serena"].toSet var setB = ["Jim", "Mary", "John", "Bob"].toSet echo setA -+- setB # Symmetric difference echo setA - setB # Difference echo setB - setA # Difference</lang> Output:
{Serena, Jim}
{Serena}
{Jim}
Objective-C
<lang objc>#import <Foundation/Foundation.h>
int main(int argc, const char *argv[]) {
@autoreleasepool {
NSSet* setA = [NSSet setWithObjects:@"John", @"Serena", @"Bob", @"Mary", @"Serena", nil]; NSSet* setB = [NSSet setWithObjects:@"Jim", @"Mary", @"John", @"Jim", @"Bob", nil];
// Present our initial data set NSLog(@"In set A: %@", setA); NSLog(@"In set B: %@", setB);
// Get our individual differences. NSMutableSet* notInSetA = [NSMutableSet setWithSet:setB]; [notInSetA minusSet:setA]; NSMutableSet* notInSetB = [NSMutableSet setWithSet:setA]; [notInSetB minusSet:setB];
// The symmetric difference is the concatenation of the two individual differences NSMutableSet* symmetricDifference = [NSMutableSet setWithSet:notInSetA]; [symmetricDifference unionSet:notInSetB];
// Present our results NSLog(@"Not in set A: %@", notInSetA); NSLog(@"Not in set B: %@", notInSetB); NSLog(@"Symmetric Difference: %@", symmetricDifference);
} return 0;
}</lang>
OCaml
<lang ocaml>let unique lst =
let f lst x = if List.mem x lst then lst else x::lst in List.rev (List.fold_left f [] lst)
let ( -| ) a b =
unique (List.filter (fun v -> not (List.mem v b)) a)
let ( -|- ) a b = (b -| a) @ (a -| b)</lang> in the toplevel: <lang ocaml># let a = [ "John"; "Bob"; "Mary"; "Serena" ]
and b = [ "Jim"; "Mary"; "John"; "Bob" ] ;;
val a : string list = ["John"; "Bob"; "Mary"; "Serena"] val b : string list = ["Jim"; "Mary"; "John"; "Bob"]
- a -|- b ;;
- : string list = ["Jim"; "Serena"]
- a -| b ;;
- : string list = ["Serena"]
- b -| a ;;
- : string list = ["Jim"]</lang>
ooRexx
<lang ooRexx>a = .set~of("John", "Bob", "Mary", "Serena") b = .set~of("Jim", "Mary", "John", "Bob") -- the xor operation is a symmetric difference do item over a~xor(b)
say item
end</lang> Output:
Serena Jim
Oz
Oz does not have a general set data type. We can implement some basic set operations in terms of list functions and use them to define the symmetric difference: <lang oz>declare
fun {SymDiff A B}
{Union {Diff A B} {Diff B A}}
end
%% implement sets in terms of lists
fun {MakeSet Xs}
set({Nub2 Xs nil})
end
fun {Diff set(A) set(B)}
set({FoldL B List.subtract A})
end
fun {Union set(A) set(B)}
set({Append A B})
end
%% --
fun {Nub2 Xs Ls}
case Xs of nil then nil
[] X|Xr andthen {Member X Ls} then {Nub2 Xr Ls}
[] X|Xr then X|{Nub2 Xr X|Ls}
end
end
in
{Show {SymDiff
{MakeSet [john bob mary serena]} {MakeSet [jim mary john bob]}}}
{Show {SymDiff
{MakeSet [john serena bob mary serena]} {MakeSet [jim mary john jim bob]}}}</lang> Oz does have a type for finite sets of non-negative integers. This is part of the constraint programming support. For the given task, we could use it like this if we assume numbers instead of names: <lang oz>declare
fun {SymDiff A B}
{FS.union {FS.diff A B} {FS.diff B A}}
end
A = {FS.value.make [1 2 3 4]}
B = {FS.value.make [5 3 1 2]}
in
{Show {SymDiff A B}}</lang>
Pascal
<lang Pascal>PROGRAM Symmetric_difference;
TYPE
TName = (Bob, Jim, John, Mary, Serena); TList = SET OF TName;
PROCEDURE Put(txt : String; ResSet : TList); VAR
I : TName;
BEGIN
Write(txt); FOR I IN ResSet DO Write(I,' '); WriteLn
END;
VAR
ListA : TList = [John, Bob, Mary, Serena]; ListB : TList = [Jim, Mary, John, Bob];
BEGIN
Put('ListA -> ', ListA);
