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Set consolidation

From Rosetta Code
Task
Set consolidation
You are encouraged to solve this task according to the task description, using any language you may know.

Given two sets of items then if any item is common to any set then the result of applying consolidation to those sets is a set of sets whose contents is:

  • The two input sets if no common item exists between the two input sets of items.
  • The single set that is the union of the two input sets if they share a common item.


Given N sets of items where N>2 then the result is the same as repeatedly replacing all combinations of two sets by their consolidation until no further consolidation between set pairs is possible. If N<2 then consolidation has no strict meaning and the input can be returned.

Example 1:
Given the two sets {A,B} and {C,D} then there is no common element between the sets and the result is the same as the input.
Example 2:
Given the two sets {A,B} and {B,D} then there is a common element B between the sets and the result is the single set {B,D,A}. (Note that order of items in a set is immaterial: {A,B,D} is the same as {B,D,A} and {D,A,B}, etc).
Example 3:
Given the three sets {A,B} and {C,D} and {D,B} then there is no common element between the sets {A,B} and {C,D} but the sets {A,B} and {D,B} do share a common element that consolidates to produce the result {B,D,A}. On examining this result with the remaining set, {C,D}, they share a common element and so consolidate to the final output of the single set {A,B,C,D}
Example 4:
The consolidation of the five sets:
{H,I,K}, {A,B}, {C,D}, {D,B}, and {F,G,H}
Is the two sets:
{A, C, B, D}, and {G, F, I, H, K}


See also



Ada[edit]

We start with specifying a generic package Set_Cons that provides the neccessary tools, such as contructing and manipulating sets, truning them, ect.:

generic
type Element is (<>);
with function Image(E: Element) return String;
package Set_Cons is
 
type Set is private;
 
-- constructor and manipulation functions for type Set
function "+"(E: Element) return Set;
function "+"(Left, Right: Element) return Set;
function "+"(Left: Set; Right: Element) return Set;
function "-"(Left: Set; Right: Element) return Set;
 
-- compare, unite or output a Set
function Nonempty_Intersection(Left, Right: Set) return Boolean;
function Union(Left, Right: Set) return Set;
function Image(S: Set) return String;
 
type Set_Vec is array(Positive range <>) of Set;
 
-- output a Set_Vec
function Image(V: Set_Vec) return String;
 
private
type Set is array(Element) of Boolean;
 
end Set_Cons;

Here is the implementation of Set_Cons:

package body Set_Cons is
 
function "+"(E: Element) return Set is
S: Set := (others => False);
begin
S(E) := True;
return S;
end "+";
 
function "+"(Left, Right: Element) return Set is
begin
return (+Left) + Right;
end "+";
 
function "+"(Left: Set; Right: Element) return Set is
S: Set := Left;
begin
S(Right) := True;
return S;
end "+";
 
function "-"(Left: Set; Right: Element) return Set is
S: Set := Left;
begin
S(Right) := False;
return S;
end "-";
 
function Nonempty_Intersection(Left, Right: Set) return Boolean is
begin
for E in Element'Range loop
if Left(E) and then Right(E) then return True;
end if;
end loop;
return False;
end Nonempty_Intersection;
 
function Union(Left, Right: Set) return Set is
S: Set := Left;
begin
for E in Right'Range loop
if Right(E) then S(E) := True;
end if;
end loop;
return S;
end Union;
 
function Image(S: Set) return String is
 
function Image(S: Set; Found: Natural) return String is
begin
for E in S'Range loop
if S(E) then
if Found = 0 then
return Image(E) & Image((S-E), Found+1);
else
return "," & Image(E) & Image((S-E), Found+1);
end if;
end if;
end loop;
return "";
end Image;
 
begin
return "{" & Image(S, 0) & "}";
end Image;
 
function Image(V: Set_Vec) return String is
begin
if V'Length = 0 then
return "";
else
return Image(V(V'First)) & Image(V(V'First+1 .. V'Last));
end if;
end Image;
 
end Set_Cons;

Given that package, the task is easy:

with Ada.Text_IO, Set_Cons;
 
procedure Set_Consolidation is
 
type El_Type is (A, B, C, D, E, F, G, H, I, K);
 
function Image(El: El_Type) return String is
begin
return El_Type'Image(El);
end Image;
 
package Helper is new Set_Cons(Element => El_Type, Image => Image);
use Helper;
 
function Consolidate(List: Set_Vec) return Set_Vec is
begin
for I in List'First .. List'Last - 1 loop
for J in I+1 .. List'Last loop
-- if List(I) and List(J) share an element
-- then recursively consolidate
-- (List(I) union List(J)) followed by List(K), K not in {I, J}
if Nonempty_Intersection(List(I), List(J)) then
return Consolidate
(Union(List(I), List(J))
& List(List'First .. I-1)
& List(I+1 .. J-1)
& List(J+1 .. List'Last));
end if;
end loop;
end loop;
return List;
end Consolidate;
 
begin
Ada.Text_IO.Put_Line(Image(Consolidate((A+B) & (C+D))));
Ada.Text_IO.Put_Line(Image(Consolidate((A+B) & (B+D))));
Ada.Text_IO.Put_Line(Image(Consolidate((A+B) & (C+D) & (D+B))));
Ada.Text_IO.Put_Line
(Image(Consolidate((H+I+K) & (A+B) & (C+D) & (D+B) & (F+G+H))));
end Set_Consolidation;
Output:
{A,B}{C,D}
{A,B,D}
{A,B,C,D}
{A,B,C,D}{F,G,H,I,K}

Aime[edit]

void
display(list l)
{
integer i;
text s;
 
i = -l_length(l);
while (i) {
record r;
text u, v;
 
o_text(s);
s = ", ";
o_text("{");
r = l_q_record(l, i);
if (r_first(r, u)) {
do {
o_text(v);
v = ", ";
o_text(u);
} while (r_greater(r, u, u));
}
o_text("}");
i += 1;
}
 
o_text("\n");
}
 
integer
intersect(record r, record u)
{
integer a;
text s;
 
a = 0;
if (r_first(r, s)) {
do {
if (r_key(u, s)) {
a = 1;
break;
}
} while (r_greater(r, s, s));
}
 
return a;
}
 
void
merge(record u, record r)
{
text s;
 
if (r_first(r, s)) {
do {
r_add(u, s, r_query(r, s));
} while (r_greater(r, s, s));
}
}
 
list
consolidate(list l)
{
integer i;
 
i = -l_length(l);
while (i) {
integer j;
record r;
 
r = l_q_record(l, i);
i += 1;
j = i;
while (j) {
record u;
 
u = l_q_record(l, j);
j += 1;
if (intersect(r, u)) {
merge(u, r);
l_delete(l, i - 1);
break;
}
}
}
 
return l;
}
 
list
L(...)
{
integer i;
list l;
 
i = -count();
while (i) {
l_link(l, -1, $i);
i += 1;
}
 
return l;
}
 
record
R(...)
{
integer i;
record r;
 
i = -count();
while (i) {
r_p_integer(r, $i, 0);
i += 1;
}
 
return r;
}
 
integer
main(void)
{
display(consolidate(L(R("A", "B"), R("C", "D"))));
display(consolidate(L(R("A", "B"), R("B", "D"))));
display(consolidate(L(R("A", "B"), R("C", "D"), R("D", "B"))));
display(consolidate(L(R("H", "I", "K"), R("A", "B"), R("C", "D"),
R("D", "B"), R("F", "G", "K"))));
 
return 0;
}
Output:
{A, B}, {C, D}
{A, B, D}
{A, B, C, D}
{A, B, C, D}, {F, G, H, I, K}

Bracmat[edit]