Put('ListB -> ', ListB);
Put('ListA >< ListB -> ', ListA >< ListB);
Put('ListA - ListB -> ', ListA - ListB);
Put('ListB - ListA -> ', ListB - ListA);
ReadLn;
END.</lang>
- Output:
ListA -> Bob John Mary Serena ListB -> Bob Jim John Mary ListA >< ListB -> Jim Serena ListA - ListB -> Serena ListB - ListA -> Jim
PARI/GP
<lang parigp>sd(u,v)={
my(r=List()); u=vecsort(u,,8); v=vecsort(v,,8); for(i=1,#u,if(!setsearch(v,u[i]),listput(r,u[i]))); for(i=1,#v,if(!setsearch(u,v[i]),listput(r,v[i]))); Vec(r)
}; sd(["John", "Serena", "Bob", "Mary", "Serena"],["Jim", "Mary", "John", "Jim", "Bob"])</lang>
Perl
<lang perl>sub symm_diff {
# two lists passed in as references
my %in_a = map(($_=>1), @{+shift});
my %in_b = map(($_=>1), @{+shift});
my @a = grep { !$in_b{$_} } keys %in_a;
my @b = grep { !$in_a{$_} } keys %in_b;
# return A-B, B-A, A xor B as ref to lists
return \@a, \@b, [ @a, @b ]
}
my @a = qw(John Serena Bob Mary Serena); my @b = qw(Jim Mary John Jim Bob );
my ($a, $b, $s) = symm_diff(\@a, \@b); print "A\\B: @$a\nB\\A: @$b\nSymm: @$s\n";</lang>
Perl 6
<lang perl6>my \A = set <John Serena Bob Mary Serena>; my \B = set <Jim Mary John Jim Bob>;
say A ∖ B; # Set subtraction say B ∖ A; # Set subtraction say A ⊖ B; # Symmetric difference</lang>
- Output:
set(Serena) set(Jim) set(Jim, Serena)
Phix
<lang Phix>function Union(sequence a, sequence b)
for i=1 to length(a) do
if not find(a[i],b) then
b = append(b,a[i])
end if
end for
return b
end function
function Difference(sequence a, sequence b) sequence res = {}
for i=1 to length(a) do
if not find(a[i],b)
and not find(a[i],res) then
res = append(res,a[i])
end if
end for
return res
end function
function Symmetric_Difference(sequence a, sequence b)
return Union(Difference(a, b), Difference(b, a))
end function
sequence a = {"John", "Serena", "Bob", "Mary", "Serena"},
b = {"Jim", "Mary", "John", "Jim", "Bob"}
?Symmetric_Difference(a,a) ?Symmetric_Difference(a,b) ?Symmetric_Difference(b,a) ?Symmetric_Difference(b,b)</lang>
- Output:
{}
{"Jim","Serena"}
{"Serena","Jim"}
{}
PHP
<lang php><?php $a = array('John', 'Bob', 'Mary', 'Serena'); $b = array('Jim', 'Mary', 'John', 'Bob');
// Remove any duplicates $a = array_unique($a); $b = array_unique($b);
// Get the individual differences, using array_diff() $a_minus_b = array_diff($a, $b); $b_minus_a = array_diff($b, $a);
// Simply merge them together to get the symmetric difference $symmetric_difference = array_merge($a_minus_b, $b_minus_a);
// Present our results. echo 'List A: ', implode(', ', $a),
"\nList B: ", implode(', ', $b),
"\nA \\ B: ", implode(', ', $a_minus_b),
"\nB \\ A: ", implode(', ', $b_minus_a),
"\nSymmetric difference: ", implode(', ', $symmetric_difference), "\n";
?></lang> This outputs:
List A: John, Bob, Mary, Serena List B: Jim, Mary, John, Bob A \ B: Serena B \ A: Jim Symmetric difference: Serena, Jim
PicoLisp
<lang PicoLisp>(de symdiff (A B)
(uniq (conc (diff A B) (diff B A))) )</lang>
Output:
(symdiff '(John Serena Bob Mary Serena) '(Jim Mary John Jim Bob)) -> (Serena Jim)
Pike
The set type in Pike is 'multiset', that is, a value may appear multiple times and the difference operator only removes equal amounts of duplicates. <lang Pike>> multiset(string) A = (< "John", "Serena", "Bob", "Mary", "Bob", "Serena" >); > multiset(string) B = (< "Jim", "Mary", "Mary", "John", "Bob", "Jim" >);
> A^B;
Result: (< "Bob", "Serena", "Serena", "Mary", "Jim", "Jim" >)</lang>
The ^ operator treats arrays like multisets.
<lang Pike>> array(string) A = ({ "John", "Serena", "Bob", "Mary", "Serena", "Bob" });
> array(string) B = ({ "Jim", "Mary", "John", "Jim", "Bob", "Mary" });
> A^B;
Result: ({ "Serena", "Serena", "Bob", "Jim", "Jim", "Mary"})
> Array.uniq((A-B)+(B-A)); Result: ({ "Serena", "Jim" })</lang> Set operations are also possible with mappings. Here the difference operator works as expected: <lang Pike>> mapping(string:int) A = ([ "John":1, "Serena":1, "Bob":1, "Mary":1 ]); > mapping(string:int) B = ([ "Jim":1, "Mary":1, "John":1, "Bob":1 ]);
> A^B; Result: ([ "Jim": 1, "Serena": 1 ])</lang> Lastly, there is a Set class. <lang Pike>> ADT.Set A = ADT.Set((< "John", "Serena", "Bob", "Mary", "Serena", "Bob" >)); > ADT.Set B = ADT.Set((< "Jim", "Mary", "John", "Jim", "Bob", "Mary" >)); > (A-B)+(B-A); Result: ADT.Set({ "Serena", "Jim" })</lang>
PL/I
<lang pli>/* PL/I ***************************************************************
- 17.08.2013 Walter Pachl
- /
- process source attributes xref;
sd: Proc Options(main);
Dcl a(4) Char(20) Var Init('John','Bob','Mary','Serena');
Dcl b(4) Char(20) Var Init('Jim','Mary','John','Bob');
Call match(a,b);
Call match(b,a);
match: Proc(x,y);
Dcl (x(*),y(*)) Char(*) Var;
Dcl (i,j) Bin Fixed(31);
Do i=1 To hbound(x);
Do j=1 To hbound(y);
If x(i)=y(j) Then Leave;
End;
If j>hbound(y) Then
Put Edit(x(i))(Skip,a);
End;
End;
End;</lang>
Output:
Serena Jim
PowerShell
<lang powershell>$A = @( "John"
"Bob"
"Mary"
"Serena" )
$B = @( "Jim"
"Mary"
"John"
"Bob" )
- Full commandlet name and full parameter names
Compare-Object -ReferenceObject $A -DifferenceObject $B
- Same commandlet using an alias and positional parameters
Compare $A $B
- A - B
Compare $A $B | Where SideIndicator -eq "<=" | Select -ExpandProperty InputObject
- B - A
Compare $A $B | Where SideIndicator -eq "=>" | Select -ExpandProperty InputObject</lang>
- Output:
InputObject SideIndicator ----------- ------------- Jim => Serena <= InputObject SideIndicator ----------- ------------- Jim => Serena <= Serena Jim
Prolog
<lang Prolog>sym_diff :-
A = ['John', 'Serena', 'Bob', 'Mary', 'Serena'],
B = ['Jim', 'Mary', 'John', 'Jim', 'Bob'],
format('A : ~w~n', [A]),
format('B : ~w~n', [B]),
list_to_set(A, SA),
list_to_set(B, SB),
format('set from A : ~w~n', [SA]),
format('set from B : ~w~n', [SB]),
subtract(SA, SB, DAB),
format('difference A\\B : ~w~n', [DAB]),
subtract(SB, SA, DBA),
format('difference B\\A : ~w~n', [DBA]),
union(DAB, DBA, Diff),
format('symetric difference : ~w~n', [Diff]).</lang>
output :
A : [John,Serena,Bob,Mary,Serena] B : [Jim,Mary,John,Jim,Bob] set from A : [John,Serena,Bob,Mary] set from B : [Jim,Mary,John,Bob] difference A\B : [Serena] difference B\A : [Jim] symetric difference : [Serena,Jim] true.