( ( consolidate
= a m z mm za zm zz
. ( removeNumFactors
= a m z
.  !arg:?a+#%*?m+?z
& !a+!m+removeNumFactors$!z
| !arg
)
&  !arg
 :  ?a
 %?`m
( %?z
&  !m
 :  ?
+ ( %@?mm
& !z:?za (?+!mm+?:?zm) ?zz
)
+ ?
)
& consolidate$(!a removeNumFactors$(!m+!zm) !za !zz)
| !arg
)
& (test=.out$(!arg "==>" consolidate$!arg))
& test$(A+B C+D)
& test$(A+B B+D)
& test$(A+B C+D D+B)
& test$(H+I+K A+B C+D D+B F+G+H)
);
Output:
A+B C+D ==> A+B C+D
A+B B+D ==> A+B+D
A+B C+D B+D ==> A+B+C+D
  H+I+K
  A+B
  C+D
  B+D
  F+G+H
  ==>
  F+G+H+I+K
  A+B+C+D

C[edit]

#include <stdio.h>
 
#define s(x) (1U << ((x) - 'A'))
 
typedef unsigned int bitset;
 
int consolidate(bitset *x, int len)
{
int i, j;
for (i = len - 2; i >= 0; i--)
for (j = len - 1; j > i; j--)
if (x[i] & x[j])
x[i] |= x[j], x[j] = x[--len];
return len;
}
 
void show_sets(bitset *x, int len)
{
bitset b;
while(len--) {
for (b = 'A'; b <= 'Z'; b++)
if (x[len] & s(b)) printf("%c ", b);
putchar('\n');
}
}
 
int main(void)
{
bitset x[] = { s('A') | s('B'), s('C') | s('D'), s('B') | s('D'),
s('F') | s('G') | s('H'), s('H') | s('I') | s('K') };
 
int len = sizeof(x) / sizeof(x[0]);
 
puts("Before:"); show_sets(x, len);
puts("\nAfter:"); show_sets(x, consolidate(x, len));
return 0;
}

The above is O(N2) in terms of number of input sets. If input is large (many sets or huge number of elements), here's an O(N) method, where N is the sum of the sizes of all input sets:

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
 
struct edge { int to; struct edge *next; };
struct node { int group; struct edge *e; };
 
int **consolidate(int **x)
{
# define alloc(v, size) v = calloc(size, sizeof(v[0]));
int group, n_groups, n_nodes;
int n_edges = 0;
struct edge *edges, *ep;
struct node *nodes;
int pos, *stack, **ret;
 
void add_edge(int a, int b) {
ep->to = b;
ep->next = nodes[a].e;
nodes[a].e = ep;
ep++;
}
 
void traverse(int a) {
if (nodes[a].group) return;
 
nodes[a].group = group;
stack[pos++] = a;
 
for (struct edge *e = nodes[a].e; e; e = e->next)
traverse(e->to);
}
 
n_groups = n_nodes = 0;
for (int i = 0; x[i]; i++, n_groups++)
for (int j = 0; x[i][j]; j++) {
n_edges ++;
if (x[i][j] >= n_nodes)
n_nodes = x[i][j] + 1;
}
 
alloc(ret, n_nodes);
alloc(nodes, n_nodes);
alloc(stack, n_nodes);
ep = alloc(edges, n_edges);
 
for (int i = 0; x[i]; i++)
for (int *s = x[i], j = 0; s[j]; j++)
add_edge(s[j], s[j + 1] ? s[j + 1] : s[0]);
 
group = 0;
for (int i = 1; i < n_nodes; i++) {
if (nodes[i].group) continue;
 
group++, pos = 0;
traverse(i);
 
stack[pos++] = 0;
ret[group - 1] = malloc(sizeof(int) * pos);
memcpy(ret[group - 1], stack, sizeof(int) * pos);
}
 
free(edges);
free(stack);
free(nodes);
 
// caller is responsible for freeing ret
return realloc(ret, sizeof(ret[0]) * (1 + group));
# undef alloc
}
 
void show_sets(int **x)
{
for (int i = 0; x[i]; i++) {
printf("%d: ", i);
for (int j = 0; x[i][j]; j++)
printf(" %d", x[i][j]);
putchar('\n');
}
}
 
int main(void)
{
int *x[] = {
(int[]) {1, 2, 0}, // 0: end of set
(int[]) {3, 4, 0},
(int[]) {3, 1, 0},
(int[]) {0}, // empty set
(int[]) {5, 6, 0},
(int[]) {7, 6, 0},
(int[]) {3, 9, 10, 0},
0 // 0: end of sets
};
 
puts("input:");
show_sets(x);
 
puts("components:");
show_sets(consolidate(x));
 
return 0;
}

C#[edit]

using System;
using System.Linq;
using System.Collections.Generic;
 
public class SetConsolidation
{
public static void Main()
{
var setCollection1 = new[] {new[] {"A", "B"}, new[] {"C", "D"}};
var setCollection2 = new[] {new[] {"A", "B"}, new[] {"B", "D"}};
var setCollection3 = new[] {new[] {"A", "B"}, new[] {"C", "D"}, new[] {"B", "D"}};
var setCollection4 = new[] {new[] {"H", "I", "K"}, new[] {"A", "B"}, new[] {"C", "D"},
new[] {"D", "B"}, new[] {"F", "G", "H"}};
var input = new[] {setCollection1, setCollection2, setCollection3, setCollection4};
 
foreach (var sets in input) {
Console.WriteLine("Start sets:");
Console.WriteLine(string.Join(", ", sets.Select(s => "{" + string.Join(", ", s) + "}")));
Console.WriteLine("Sets consolidated using Nodes:");
Console.WriteLine(string.Join(", ", ConsolidateSets1(sets).Select(s => "{" + string.Join(", ", s) + "}")));
Console.WriteLine("Sets consolidated using Set operations:");
Console.WriteLine(string.Join(", ", ConsolidateSets2(sets).Select(s => "{" + string.Join(", ", s) + "}")));
Console.WriteLine();
}
}
 
/// <summary>
/// Consolidates sets using a connected-component-finding-algorithm involving Nodes with parent pointers.
/// The more efficient solution, but more elaborate code.
/// </summary>
private static IEnumerable<IEnumerable<T>> ConsolidateSets1<T>(IEnumerable<IEnumerable<T>> sets,
IEqualityComparer<T> comparer = null)
{
if (comparer == null) comparer = EqualityComparer<T>.Default;
var elements = new Dictionary<T, Node<T>>();
foreach (var set in sets) {
Node<T> top = null;
foreach (T value in set) {
Node<T> element;
if (elements.TryGetValue(value, out element)) {
if (top != null) {
var newTop = element.FindTop();
top.Parent = newTop;
element.Parent = newTop;
top = newTop;
} else {
top = element.FindTop();
}
} else {
elements.Add(value, element = new Node<T>(value));
if (top == null) top = element;
else element.Parent = top;
}
}
}
foreach (var g in elements.Values.GroupBy(element => element.FindTop().Value))
yield return g.Select(e => e.Value);
}
 
private class Node<T>
{
public Node(T value, Node<T> parent = null) {
Value = value;
Parent = parent ?? this;
}
 
public T Value { get; }
public Node<T> Parent { get; set; }
 
public Node<T> FindTop() {
var top = this;
while (top != top.Parent) top = top.Parent;
//Set all parents to the top element to prevent repeated iteration in the future
var element = this;
while (element.Parent != top) {
var parent = element.Parent;
element.Parent = top;
element = parent;
}
return top;
}
}
 
/// <summary>
/// Consolidates sets using operations on the HashSet&lt;T&gt; class.
/// Less efficient than the other method, but easier to write.
/// </summary>
private static IEnumerable<IEnumerable<T>> ConsolidateSets2<T>(IEnumerable<IEnumerable<T>> sets,
IEqualityComparer<T> comparer = null)
{
if (comparer == null) comparer = EqualityComparer<T>.Default;
var currentSets = sets.Select(s => new HashSet<T>(s)).ToList();
int previousSize;
do {
previousSize = currentSets.Count;
for (int i = 0; i < currentSets.Count - 1; i++) {
for (int j = currentSets.Count - 1; j > i; j--) {
if (currentSets[i].Overlaps(currentSets[j])) {
currentSets[i].UnionWith(currentSets[j]);
currentSets.RemoveAt(j);
}
}
}
} while (previousSize > currentSets.Count);
foreach (var set in currentSets) yield return set.Select(value => value);
}
}
Output:
Start sets:
{A, B}, {C, D}
Sets consolidated using nodes:
{A, B}, {C, D}
Sets consolidated using Set operations:
{A, B}, {C, D}