PureBasic
Simple approach
<lang PureBasic>Dim A.s(3) Dim B.s(3)
A(0)="John": A(1)="Bob": A(2)="Mary": A(3)="Serena" B(0)="Jim": B(1)="Mary":B(2)="John": B(3)="Bob"
For a=0 To ArraySize(A()) ; A-B
For b=0 To ArraySize(B())
If A(a)=B(b)
Break
ElseIf b=ArraySize(B())
Debug A(a)
EndIf
Next b
Next a
For b=0 To ArraySize(B()) ; B-A
For a=0 To ArraySize(A())
If A(a)=B(b)
Break
ElseIf a=ArraySize(A())
Debug B(b)
EndIf
Next a
Next b</lang>
Solution using lists
<lang PureBasic>DataSection
SetA: Data.i 4 Data.s "John", "Bob", "Mary", "Serena" ; Data.i 5 ; Data.s "John", "Serena", "Bob", "Mary", "Serena" SetB: Data.i 4 Data.s "Jim", "Mary", "John", "Bob" ; Data.i 5 ; Data.s "Jim", "Mary", "John", "Jim", "Bob"
EndDataSection
Procedure addElementsToSet(List x.s())
;requires the read pointer to be set prior to calling by using 'Restore' Protected i, count Read.i count For i = 1 To count AddElement(x()) Read.s x() Next
EndProcedure
Procedure displaySet(List x.s())
Protected i, count = ListSize(x())
FirstElement(x())
For i = 1 To count
Print(x())
NextElement(x())
If i <> count: Print(", "): EndIf
Next
PrintN("")
EndProcedure
Procedure symmetricDifference(List a.s(), List b.s(), List result.s())
Protected ACount = ListSize(a()), BCount = ListSize(b()), prev.s
;this may leave set a and b in a different order
SortList(a(),#PB_Sort_Ascending)
SortList(b(),#PB_Sort_Ascending)
FirstElement(a())
FirstElement(b())
LastElement(result()) ;add to end of result()
While ACount > 0 Or BCount > 0
If ACount <> 0 And BCount <> 0 And a() = b()
ACount - 1: NextElement(a())
BCount - 1: NextElement(b())
ElseIf BCount = 0 Or (ACount <> 0 And a() < b())
AddElement(result()): result() = a()
prev = a(): Repeat: ACount - 1: NextElement(a()): Until ACount = 0 Or (a() <> prev)
ElseIf ACount = 0 Or (BCount <> 0 And a() > b())
AddElement(result()): result() = b()
prev = b(): Repeat: BCount - 1: NextElement(b()): Until BCount = 0 Or (b() <> prev)
EndIf
Wend
EndProcedure
If OpenConsole()
NewList a.s(): Restore SetA: addElementsToSet(a())
NewList b.s(): Restore SetB: addElementsToSet(b())
Print("Set A: "): displaySet(a())
Print("Set B: "): displaySet(b())
NewList sd.s()
symmetricDifference(a(), b(), sd())
Print("Symmetric Difference: "): displaySet(sd())
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit")
Input()
CloseConsole()
EndIf</lang> Sample output:
Set A: John, Bob, Mary, Serena Set B: Jim, Mary, John, Bob Symmetric Difference: Jim, Serena
Python
Python's set type supports difference as well as symmetric difference operators.
Python 3.x and Python 2.7 have syntax for set literals:
<lang python>>>> setA = {"John", "Bob", "Mary", "Serena"} >>> setB = {"Jim", "Mary", "John", "Bob"} >>> setA ^ setB # symmetric difference of A and B {'Jim', 'Serena'} >>> setA - setB # elements in A that are not in B {'Serena'} >>> setB - setA # elements in B that are not in A {'Jim'} >>> setA | setB # elements in A or B (union) {'John', 'Bob', 'Jim', 'Serena', 'Mary'} >>> setA & setB # elements in both A and B (intersection) {'Bob', 'John', 'Mary'}</lang>
Note that the order of set elements is undefined.
Earlier versions of Python:
<lang python>>>> setA = set(["John", "Bob", "Mary", "Serena"]) >>> setB = set(["Jim", "Mary", "John", "Bob"]) >>> setA ^ setB # symmetric difference of A and B set(['Jim', 'Serena']) >>> setA - setB # elements in A that are not in B set(['Serena']) >>> # and so on...</lang>
There is also a method call interface for these operations. In contrast to the operators above, they accept any iterables as arguments not just sets.