Start sets:
{A, B}, {B, D}
Sets consolidated using nodes:
{A, B, D}
Sets consolidated using Set operations:
{A, B, D}

Start sets:
{A, B}, {C, D}, {B, D}
Sets consolidated using nodes:
{A, B, C, D}
Sets consolidated using Set operations:
{A, B, D, C}

Start sets:
{H, I, K}, {A, B}, {C, D}, {D, B}, {F, G, H}
Sets consolidated using nodes:
{H, I, K, F, G}, {A, B, C, D}
Sets consolidated using Set operations:
{H, I, K, F, G}, {A, B, D, C}

Common Lisp[edit]

Translation of: Racket
(defun consolidate (ss)
(labels ((comb (cs s)
(cond ((null s) cs)
((null cs) (list s))
((null (intersection s (first cs)))
(cons (first cs) (comb (rest cs) s)))
((consolidate (cons (union s (first cs)) (rest cs)))))))
(reduce #'comb ss :initial-value nil)))
Output:
> (consolidate '((a b) (c d)))
((A B) (C D))
> (consolidate '((a b) (b c)))
((C A B))
> (consolidate '((a b) (c d) (d b)))
((C D A B))
> (consolidate '((h i k) (a b) (c d) (d b) (f g h)))
((F G H I K) (C D A B))

D[edit]

Translation of: Go
import std.stdio, std.algorithm, std.array;
 
dchar[][] consolidate(dchar[][] sets) @safe {
foreach (set; sets)
set.sort();
 
foreach (i, ref si; sets[0 .. $ - 1]) {
if (si.empty)
continue;
foreach (ref sj; sets[i + 1 .. $])
if (!sj.empty && !si.setIntersection(sj).empty) {
sj = si.setUnion(sj).uniq.array;
si = null;
}
}
 
return sets.filter!"!a.empty".array;
}
 
void main() @safe {
[['A', 'B'], ['C','D']].consolidate.writeln;
 
[['A','B'], ['B','D']].consolidate.writeln;
 
[['A','B'], ['C','D'], ['D','B']].consolidate.writeln;
 
[['H','I','K'], ['A','B'], ['C','D'],
['D','B'], ['F','G','H']].consolidate.writeln;
}
Output:
["AB", "CD"]
["ABD"]
["ABCD"]
["ABCD", "FGHIK"]

Recursive version, as described on talk page.

import std.stdio, std.algorithm, std.array;
 
dchar[][] consolidate(dchar[][] sets) @safe {
foreach (set; sets)
set.sort();
 
dchar[][] consolidateR(dchar[][] s) {
if (s.length < 2)
return s;
auto r = [s[0]];
foreach (x; consolidateR(s[1 .. $])) {
if (!r[0].setIntersection(x).empty) {
r[0] = r[0].setUnion(x).uniq.array;
} else
r ~= x;
}
return r;
}
 
return consolidateR(sets);
}
 
void main() @safe {
[['A', 'B'], ['C','D']].consolidate.writeln;
 
[['A','B'], ['B','D']].consolidate.writeln;
 
[['A','B'], ['C','D'], ['D','B']].consolidate.writeln;
 
[['H','I','K'], ['A','B'], ['C','D'],
['D','B'], ['F','G','H']].consolidate.writeln;
}
["AB", "CD"]
["ABD"]
["ABCD"]
["FGHIK", "ABCD"]

EchoLisp[edit]

 
;; utility : make a set of sets from a list
(define (make-set* s)
(or (when (list? s) (make-set (map make-set* s))) s))
 
;; union of all sets which intersect - O(n^2)
(define (make-big ss)
(make-set
(for/list ((u ss))
(for/fold (big u) ((v ss)) #:when (set-intersect? big v) (set-union big v)))))
 
;; remove sets which are subset of another one - O(n^2)
(define (remove-small ss)
(for/list ((keep ss))
#:when (for/and ((v ss)) #:continue (set-equal? keep v) (not (set-subset? v keep)))
keep))
 
(define (consolidate ss) (make-set (remove-small (make-big ss))))
 
(define S (make-set* ' ((h i k) ( a b) ( b c) (c d) ( f g h))))
{ { a b } { b c } { c d } { f g h } { h i k } }
 
(consolidate S)
{ { a b c d } { f g h i k } }
 
 


Egison[edit]

 
(define $consolidate
(lambda [$xss]
(match xss (multiset (set char))
{[<cons <cons $m $xs>
<cons <cons ,m $ys>
$rss>>
(consolidate {(unique/m char {m @xs @ys}) @rss})]
[_ xss]})))
 
(test (consolidate {{'H' 'I' 'K'} {'A' 'B'} {'C' 'D'} {'D' 'B'} {'F' 'G' 'H'}}))
 
Output:
 
{"DBAC" "HIKFG"}
 

Ela[edit]

This solution emulate sets using linked lists:

open list
 
merge [] ys = ys
merge (x::xs) ys | x `elem` ys = merge xs ys
| else = merge xs (x::ys)
 
consolidate (_::[])@xs = xs
consolidate (x::xs) = conso [x] (consolidate xs)
where conso xs [] = xs
conso (x::xs)@r (y::ys) | intersect x y <> [] = conso ((merge x y)::xs) ys
| else = conso (r ++ [y]) ys

Usage:

open monad io
 
:::IO
 
do
x <- return $ consolidate [['H','I','K'], ['A','B'], ['C','D'], ['D','B'], ['F','G','H']]
putLn x
y <- return $ consolidate [['A','B'], ['B','D']]
putLn y
Output:
[['K','I','F','G','H'],['A','C','D','B']]
[['A','B','D']]

Elixir[edit]

defmodule RC do
def set_consolidate(sets, result\\[])
def set_consolidate([], result), do: result
def set_consolidate([h|t], result) do
case Enum.find(t, fn set -> not MapSet.disjoint?(h, set) end) do
nil -> set_consolidate(t, [h | result])
set -> set_consolidate([MapSet.union(h, set) | t -- [set]], result)
end
end
end
 
examples = [[[:A,:B], [:C,:D]],
[[:A,:B], [:B,:D]],
[[:A,:B], [:C,:D], [:D,:B]],
[[:H,:I,:K], [:A,:B], [:C,:D], [:D,:B], [:F,:G,:H]]]
|> Enum.map(fn sets ->
Enum.map(sets, fn set -> MapSet.new(set) end)
end)
 
Enum.each(examples, fn sets ->
IO.write "#{inspect sets} =>\n\t"
IO.inspect RC.set_consolidate(sets)
end)
Output:
[#MapSet<[:A, :B]>, #MapSet<[:C, :D]>] =>
	[#MapSet<[:C, :D]>, #MapSet<[:A, :B]>]
[#MapSet<[:A, :B]>, #MapSet<[:B, :D]>] =>
	[#MapSet<[:A, :B, :D]>]
[#MapSet<[:A, :B]>, #MapSet<[:C, :D]>, #MapSet<[:B, :D]>] =>
	[#MapSet<[:A, :B, :C, :D]>]
[#MapSet<[:H, :I, :K]>, #MapSet<[:A, :B]>, #MapSet<[:C, :D]>, #MapSet<[:B, :D]>, #MapSet<[:F, :G, :H]>] =>
	[#MapSet<[:A, :B, :C, :D]>, #MapSet<[:F, :G, :H, :I, :K]>]

F#[edit]

let (|SeqNode|SeqEmpty|) s =
if Seq.isEmpty s then SeqEmpty
else SeqNode ((Seq.head s), Seq.skip 1 s)
 
let SetDisjunct x y = Set.isEmpty (Set.intersect x y)
 
let rec consolidate s = seq {
match s with
| SeqEmpty -> ()
| SeqNode (this, rest) ->
let consolidatedRest = consolidate rest
for that in consolidatedRest do
if (SetDisjunct this that) then yield that
yield Seq.fold (fun x y -> if not (SetDisjunct x y) then Set.union x y else x) this consolidatedRest
}
 
[<EntryPoint>]
let main args =
let makeSeqOfSet listOfList = List.map (fun x -> Set.ofList x) listOfList |> Seq.ofList
List.iter (fun x -> printfn "%A" (consolidate (makeSeqOfSet x))) [
[["A";"B"]; ["C";"D"]];
[["A";"B"]; ["B";"C"]];
[["A";"B"]; ["C";"D"]; ["D";"B"]];
[["H";"I";"K"]; ["A";"B"]; ["C";"D"]; ["D";"B"]; ["F";"G";"H"]]
]
0
Output:
seq [set ["C"; "D"]; set ["A"; "B"]]
seq [set ["A"; "B"; "C"]]
seq [set ["A"; "B"; "C"; "D"]]
seq [set ["A"; "B"; "C"; "D"]; set ["F"; "G"; "H"; "I"; "K"]]

Go[edit]

Translation of: Python
package main
 
import "fmt"
 
type set map[string]bool
 
var testCase = []set{
set{"H": true, "I": true, "K": true},
set{"A": true, "B": true},
set{"C": true, "D": true},
set{"D": true, "B": true},
set{"F": true, "G": true, "H": true},
}
 
func main() {
fmt.Println(consolidate(testCase))
}
 
func consolidate(sets []set) []set {
setlist := []set{}
for _, s := range sets {
if s != nil && len(s) > 0 {
setlist = append(setlist, s)
}
}
for i, s1 := range setlist {
if len(s1) > 0 {
for _, s2 := range setlist[i+1:] {
if s1.disjoint(s2) {
continue
}
for e := range s1 {
s2[e] = true
delete(s1, e)
}
s1 = s2
}
}
}
r := []set{}
for _, s := range setlist {
if len(s) > 0 {
r = append(r, s)
}
}
return r
}
 
func (s1 set) disjoint(s2 set) bool {
for e := range s2 {
if s1[e] {
return false
}
}
return true
}
Output:
[map[A:true C:true B:true D:true] map[G:true F:true I:true H:true K:true]]

Haskell[edit]

import qualified Data.Set as S
 
consolidate :: Ord a => [S.Set a] -> [S.Set a]
consolidate = foldl comb []
where comb [] s' = [s']
comb (s:ss) s'
| S.null (s `S.intersection` s'
) = s : comb ss s'
| otherwise = comb ss (s `S.union` s'
)
 
Output:
*Main> consolidate [S.fromList "ab", S.fromList "dc"]
[fromList "ab",fromList "cd"]
*Main> consolidate [S.fromList "ab", S.fromList "bc"]
[fromList "abc"]
*Main> consolidate [S.fromList "ab", S.fromList "cd", S.fromList "db"]
[fromList "abcd"]
*Main> consolidate [S.fromList "hik", S.fromList "ab", S.fromList "cd", S.fromList "db", S.fromList "fgh"]
[fromList "abcd",fromList "fghik"]

J[edit]

consolidate=:4 :0/
b=. y 1&e.@e.&> x
(1,-.b)#(~.;x,b#y);y
)

Examples:

   consolidate 'ab';'cd'
┌──┬──┐
│ab│cd│
└──┴──┘
consolidate 'ab';'bd'
┌───┐
│abd│
└───┘
consolidate 'ab';'cd';'db'
┌────┐
│abcd│
└────┘
consolidate 'hij';'ab';'cd';'db';'fgh'
┌─────┬────┐
│hijfg│abcd│
└─────┴────┘

Java[edit]

Translation of: D
Works with: Java version 7
import java.util.*;
 
public class SetConsolidation {
 
public static void main(String[] args) {
List<Set<Character>> h1 = hashSetList("AB", "CD");
System.out.println(consolidate(h1));
 
List<Set<Character>> h2 = hashSetList("AB", "BD");
System.out.println(consolidateR(h2));
 
List<Set<Character>> h3 = hashSetList("AB", "CD", "DB");
System.out.println(consolidate(h3));
 
List<Set<Character>> h4 = hashSetList("HIK", "AB", "CD", "DB", "FGH");
System.out.println(consolidateR(h4));
}
 
// iterative
private static <E> List<Set<E>>
consolidate(Collection<? extends Set<E>> sets) {
List<Set<E>> r = new ArrayList<>();
for (Set<E> s : sets) {
List<Set<E>> new_r = new ArrayList<>();
new_r.add(s);
for (Set<E> x : r) {
if (!Collections.disjoint(s, x)) {
s.addAll(x);
} else {
new_r.add(x);
}
}
r = new_r;
}
return r;
}
 
// recursive
private static <E> List<Set<E>> consolidateR(List<Set<E>> sets) {
if (sets.size() < 2)
return sets;
List<Set<E>> r = new ArrayList<>();
r.add(sets.get(0));
for (Set<E> x : consolidateR(sets.subList(1, sets.size()))) {
if (!Collections.disjoint(r.get(0), x)) {
r.get(0).addAll(x);
} else {
r.add(x);
}
}
return r;
}
 
private static List<Set<Character>> hashSetList(String... set) {
List<Set<Character>> r = new ArrayList<>();
for (int i = 0; i < set.length; i++) {
r.add(new HashSet<Character>());
for (int j = 0; j < set[i].length(); j++)
r.get(i).add(set[i].charAt(j));
}
return r;
}
}
[A, B] [D, C] 
[D, A, B] 
[D, A, B, C] 
[F, G, H, I, K] [D, A, B, C]

jq[edit]

Infrastructure:

Currently, jq does not have a "Set" library, so to save space here, we will use simple but inefficient implementations of set-oriented functions as they are fast for sets of moderate size. Nevertheless, we will represent sets as sorted arrays.

def to_set: unique;
 
def union(A; B): (A + B) | unique;
 
# boolean
def intersect(A;B):
reduce A[] as $x (false; if . then . else (B|index($x)) end) | not | not;

Consolidation:

For clarity, the helper functions are presented as top-level functions, but they could be defined as inner functions of the main function, consolidate/0.

# Input: [i, j, sets] with i < j
# Return [i,j] for a pair that can be combined, else null
def combinable:
.[0] as $i | .[1] as $j | .[2] as $sets
| ($sets|length) as $length
| if intersect($sets[$i]; $sets[$j]) then [$i, $j]
elif $i < $j - 1 then (.[0] += 1 | combinable)
elif $j < $length - 1 then [0, $j+1, $sets] | combinable
else null
end;
 
# Given an array of arrays, remove the i-th and j-th elements,
# and add their union:
def update(i;j):
if i > j then update(j;i)
elif i == j then del(.[i])
else
union(.[i]; .[j]) as $c
| union(del(.[j]) | del(.[i]); [$c])
end;
 
# Input: a set of sets
def consolidate:
if length <= 1 then .
else
([0, 1, .] | combinable) as $c
| if $c then update($c[0]; $c[1]) | consolidate
else .
end
end;
 

Examples:

def tests:
[["A", "B"], ["C","D"]],
[["A","B"], ["B","D"]],
[["A","B"], ["C","D"], ["D","B"]],
[["H","I","K"], ["A","B"], ["C","D"], ["D","B"], ["F","G","H"]]
;
 
def test:
tests | to_set | consolidate;
 
test
Output:
$ jq -c -n -f Set_consolidation.rc
[["A","B"],["C","D"]]
[["A","B","D"]]
[["A","B","C","D"]]
[["A","B","C","D"],["F","G","H","I","K"]]