<lang python>>>> setA.symmetric_difference(setB) {'Jim', 'Serena'} >>> setA.difference(setB) {'Serena'} >>> setB.difference(setA) {'Jim'} >>> setA.union(setB) {'Jim', 'Mary', 'Serena', 'John', 'Bob'} >>> setA.intersection(setB) {'Mary', 'John', 'Bob'}</lang>
R
<lang R>a <- c( "John", "Bob", "Mary", "Serena" ) b <- c( "Jim", "Mary", "John", "Bob" ) c(setdiff(b, a), setdiff(a, b))
a <- c("John", "Serena", "Bob", "Mary", "Serena") b <- c("Jim", "Mary", "John", "Jim", "Bob") c(setdiff(b, a), setdiff(a, b)) </lang> In both cases answer is: <lang R>[1] "Jim" "Serena"</lang>
Racket
<lang racket>
- lang racket
(define A (set "John" "Bob" "Mary" "Serena")) (define B (set "Jim" "Mary" "John" "Bob"))
(set-symmetric-difference A B) (set-subtract A B) (set-subtract B A) </lang>
REBOL
<lang rebol>a: [John Serena Bob Mary Serena] b: [Jim Mary John Jim Bob] difference a b</lang> Result is
[Serena Jim]
REXX
version 1
This REXX version shows the symmetric difference and symmetric AND between two lists, the lists have duplicate elements to show their proper handling.
The lists (and output) are formatted as a set.
The set elements may contain any character permitted with a REXX literal, including the literal character itself (expressed as a double literal delimiter), blanks, brackets, commas, and also a null value. <lang rexx>/*REXX program finds symmetric difference and symmetric AND (between two lists). */ a= '["John", "Serena", "Bob", "Mary", "Serena"]' /*note the duplicate element: Serena */ b= '["Jim", "Mary", "John", "Jim", "Bob"]' /* " " " " Jim */ a.=0; SD.=0; SA.=0; SD=; SA= /*falsify booleans; zero & nullify vars*/ a.1=a; say '──────────────list A =' a /*assign a list and display it to term.*/ a.2=b; say '──────────────list B =' b /* " " " " " " " " */
/* [↓] parse the two lists. */
do k=1 for 2 /*process both lists (stemmed array). */
a.k=strip( strip(a.k, , "["), ,']') /*strip leading and trailing brackets. */
do j=1 until a.k= /*parse names [they may have blanks]. */
a.k=strip(a.k, , ',') /*strip all commas (if there are any). */
parse var a.k '"' _ '"' a.k /*obtain the name of the list. */
a.k.j=_ /*store the name of the list. */
a.k._=1 /*make a boolean value. */
end /*j*/
a.k.0=j-1 /*the number of this list (of names). */
end /*k*/
say /* [↓] find the symmetric difference. */
do k=1 for 2; ko=word(2 1, k) /*process both lists; KO=other list. */
do j=1 for a.k.0; _=a.k.j /*process the list names. */
if \a.ko._ & \SD._ then do; SD._=1 /*if not in both, then ··· */
SD=SD '"'_'",' /*add to symmetric difference list. */
end
end /*j*/
end /*k*/
/* [↓] SD ≡ symmetric difference. */
SD= "["strip( strip(SD), 'T', ",")']' /*clean up and add brackets [ ] to it.*/ say 'symmetric difference =' SD /*display the symmetric difference. */
/* [↓] locate the symmetric AND. */
do j=1 for a.1.0; _=a.1.j /*process the A list names. */
if a.1._ & a.2._ & \SA._ then do; SA._=1 /*if it's common to both, then ··· */
SA=SA '"'_'",' /*add to symmetric AND list. */
end
end /*j*/
say /* [↓] SA ≡ symmetric AND. */ SA= "["strip( strip(SA), 'T', ",")']' /*clean up and add brackets [ ] to it.*/ say ' symmetric AND =' SA /*stick a fork in it, we're all done. */</lang>
- output when using the in-program lists:
──────────────list A = ["John", "Serena", "Bob", "Mary", "Serena"]
──────────────list B = ["Jim", "Mary", "John", "Jim", "Bob"]
symmetric difference = ["Serena", "Jim"]
symmetric AND = ["John", "Bob", "Mary"]
version 1.5
This REXX version shows the symmetric difference and symmetric AND between two lists, the lists have items that have imbedded blanks in them as well as some punctuation, and also a null element. <lang rexx>/*REXX pgm finds symmetric difference and symm. AND (between two lists).*/ a.=0 /*falsify the booleans*/ a= '["Zahn", "Yi", "Stands with a Fist", "", "Hungry Wolf", "Yi"]' b= '["Draag Ng [Jr.]", "Patzy", "Zahn", "Yi", "Robert the Bruce"]'
∙ ∙ ∙</lang>
- output when using the in-program lists (which has imbedded blanks):
──────────────list A = ["Zahn", "Yi", "Stands with a Fist", "", "Hungry Wolf", "Yi"]
──────────────list B = ["Draag Ng [Jr.]", "Patzy", "Zahn", "Yi", "Robert the Bruce"]
symmetric difference = ["Stands with a Fist", "", "Hungry Wolf", "Draag Ng [Jr.]", "Patzy"]
symmetric AND = ["Zahn", "Yi"]
version 2
<lang rexx>/* REXX ---------------------------------------------------------------
- 14.12.2013 Walter Pachl a short solution
- 16.12.2013 fix duplicate element problem in input
- 16.12.2013 added duplicate to t.