Julia[edit]

The consolidate Function

Here I assume that the data are contained in a list of sets. Perhaps a recursive solution would be more elegant, but in this case playing games with a stack works well enough.

 
function consolidate{T}(a::Array{Set{T},1})
1 < length(a) || return a
b = copy(a)
c = Set{T}[]
while 1 < length(b)
x = shift!(b)
cme = true
for (i, y) in enumerate(b)
 !isempty(intersect(x, y)) || continue
cme = false
b[i] = union(x, y)
break
end
 !cme || push!(c, x)
end
push!(c, b[1])
return c
end
 

Main

 
p = Set(["A", "B"])
q = Set(["C", "D"])
r = Set(["B", "D"])
s = Set(["H", "I", "K"])
t = Set(["F", "G", "H"])
 
println("p = ", p)
println("q = ", q)
println("r = ", r)
println("s = ", s)
println("t = ", t)
 
println("consolidate([p, q]) =\n ", consolidate([p, q]))
println("consolidate([p, r]) =\n ", consolidate([p, r]))
println("consolidate([p, q, r]) =\n ", consolidate([p, q, r]))
println("consolidate([p, q, r, s, t]) =\n ",
consolidate([p, q, r, s, t]))
 
Output:
p = Set{ASCIIString}({"B","A"})
q = Set{ASCIIString}({"C","D"})
r = Set{ASCIIString}({"B","D"})
s = Set{ASCIIString}({"I","K","H"})
t = Set{ASCIIString}({"G","F","H"})
consolidate([p, q]) =
    [Set{ASCIIString}({"B","A"}),Set{ASCIIString}({"C","D"})]
consolidate([p, r]) =
    [Set{ASCIIString}({"B","A","D"})]
consolidate([p, q, r]) =
    [Set{ASCIIString}({"B","A","C","D"})]
consolidate([p, q, r, s, t]) =
    [Set{ASCIIString}({"B","A","C","D"}),Set{ASCIIString}({"I","G","K","H","F"})]

Kotlin[edit]

// version 1.0.6
 
fun<T : Comparable<T>> consolidateSets(sets: Array<Set<T>>): Set<Set<T>> {
val size = sets.size
val consolidated = BooleanArray(size) // all false by default
var i = 0
while (i < size - 1) {
if (!consolidated[i]) {
while (true) {
var intersects = 0
for (j in (i + 1) until size) {
if (consolidated[j]) continue
if (sets[i].intersect(sets[j]).isNotEmpty()) {
sets[i] = sets[i].union(sets[j])
consolidated[j] = true
intersects++
}
}
if (intersects == 0) break
}
}
i++
}
return (0 until size).filter { !consolidated[it] }.map { sets[it].toSortedSet() }.toSet()
}
 
fun main(args: Array<String>) {
val unconsolidatedSets = arrayOf(
arrayOf(setOf('A', 'B'), setOf('C', 'D')),
arrayOf(setOf('A', 'B'), setOf('B', 'D')),
arrayOf(setOf('A', 'B'), setOf('C', 'D'), setOf('D', 'B')),
arrayOf(setOf('H', 'I', 'K'), setOf('A', 'B'), setOf('C', 'D'), setOf('D', 'B'), setOf('F', 'G', 'H'))
)
for (sets in unconsolidatedSets) println(consolidateSets(sets))
}
Output:
[[A, B], [C, D]]
[[A, B, D]]
[[A, B, C, D]]
[[F, G, H, I, K], [A, B, C, D]]

Mathematica[edit]

reduce[x_] :=
Block[{pairs, unique},
pairs =
DeleteCases[
Subsets[Range@
[email protected], {2}], _?(Intersection @@ x[[#]] == {} &)];
unique = Complement[[email protected]@x, [email protected]];
Join[Union[Flatten[x[[#]]]] & /@ pairs, x[[unique]]]]
 
consolidate[x__] := FixedPoint[reduce, {x}]
consolidate[{a, b}, {c, d}]
-> {{a, b}, {c, d}}

consolidate[{a, b}, {b, d}]
-> {{a, b, d}}

consolidate[{a, b}, {c, d}, {d, b}]
-> {{a, b, c, d}}

consolidate[{h, i, k}, {a, b}, {c, d}, {d, b}, {f, g, h}]
-> {{a,b,c,d},{f,g,h,i,k}}

OCaml[edit]

let join a b =
List.fold_left (fun acc v ->
if List.mem v acc then acc else v::acc
) b a
 
let share a b = List.exists (fun x -> List.mem x b) a
 
let extract p lst =
let rec aux acc = function
| x::xs -> if p x then Some (x, List.rev_append acc xs) else aux (x::acc) xs
| [] -> None
in
aux [] lst
 
let consolidate sets =
let rec aux acc = function
| [] -> List.rev acc
| x::xs ->
match extract (share x) xs with
| Some (y, ys) -> aux acc ((join x y) :: ys)
| None -> aux (x::acc) xs
in
aux [] sets
 
let print_sets sets =
print_string "{ ";
List.iter (fun set ->
print_string "{";
print_string (String.concat " " set);
print_string "} "
) sets;
print_endline "}"
 
let () =
print_sets (consolidate [["A";"B"]; ["C";"D"]]);
print_sets (consolidate [["A";"B"]; ["B";"C"]]);
print_sets (consolidate [["A";"B"]; ["C";"D"]; ["D";"B"]]);
print_sets (consolidate [["H";"I";"K"]; ["A";"B"]; ["C";"D"]; ["D";"B"];
["F";"G";"H"]]);
;;
Output:
{ {A B} {C D} }
{ {A B C} }
{ {B A C D} }
{ {K I F G H} {B A C D} }

ooRexx[edit]

/* REXX ***************************************************************
* 04.08.2013 Walter Pachl using ooRexx features
* (maybe not in the best way -improvements welcome!)
* but trying to demonstrate the algorithm
**********************************************************************/

s.1=.array~of(.set~of('A','B'),.set~of('C','D'))
s.2=.array~of(.set~of('A','B'),.set~of('B','D'))
s.3=.array~of(.set~of('A','B'),.set~of('C','D'),.set~of('D','B'))
s.4=.array~of(.set~of('H','I','K'),.set~of('A','B'),.set~of('C','D'),,
.set~of('B','D'),.set~of('F','G','H'))
s.5=.array~of(.set~of('snow','ice','slush','frost','fog'),,
.set~of('iceburgs','icecubes'),,
.set~of('rain','fog','sleet'))
s.6=.array~of('one')
s.7=.array~new
s.8=.array~of('')
Do si=1 To 8 /* loop through the test data */
na=s.si /* an array of sets */
head='Output(s):'
Say left('Input' si,10) list_as(na) /* show the input */
Do While na~items()>0 /* while the array ain't empty*/
na=cons(na) /* consolidate and get back */
/* array of remaining sets */
head=' '
End
Say '====' /* separator line */
End
Exit
 
cons: Procedure Expose head
/**********************************************************************
* consolidate the sets in the given array
**********************************************************************/

Use Arg a
w=a /* work on a copy */
n=w~items() /* number of sets in the array*/
Select
When n=0 Then /* no set in array */
Return .array~new /* retuns an empty array */
When n=1 Then Do /* one set in array */
Say head list(w[1]) /* show its contents */
Return .array~new /* retuns an empty array */
End
Otherwise Do /* at least two sets are there*/
b=.array~new /* use for remaining sets */
r=w[n] /* start with last set */
try=1
Do until changed=0 /* loop until result is stable*/
changed=0
new=0
n=w~items() /* number of sets */
Do i=1 To n-try /* loop first through n-1 sets*/
try=0 /* then through all of them */
is=r~intersection(w[i])
If is~items>0 Then Do /* any elements in common */
r=r~union(w[i]) /* result is the union */
Changed=1 /* and result is now larger */
End
Else Do /* no elemen in common */
new=new+1 /* add the set to the array */
b[new]=w[i] /* of remaining sets */
End
End
If b~items()=0 Then Do /* no remaining sets */
w=.array~new
Leave /* we are done */
End
w=b /* repeat with remaining sets */
b=.array~new /* prepare for next iteration */
End
End
Say head list(r) /* show one consolidated set */
End
Return w /* return array of remaining */
 
list: Procedure
/**********************************************************************
* list elements of given set
**********************************************************************/

Call trace ?O
Use Arg set
arr=set~makeArray
arr~sort()
ol='('
Do i=1 To arr~items()
If i=1 Then
ol=ol||arr[i]
Else
ol=ol||','arr[i]
End
Return ol')'
 
list_as: Procedure
/**********************************************************************
* List an array of sets
**********************************************************************/

Call trace ?O
Use Arg a
n=a~items()
If n=0 Then
ol='no element in array'
Else Do
ol=''
Do i=1 To n
ol=ol '('
arr=a[i]~makeArray
Do j=1 To arr~items()
If j=1 Then
ol=ol||arr[j]
Else
ol=ol','arr[j]
End
ol=ol') '
End
End
Return strip(ol)
Output:
Input 1    (B,A)  (C,D)
Output(s): (C,D)
           (A,B)
====
Input 2    (B,A)  (B,D)
Output(s): (A,B,D)
====
Input 3    (B,A)  (C,D)  (B,D)
Output(s): (A,B,C,D)
====
Input 4    (H,I,K)  (B,A)  (C,D)  (F,G,H)
Output(s): (F,G,H,I,K)
           (A,B,C,D)
====
Input 5    (snow,fog,ice,frost,slush)  (icecubes,iceburgs)  (fog,sleet,rain)
Output(s): (fog,frost,ice,rain,sleet,slush,snow)
           (iceburgs,icecubes)
====
Input 6    (one)
Output(s): (one)
====
Input 7    no element in array
====
Input 8    ()
Output(s): ()
====

PARI/GP[edit]

cons(V)={
my(v,u,s);
for(i=1,#V,
v=V[i];
for(j=i+1,#V,
u=V[j];
if(#setintersect(u,v),V[i]=v=vecsort(setunion(u,v));V[j]=[];s++)
)
);
V=select(v->#v,V);
if(s,cons(V),V)
};

Perl[edit]

We implement the key data structure, a set of sets, as an array containing references to arrays of scalars.

use strict;
use English;
use Smart::Comments;
 
my @ex1 = consolidate( (['A', 'B'], ['C', 'D']) );
### Example 1: @ex1
my @ex2 = consolidate( (['A', 'B'], ['B', 'D']) );
### Example 2: @ex2
my @ex3 = consolidate( (['A', 'B'], ['C', 'D'], ['D', 'B']) );
### Example 3: @ex3
my @ex4 = consolidate( (['H', 'I', 'K'], ['A', 'B'], ['C', 'D'], ['D', 'B'], ['F', 'G', 'H']) );
### Example 4: @ex4
exit 0;
 
sub consolidate {
scalar(@ARG) >= 2 or return @ARG;
my @result = ( shift(@ARG) );
my @recursion = consolidate(@ARG);
foreach my $r (@recursion) {
if (set_intersection($result[0], $r)) {
$result[0] = [ set_union($result[0], $r) ];
}
else {
push @result, $r;
}
}
return @result;
}
 
sub set_union {
my ($a, $b) = @ARG;
my %union;
foreach my $a_elt (@{$a}) { $union{$a_elt}++; }
foreach my $b_elt (@{$b}) { $union{$b_elt}++; }
return keys(%union);
}
 
sub set_intersection {
my ($a, $b) = @ARG;
my %a_hash;
foreach my $a_elt (@{$a}) { $a_hash{$a_elt}++; }
my @result;
foreach my $b_elt (@{$b}) {
push(@result, $b_elt) if exists($a_hash{$b_elt});
}
return @result;
}
Output:
### Example 1: [
###              [
###                'A',
###                'B'
###              ],
###              [
###                'C',
###                'D'
###              ]
###            ]

### Example 2: [
###              [
###                'D',
###                'B',
###                'A'
###              ]
###            ]

### Example 3: [
###              [
###                'A',
###                'C',
###                'D',
###                'B'
###              ]
###            ]

### Example 4: [
###              [
###                'H',
###                'F',
###                'K',
###                'G',
###                'I'
###              ],
###              [
###                'D',
###                'B',
###                'A',
###                'C'
###              ]
###            ]

Perl 6[edit]

multi consolidate() { () }
multi consolidate(Set \this is copy, *@those) {
gather {
for consolidate |@those -> \that {
if this ∩ that { this = this ∪ that }
else { take that }
}
take this;
}
}
 
enum Elems <A B C D E F G H I J K>;
say $_, "\n ==> ", consolidate |$_
for [set(A,B), set(C,D)],
[set(A,B), set(B,D)],
[set(A,B), set(C,D), set(D,B)],
[set(H,I,K), set(A,B), set(C,D), set(D,B), set(F,G,H)];
Output:
set(A, B) set(C, D)
    ==> set(C, D) set(A, B)
set(A, B) set(B, D)
    ==> set(A, B, D)
set(A, B) set(C, D) set(D, B)
    ==> set(A, B, C, D)
set(H, I, K) set(A, B) set(C, D) set(D, B) set(F, G, H)
    ==> set(A, B, C, D) set(H, I, K, F, G)

PicoLisp[edit]

Translation of: Python
(de consolidate (S)
(when S
(let R (cons (car S))
(for X (consolidate (cdr S))
(if (mmeq X (car R))
(set R (uniq (conc X (car R))))
(conc R (cons X)) ) )
R ) ) )

Test:

: (consolidate '((A B) (C D)))
-> ((A B) (C D))
: (consolidate '((A B) (B D)))
-> ((B D A))
: (consolidate '((A B) (C D) (D B)))
-> ((D B C A))
: (consolidate '((H I K) (A B) (C D) (D B) (F G H)))
-> ((F G H I K) (D B C A))

PL/I[edit]

Set: procedure options (main);     /* 13 November 2013 */
declare set(20) character (200) varying;
declare e character (1);
declare (i, n) fixed binary;
 
set = '';
n = 1;
do until (e = ']');
get edit (e) (a(1)); put edit (e) (a(1));
if e = '}' then n = n + 1; /* end of set. */
if e ^= '{' & e ^= ',' & e ^= '}' & e ^= ' ' then
set(n) = set(n) || e; /* Build set */
end;
/* We have read in all sets. */
n = n - 1; /* we have n sets */
/* Display the sets: */
put skip list ('The original sets:');
do i = 1 to n;
call print(i);
end;
/* Look for sets to combine: */
do i = 2 to n;
if length(set(i)) > 0 then
if search(set(1), set(i)) > 0 then
/* there's at least one common element */
do; call combine (1, i); set(i) = ''; end;
end;
 
put skip (2) list ('Results:');
do i = 1 to n;
if length(set(i)) > 0 then call print (i);
end;
 
combine: procedure (p, q);
declare (p, q) fixed binary;
declare e character (1);
declare i fixed binary;
 
do i = 1 to length(set(q));
e = substr(set(q), i, 1);
if index(set(p), e) = 0 then set(p) = set(p) || e;
end;
 
end combine;
 
print: procedure(k);
declare k fixed binary;
declare i fixed binary;
 
put edit ('{') (a);
do i = 1 to length(set(k));
put edit (substr(set(k), i, 1)) (a);
if i < length(set(k)) then put edit (',') (a);
end;
put edit ('} ') (a);
end print;
 
end Set;
The original sets: {A,B} 

Results: {A,B}

The original sets: {A,B} {C,D} 

Results: {A,B} {C,D}

The original sets: {A,B} {B,C} 

Results: {A,B,C}

The original sets: {A,B} {C,D} {E,B,F,G,H} 

Results: {A,B,E,F,G,H} {C,D} 

Python[edit]