- Handles only sets the elements of which do not contain blanks
- --------------------------------------------------------------------*/
s='John Bob Mary Serena' t='Jim Mary John Bob Jim ' Say difference(s,t) Exit difference: Parse Arg a,b res= Do i=1 To words(a)
If wordpos(word(a,i),b)=0 Then Call out word(a,i) End
Do i=1 To words(b)
If wordpos(word(b,i),a)=0 Then Call out word(b,i) End
Return strip(res) out: parse Arg e If wordpos(e,res)=0 Then res=res e Return</lang> Output:
Serena Jim
Ring
<lang ring> alist = [] blist = [] alist = ["john", "bob", "mary", "serena"] blist = ["jim", "mary", "john", "bob"]
alist2 = [] for i = 1 to len(alist)
flag = 0
for j = 1 to len(blist)
if alist[i] = blist[j] flag = 1 ok
next
if (flag = 0) add(alist2, alist[i]) ok
next
blist2 = [] for j = 1 to len(alist)
flag = 0
for i = 1 to len(blist)
if alist[i] = blist[j] flag = 1 ok
next
if (flag = 0) add(blist2, blist[j]) ok
next see "a xor b :" see nl see alist2 see blist2 see nl see "a-b :" see nl see alist2 see nl see "b-a :" see nl see blist2 see nl </lang>
Ruby
With arrays: <lang ruby>a = ["John", "Serena", "Bob", "Mary", "Serena"] b = ["Jim", "Mary", "John", "Jim", "Bob"]
- the union minus the intersection:
p sym_diff = (a | b)-(a & b) # => ["Serena", "Jim"]</lang> Class Set has a symmetric difference operator built-in: <lang ruby>require 'set' a = Set["John", "Serena", "Bob", "Mary", "Serena"] #Set removes duplicates b = Set["Jim", "Mary", "John", "Jim", "Bob"] p sym_diff = a ^ b # => #<Set: {"Jim", "Serena"}></lang>
Run BASIC
<lang runbasic> setA$ = "John,Bob,Mary,Serena" setB$ = "Jim,Mary,John,Bob"
x$ = b$(setA$,setB$) print word$(x$,1,",") c$ = c$ + x$
x$ = b$(setB$,setA$) print word$(x$,1,",") print c$;x$ end function b$(a$,b$)
i = 1 while word$(a$,i,",") <> "" a1$ = word$(a$,i,",") j = instr(b$,a1$) if j <> 0 then b$ = left$(b$,j-1) + mid$(b$,j+len(a1$)+1) i = i + 1
wend end function</lang>
Jim Serena Jim,Serena
Scala
<lang Scala>scala> val s1 = Set("John", "Serena", "Bob", "Mary", "Serena") s1: scala.collection.immutable.Set[java.lang.String] = Set(John, Serena, Bob, Mary)
scala> val s2 = Set("Jim", "Mary", "John", "Jim", "Bob") s2: scala.collection.immutable.Set[java.lang.String] = Set(Jim, Mary, John, Bob)
scala> (s1 diff s2) union (s2 diff s1) res46: scala.collection.immutable.Set[java.lang.String] = Set(Serena, Jim)</lang>
Scheme
Pure R7RS
In pure Scheme, to illustrate implementation of the algorithms:
<lang scheme> (import (scheme base)
(scheme write))
- -- given two sets represented as lists, return (A \ B)
(define (a-without-b a b)
(cond ((null? a)
'())
((member (car a) (cdr a)) ; drop head of a if it's a duplicate
(a-without-b (cdr a) b))
((member (car a) b) ; head of a is in b so drop it
(a-without-b (cdr a) b))
(else ; head of a not in b, so keep it
(cons (car a) (a-without-b (cdr a) b)))))
- -- given two sets represented as lists, return symmetric difference
(define (symmetric-difference a b)
(append (a-without-b a b)
(a-without-b b a)))
- -- test case
(define A '(John Bob Mary Serena)) (define B '(Jim Mary John Bob))
(display "A\\B: ") (display (a-without-b A B)) (newline) (display "B\\A: ") (display (a-without-b B A)) (newline) (display "Symmetric difference: ") (display (symmetric-difference A B)) (newline)
- -- extra test as we are using lists
(display "Symmetric difference 2: ") (display (symmetric-difference '(John Serena Bob Mary Serena)
'(Jim Mary John Jim Bob))) (newline)
</lang>
- Output:
A\B: (Serena) B\A: (Jim) Symmetric difference: (Serena Jim) Symmetric difference 2: (Serena Jim)
Using a standard library
SRFI 1 is one of the most popular SRFIs. It deals with lists, but also has functions treating lists as sets. The lset functions assume the inputs are sets, so we must delete duplicates if this property is not guaranteed on input.