Python: Iterative[edit]

def consolidate(sets):
setlist = [s for s in sets if s]
for i, s1 in enumerate(setlist):
if s1:
for s2 in setlist[i+1:]:
intersection = s1.intersection(s2)
if intersection:
s2.update(s1)
s1.clear()
s1 = s2
return [s for s in setlist if s]

Python: Recursive[edit]

def conso(s):
if len(s) < 2: return s
 
r, b = [s[0]], conso(s[1:])
for x in b:
if r[0].intersection(x): r[0].update(x)
else: r.append(x)
return r

Python: Testing[edit]

The _test function contains solutions to all the examples as well as a check to show the order-independence of the sets given to the consolidate function.

def _test(consolidate=consolidate):
 
def freze(list_of_sets):
'return a set of frozensets from the list of sets to allow comparison'
return set(frozenset(s) for s in list_of_sets)
 
# Define some variables
A,B,C,D,E,F,G,H,I,J,K = 'A,B,C,D,E,F,G,H,I,J,K'.split(',')
# Consolidate some lists of sets
assert (freze(consolidate([{A,B}, {C,D}])) == freze([{'A', 'B'}, {'C', 'D'}]))
assert (freze(consolidate([{A,B}, {B,D}])) == freze([{'A', 'B', 'D'}]))
assert (freze(consolidate([{A,B}, {C,D}, {D,B}])) == freze([{'A', 'C', 'B', 'D'}]))
assert (freze(consolidate([{H,I,K}, {A,B}, {C,D}, {D,B}, {F,G,H}])) ==
freze([{'A', 'C', 'B', 'D'}, {'G', 'F', 'I', 'H', 'K'}]))
assert (freze(consolidate([{A,H}, {H,I,K}, {A,B}, {C,D}, {D,B}, {F,G,H}])) ==
freze([{'A', 'C', 'B', 'D', 'G', 'F', 'I', 'H', 'K'}]))
assert (freze(consolidate([{H,I,K}, {A,B}, {C,D}, {D,B}, {F,G,H}, {A,H}])) ==
freze([{'A', 'C', 'B', 'D', 'G', 'F', 'I', 'H', 'K'}]))
# Confirm order-independence
from copy import deepcopy
import itertools
sets = [{H,I,K}, {A,B}, {C,D}, {D,B}, {F,G,H}, {A,H}]
answer = consolidate(deepcopy(sets))
for perm in itertools.permutations(sets):
assert consolidate(deepcopy(perm)) == answer
 
assert (answer == [{'A', 'C', 'B', 'D', 'G', 'F', 'I', 'H', 'K'}])
assert (len(list(itertools.permutations(sets))) == 720)
 
print('_test(%s) complete' % consolidate.__name__)
 
if __name__ == '__main__':
_test(consolidate)
_test(conso)
Output:
_test(consolidate) complete
_test(conso) complete

Racket[edit]

 
#lang racket
(define (consolidate ss)
(define (comb s cs)
(cond [(set-empty? s) cs]
[(empty? cs) (list s)]
[(set-empty? (set-intersect s (first cs)))
(cons (first cs) (comb s (rest cs)))]
[(consolidate (cons (set-union s (first cs)) (rest cs)))]))
(foldl comb '() ss))
 
(consolidate (list (set 'a 'b) (set 'c 'd)))
(consolidate (list (set 'a 'b) (set 'b 'c)))
(consolidate (list (set 'a 'b) (set 'c 'd) (set 'd 'b)))
(consolidate (list (set 'h 'i 'k) (set 'a 'b) (set 'c 'd) (set 'd 'b) (set 'f 'g 'h)))
 
Output:
 
(list (set 'b 'a) (set 'd 'c))
(list (set 'a 'b 'c))
(list (set 'a 'b 'd 'c))
(list (set 'g 'h 'k 'i 'f) (set 'a 'b 'd 'c))
 


REXX[edit]

/*REXX program  demonstrates  a method  of  consolidating  some sample  sets.           */
@.=; @.1 = '{A,B} {C,D}'
@.2 = "{A,B} {B,D}"
@.3 = '{A,B} {C,D} {D,B}'
@.4 = '{H,I,K} {A,B} {C,D} {D,B} {F,G,H}'
@.5 = '{snow,ice,slush,frost,fog} {icebergs,icecubes} {rain,fog,sleet}'
 
do j=1 while @.j\=='' /*traipse through each of sample sets. */
call SETconsolidate @.j /*have the function do the heavy work. */
end /*j*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
isIn: return wordpos(arg(1), arg(2))\==0 /*is (word) argument 1 in the set arg2?*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
SETconsolidate: procedure; parse arg old; #=words(old); new=
say ' the old set=' space(old)
 
do k=1 for # /* [↓] change all commas to a blank. */
 !.k=translate(word(old,k), , '},{') /*create a list of words (aka, a set).*/
end /*k*/ /* [↑] ··· and also remove the braces.*/
 
do until \changed; changed=0 /*consolidate some sets (well, maybe).*/
do set=1 for #-1
do item=1 for words(!.set); x=word(!.set, item)
do other=set+1 to #
if isIn(x, !.other) then do; changed=1 /*it's changed*/
 !.set=!.set !.other;  !.other=
iterate set
end
end /*other*/
end /*item */
end /*set */
end /*until ¬changed*/
 
do set=1 for #; $= /*elide dups*/
do items=1 for words(!.set); x=word(!.set, items)
if x==',' then iterate; if x=='' then leave
$=$ x /*build new. */
do until \isIn(x, !.set)
_=wordpos(x, !.set)
 !.set=subword(!.set, 1, _-1) ',' subword(!.set, _+1) /*purify set*/
end /*until ¬isIn ··· */
end /*items*/
 !.set=translate(strip($), ',', " ")
end /*set*/
 
do i=1 for #; if !.i=='' then iterate /*ignore any set that is a null set. */
new=space(new '{'!.i"}") /*prepend and append a set identifier. */
end /*i*/
 
say ' the new set=' new; say
return

output   when using the (internal) default supplied sample sets:

 the old set= {A,B} {C,D}
 the new set= {A,B} {C,D}

 the old set= {A,B} {B,D}
 the new set= {A,B,D}

 the old set= {A,B} {C,D} {D,B}
 the new set= {A,B,D,C}

 the old set= {H,I,K} {A,B} {C,D} {D,B} {F,G,H}
 the new set= {H,I,K,F,G} {A,B,D,C}

 the old set= {snow,ice,slush,frost,fog} {icebergs,icecubes} {rain,fog,sleet}
 the new set= {snow,ice,slush,frost,fog,rain,sleet} {icebergs,icecubes}

Ruby[edit]

require 'set'
 
tests = [[[:A,:B], [:C,:D]],
[[:A,:B], [:B,:D]],
[[:A,:B], [:C,:D], [:D,:B]],
[[:H,:I,:K], [:A,:B], [:C,:D], [:D,:B], [:F,:G,:H]]]
tests.map!{|sets| sets.map(&:to_set)}
 
tests.each do |sets|
until sets.combination(2).none?{|a,b| a.merge(b) && sets.delete(b) if a.intersect?(b)}
end
p sets
end
Output:
[#<Set: {:A, :B}>, #<Set: {:C, :D}>]
[#<Set: {:A, :B, :D}>]
[#<Set: {:A, :B, :D, :C}>]
[#<Set: {:H, :I, :K, :F, :G}>, #<Set: {:A, :B, :D, :C}>]

Note: After execution, the contents of tests are exchanged.