<lang scheme> (import (scheme base)
(scheme write)
(srfi 1))
(define (a-without-b a b)
(lset-difference equal?
(delete-duplicates a)
(delete-duplicates b)))
(define (symmetric-difference a b)
(lset-xor equal?
(delete-duplicates a)
(delete-duplicates b)))
- -- test case
(define A '(John Bob Mary Serena)) (define B '(Jim Mary John Bob))
(display "A\\B: ") (display (a-without-b A B)) (newline) (display "B\\A: ") (display (a-without-b B A)) (newline) (display "Symmetric difference: ") (display (symmetric-difference A B)) (newline)
- -- extra test as we are using lists
(display "Symmetric difference 2: ") (display (symmetric-difference '(John Serena Bob Mary Serena)
'(Jim Mary John Jim Bob))) (newline)
</lang>
Seed7
<lang seed7>$ include "seed7_05.s7i";
const type: striSet is set of string;
enable_output(striSet);
const proc: main is func
local
const striSet: setA is {"John", "Bob" , "Mary", "Serena"};
const striSet: setB is {"Jim" , "Mary", "John", "Bob" };
begin
writeln(setA >< setB);
end func;</lang>
Output:
{Jim, Serena}
Sidef
<lang ruby>var a = ["John", "Serena", "Bob", "Mary", "Serena"]; var b = ["Jim", "Mary", "John", "Jim", "Bob"]; a ^ b -> unique.dump.say;</lang>
- Output:
["Serena", "Jim"]
Smalltalk
<lang smalltalk>|A B| A := Set new. B := Set new. A addAll: #( 'John' 'Bob' 'Mary' 'Serena' ). B addAll: #( 'Jim' 'Mary' 'John' 'Bob' ).
( (A - B) + (B - A) ) displayNl.</lang> Output is
Set ('Jim' 'Serena' )
SQL/PostgreSQL
<lang SQL>create or replace function arrxor(anyarray,anyarray) returns anyarray as $$ select ARRAY(
(
select r.elements
from (
(select 1,unnest($1))
union all
(select 2,unnest($2))
) as r (arr, elements)
group by 1
having min(arr) = max(arr)
)
) $$ language sql strict immutable;</lang> Usage: <lang sql>select arrxor('{this,is,a,test}'::text[],'{also,part,of,a,test}'::text[]);</lang> Output:
arrxor ------------------------ also,is,of,part,this
Swift
Swift's Set type supports difference as well as symmetric difference operators.
<lang swift>let setA : Set<String> = ["John", "Bob", "Mary", "Serena"] let setB : Set<String> = ["Jim", "Mary", "John", "Bob"] println(setA.exclusiveOr(setB)) // symmetric difference of A and B println(setA.subtract(setB)) // elements in A that are not in B</lang>
- Output:
["Jim", "Serena"] ["Serena"]
Tcl
It's common to represent sets as an unordered list of elements. (It is also the most efficient representation.) The struct::set package contains operations for working on such sets-as-lists.
<lang tcl>package require struct::set
set A {John Bob Mary Serena} set B {Jim Mary John Bob}
set AnotB [struct::set difference $A $B] set BnotA [struct::set difference $B $A] set SymDiff [struct::set union $AnotB $BnotA]
puts "A\\B = $AnotB" puts "B\\A = $BnotA" puts "A\u2296B = $SymDiff"
- Of course, the library already has this operation directly...