Scala[edit]

object SetConsolidation extends App {
def consolidate[Type](sets: Set[Set[Type]]): Set[Set[Type]] = {
var result = sets // each iteration combines two sets and reiterates, else returns
for (i <- sets; j <- sets - i; k = i.intersect(j);
if result == sets && k.nonEmpty) result = result - i - j + i.union(j)
if (result == sets) sets else consolidate(result)
}
 
// Tests:
def parse(s: String) =
s.split(",").map(_.split("").toSet).toSet
def pretty[Type](sets: Set[Set[Type]]) =
sets.map(_.mkString("{",",","}")).mkString(" ")
val tests = List(
parse("AB,CD") -> Set(Set("A", "B"), Set("C", "D")),
parse("AB,BD") -> Set(Set("A", "B", "D")),
parse("AB,CD,DB") -> Set(Set("A", "B", "C", "D")),
parse("HIK,AB,CD,DB,FGH") -> Set(Set("A", "B", "C", "D"), Set("F", "G", "H", "I", "K"))
)
require(Set("A", "B", "C", "D") == Set("B", "C", "A", "D"))
assert(tests.forall{case (test, expect) =>
val result = consolidate(test)
println(s"${pretty(test)} -> ${pretty(result)}")
expect == result
})
 
}
Output:
{A,B} {C,D} -> {A,B} {C,D}
{A,B} {B,D} -> {A,B,D}
{A,B} {C,D} {D,B} -> {C,D,A,B}
{D,B} {F,G,H} {A,B} {C,D} {H,I,K} -> {F,I,G,H,K} {A,B,C,D}

Sidef[edit]

Translation of: Perl 6
func consolidate() { [] }
func consolidate(this, *those) {
gather {
consolidate(those...).each { |that|
if (this & that) { this |= that }
else { take that }
}
take this;
}
}
 
enum |A="A", B, C, D, _E, F, G, H, I, _J, K|;
 
func format(ss) {
ss.map{ '(' + .join(' ') + ')' }.join(' ')
}
 
[
[[A,B], [C,D]],
[[A,B], [B,D]],
[[A,B], [C,D], [D,B]],
[[H,I,K], [A,B], [C,D], [D,B], [F,G,H]]
].each { |ss|
say (format(ss), "\n\t==> ", format(consolidate(ss...)));
}
Output:
(A B) (C D)
	==> (C D) (A B)
(A B) (B D)
	==> (A D B)
(A B) (C D) (D B)
	==> (A C D B)
(H I K) (A B) (C D) (D B) (F G H)
	==> (A C D B) (I K F G H)

Tcl[edit]

Translation of: Python
Library: Tcllib (Package: struct::set)

This uses just the recursive version, as this is sufficient to handle substantial merges.

package require struct::set
 
proc consolidate {sets} {
if {[llength $sets] < 2} {
return $sets
}
 
set r [list {}]
set r0 [lindex $sets 0]
foreach x [consolidate [lrange $sets 1 end]] {
if {[struct::set size [struct::set intersect $x $r0]]} {
struct::set add r0 $x
} else {
lappend r $x
}
}
return [lset r 0 $r0]
}

Demonstrating:

puts 1:[consolidate {{A B} {C D}}]
puts 2:[consolidate {{A B} {B D}}]
puts 3:[consolidate {{A B} {C D} {D B}}]
puts 4:[consolidate {{H I K} {A B} {C D} {D B} {F G H}}]
Output:
1:{A B} {C D}
2:{D A B}
3:{D A B C}
4:{H I F G K} {D A B C}

TXR[edit]

Original solution:

(defun mkset (p x) (set [p x] (or [p x] x)))
 
(defun fnd (p x) (if (eq [p x] x) x (fnd p [p x])))
 
(defun uni (p x y)
(let ((xr (fnd p x)) (yr (fnd p y)))
(set [p xr] yr)))
 
(defun consoli (sets)
(let ((p (hash)))
(each ((s sets))
(each ((e s))
(mkset p e)
(uni p e (car s))))
(hash-values
[group-by (op fnd p) (hash-keys
[group-by identity (flatten sets)])])))
 
;; tests
 
(each ((test '(((a b) (c d))
((a b) (b d))
((a b) (c d) (d b))
((h i k) (a b) (c d) (d b) (f g h)))))
(format t "~s -> ~s\n" test (consoli test)))
Output:
((a b) (c d)) -> ((b a) (d c))
((a b) (b d)) -> ((b a d))
((a b) (c d) (d b)) -> ((b a d c))
((h i k) (a b) (c d) (d b) (f g h)) -> ((g f k i h) (b a d c)
Translation of: Racket
(defun mkset (items) [group-by identity items])
 
(defun empty-p (set) (zerop (hash-count set)))
 
(defun consoli (ss)
(defun combi (cs s)
(cond ((empty-p s) cs)
((null cs) (list s))
((empty-p (hash-isec s (first cs)))
(cons (first cs) (combi (rest cs) s)))
(t (consoli (cons (hash-uni s (first cs)) (rest cs))))))
[reduce-left combi ss nil])
 
;; tests
(each ((test '(((a b) (c d))
((a b) (b d))
((a b) (c d) (d b))
((h i k) (a b) (c d) (d b) (f g h)))))
(format t "~s -> ~s\n" test
[mapcar hash-keys (consoli [mapcar mkset test])]))
Output:
((a b) (c d)) -> ((b a) (d c))
((a b) (b d)) -> ((d b a))
((a b) (c d) (d b)) -> ((d c b a))
((h i k) (a b) (c d) (d b) (f g h)) -> ((g f k i h) (d c b a))

VBScript[edit]

 
Function consolidate(s)
sets = Split(s,",")
n = UBound(sets)
For i = 1 To n
p = i
ts = ""
For j = i To 1 Step -1
If ts = "" Then
p = j
End If
ts = ""
For k = 1 To Len(sets(p))
If InStr(1,sets(j-1),Mid(sets(p),k,1)) = 0 Then
ts = ts & Mid(sets(p),k,1)
End If
Next
If Len(ts) < Len(sets(p)) Then
sets(j-1) = sets(j-1) & ts
sets(p) = "-"
ts = ""
Else
p = i
End If
Next
Next
consolidate = s & " = " & Join(sets," , ")
End Function
 
'testing
test = Array("AB","AB,CD","AB,CD,DB","HIK,AB,CD,DB,FGH")
For Each t In test
WScript.StdOut.WriteLine consolidate(t)
Next
 
Output:
AB = AB
AB,CD = AB , CD
AB,CD,DB = ABCD , - , -
HIK,AB,CD,DB,FGH = HIKFG , ABCD , - , - , -

zkl[edit]

Translation of: Tcl
fcn consolidate(sets){  // set are munged if they are read/write
if(sets.len()<2) return(sets);
r,r0 := List(List()),sets[0];
foreach x in (consolidate(sets[1,*])){
i,ni:=x.filter22(r0.holds); //-->(intersection, !intersection)
if(i) r0=r0.extend(ni);
else r.append(x);
}
r[0]=r0;
r
}
fcn prettize(sets){
sets.apply("concat"," ").pump(String,"(%s),".fmt)[0,-1]
}
 
foreach sets in (T(
T(L("A","B")),
T(L("A","B"),L("C","D")),
T(L("A","B"),L("B","D")),
T(L("A","B"),L("C","D"),L("D","B")),
T(L("H","I","K"),L("A","B"),L("C","D"),L("D","B"),L("F","G","H")),
T(L("A","H"),L("H","I","K"),L("A","B"),L("C","D"),L("D","B"),L("F","G","H")),
T(L("H","I","K"),L("A","B"),L("C","D"),L("D","B"),L("F","G","H"), L("A","H")),
)){
prettize(sets).print(" --> ");
consolidate(sets) : prettize(_).println();
}
Output:
(A B) --> (A B)
(A B),(C D) --> (A B),(C D)
(A B),(B D) --> (A B D)
(A B),(C D),(D B) --> (A B C D)
(H I K),(A B),(C D),(D B),(F G H) --> (H I K F G),(A B C D)
(A H),(H I K),(A B),(C D),(D B),(F G H) --> (A H I K F G B C D)
(H I K),(A B),(C D),(D B),(F G H),(A H) --> (H I K A B C D F G)