puts "Direct Check: [struct::set symdiff $A $B]"</lang>
Produces this output:
A\B = Serena B\A = Jim A⊖B = Jim Serena Direct Check: Jim Serena
TUSCRIPT
<lang tuscript>$$ MODE TUSCRIPT a="John'Bob'Mary'Serena" b="Jim'Mary'John'Bob"
DICT names CREATE
SUBMACRO checknames !var,val PRINT val,": ",var
LOOP n=var DICT names APPEND/QUIET n,num,cnt,val;" " ENDLOOP
ENDSUBMACRO
CALL checknames (a,"a") CALL checknames (b,"b")
DICT names UNLOAD names,num,cnt,val
LOOP n=names,v=val PRINT n," in: ",v ENDLOOP</lang> Output:
a: John'Bob'Mary'Serena b: Jim'Mary'John'Bob John in: a b Bob in: a b Mary in: a b Serena in: a Jim in: b
UNIX Shell
<lang bash>uniq() {
u=("$@")
for ((i=0;i<${#u[@]};i++)); do
for ((j=i+1;j<=${#u[@]};j++)); do
[ "${u[$i]}" = "${u[$j]}" ] && unset u[$i]
done
done
u=("${u[@]}")
}
a=(John Serena Bob Mary Serena) b=(Jim Mary John Jim Bob)
uniq "${a[@]}" au=("${u[@]}") uniq "${b[@]}" bu=("${u[@]}")
ab=("${au[@]}") for ((i=0;i<=${#au[@]};i++)); do
for ((j=0;j<=${#bu[@]};j++)); do
[ "${ab[$i]}" = "${bu[$j]}" ] && unset ab[$i]
done
done ab=("${ab[@]}")
ba=("${bu[@]}") for ((i=0;i<=${#bu[@]};i++)); do
for ((j=0;j<=${#au[@]};j++)); do
[ "${ba[$i]}" = "${au[$j]}" ] && unset ba[$i]
done
done ba=("${ba[@]}")
sd=("${ab[@]}" "${ba[@]}")
echo "Set A = ${a[@]}" echo " = ${au[@]}" echo "Set B = ${b[@]}" echo " = ${bu[@]}" echo "A - B = ${ab[@]}" echo "B - A = ${ba[@]}" echo "Symmetric difference = ${sd[@]}"</lang> Output:
Set A = John Serena Bob Mary Serena
= John Bob Mary Serena
Set B = Jim Mary John Jim Bob
= Mary John Jim Bob
A - B = Serena
B - A = Jim
Symmetric difference = Serena Jim
Ursala
<lang Ursala>a = <'John','Bob','Mary','Serena'> b = <'Jim','Mary','John','Bob'>
- cast %sLm
main =
<
'a': a, 'b': b, 'a not b': ~&j/a b, 'b not a': ~&j/b a, 'symmetric difference': ~&jrljTs/a b></lang>
output:
< 'a': <'John','Bob','Mary','Serena'>, 'b': <'Jim','Mary','John','Bob'>, 'a not b': <'Serena'>, 'b not a': <'Jim'>, 'symmetric difference': <'Jim','Serena'>>
Yabasic
<lang Yabasic>lista1$ = "John Serena Bob Mary Serena" lista2$ = "Jim Mary John Jim Bob"
lista1$ = quitadup$(lista1$) lista2$ = quitadup$(lista2$) res$ = quitacomun$(lista1$, lista2$) res$ = res$ + quitacomun$(lista2$, lista1$) print res$
sub quitadup$(l$)
l$ = l$ + " "
return quitarep$(l$)
end sub
sub quitacomun$(l1$, l2$)
l1$ = l1$ + " "
l2$ = l2$ + " "
return quitarep$(l1$, l2$)
end sub
sub quitarep$(l1$, l2$)
local pos, n, x, listar$, nombre$, largo
largo = len(l1$) pos = 1 while(true) n = instr(l1$, " ", pos) if n > 0 then nombre$ = mid$(l1$, pos, n-pos) if numparams = 1 then x = instr(listar$, nombre$) else x = instr(l2$, nombre$) end if if x = 0 listar$ = listar$ + nombre$ + " " pos = n + 1 else return listar$ end if wend end sub </lang>
zkl
<lang zkl>fcn setCommon(list1,list2){ list1.filter(list2.holds); } fcn sdiff(list1,list2)
{ list1.extend(list2).copy().removeEach(setCommon(list1,list2)) }</lang>
<lang zkl>a:=T("John","Bob","Mary","Serena"); b:=T("Jim","Mary","John","Bob"); sdiff(a,b).println();</lang> To deal with duplicates, use Remove duplicate elements#zkl: <lang zkl>a:=T("John", "Serena", "Bob", "Mary", "Serena"); b:=T("Jim", "Mary", "John", "Jim", "Bob"); sdiff(a,b) : Utils.Helpers.listUnique(_).println();</lang>
- Output:
L("Serena","Jim")
L("Serena","Jim")
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