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
We start with specifying a generic package Set_Cons that provides the neccessary tools, such as contructing and manipulating sets, truning them, etc.:
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
display(list l)
{
for (integer i, record r in l) {
text u, v;
o_text(i ? ", {" : "{");
for (u in r) {
o_(v, u);
v = ", ";
}
o_text("}");
}
o_text("\n");
}
intersect(record r, record u)
{
trap_q(r_vcall, r, r_put, 1, record().copy(u), 0);
}
consolidate(list l)
{
for (integer i, record r in l) {
integer j;
j = i - ~l;
while (j += 1) {
if (intersect(r, l[j])) {
r.wcall(r_add, 1, 2, l[j]);
l.delete(i);
i -= 1;
break;
}
}
}
l;
}
R(...)
{
ucall.2(r_put, 1, record(), 0);
}
main(void)
{
display(consolidate(list(R("A", "B"), R("C", "D"))));
display(consolidate(list(R("A", "B"), R("B", "D"))));
display(consolidate(list(R("A", "B"), R("C", "D"), R("D", "B"))));
display(consolidate(list(R("H", "I", "K"), R("A", "B"), R("C", "D"),
R("D", "B"), R("F", "G", "K"))));
0;
}- Output:
{A, B}, {C, D}
{A, B, D}
{A, B, C, D}
{A, B, C, D}, {F, G, H, I, K}
APL
consolidate ← (⊢((⊂∘∪∘∊(/⍨)),(/⍨)∘~)(((⊃∘⍒+/)⊃↓)∘.(∨/∊)⍨))⍣≡
- Output:
consolidate 'AB' 'CD'
AB CD
consolidate 'AB' 'BD'
ABD
consolidate 'AB' 'CD' 'DB'
ABCD
consolidate 'HIK' 'AB' 'CD' 'DB' 'FGH'
HIKFG ABCD
AutoHotkey
SetConsolidation(sets){
arr2 := [] , arr3 := [] , arr4 := [] , arr5 := [], result:=[]
; sort each set individually
for i, obj in sets
{
arr1 := []
for j, v in obj
arr1[v] := true
arr2.push(arr1)
}
; sort by set's first item
for i, obj in arr2
for k, v in obj
{
arr3[k . i] := obj
break
}
; use numerical index
for k, obj in arr3
arr4[A_Index] := obj
j := 1
for i, obj in arr4
{
common := false
for k, v in obj
if arr5[j-1].HasKey(k)
{
common := true
break
}
if common
for k, v in obj
arr5[j-1, k] := true
else
arr5[j] := obj, j++
}
; clean up
for i, obj in arr5
for k , v in obj
result[i, A_Index] := k
return result
}
Examples:
test1 := [["A","B"], ["C","D"]]
test2 := [["A","B"], ["B","D"]]
test3 := [["A","B"], ["C","D"], ["D","B"]]
test4 := [["H","I","K"], ["A","B"], ["C","D"], ["D","B"], ["F","G","H"]]
result := "["
loop, 4
{
for i, obj in SetConsolidation(test%A_Index%)
{
output := "["
for j, v in obj
output .= """" v ""","
result .= RTrim(output, ", ") . "] , "
}
result := RTrim(result, ", ") "]`n["
}
MsgBox % RTrim(result, "`n[")
return
- Output:
[["A","B"] , ["C","D"]] [["A","B","D"]] [["A","B","C","D"]] [["A","B","C","D"] , ["F","G","H","I","K"]]
BASIC
BASIC256
dim test$(4)
test$[0] = "AB"
test$[1] = "AB,CD"
test$[2] = "AB,CD,DB"
test$[3] = "HIK,AB,CD,DB,FGH"
for t = 0 to 3 #test$[?]
print Consolidate(test$[t])
next t
end
function Consolidate(s$)
dim sets$(100)
# Split the string into substrings
pio = 1
n = 0
for i = 1 to length(s$)
if mid(s$, i, 1) = "," then
fin = i - 1
sets$[n] = mid(s$, pio, fin - pio + 1)
pio = i + 1
n += 1
end if
next i
sets$[n] = mid(s$, pio, length(s$) - pio + 1)
# Main logic
for i = 0 to n
p = i
ts$ = ""
for j = i to 0 step -1
if ts$ = "" then p = j
ts$ = ""
for k = 1 to length(sets$[p])
if j > 0 then
if instr(sets$[j-1], mid(sets$[p], k, 1)) = 0 then
ts$ += mid(sets$[p], k, 1)
end if
end if
next k
if length(ts$) < length(sets$[p]) then
if j > 0 then
sets$[j-1] = sets$[j-1] + ts$
sets$[p] = "-"
ts$ = ""
end if
else
p = i
end if
next j
next i
# Join the substrings into a string
temp$ = sets$[0]
for i = 1 to n
temp$ += "," + sets$[i]
next i
return s$ + " = " + temp$
end function
- Output:
Same as FreeBASIC entry.
Chipmunk Basic
Same code as GW-BASIC
FreeBASIC
Function Consolidate(s As String) As String
Dim As Integer i, j, k, p, n, pio, fin
Dim As String ts, sets(0 To 100), temp
' Split the string into substrings
pio = 1
n = 0
For i = 1 To Len(s)
If Mid(s, i, 1) = "," Then
fin = i - 1
sets(n) = Mid(s, pio, fin - pio + 1)
pio = i + 1
n += 1
End If
Next i
sets(n) = Mid(s, pio, Len(s) - pio + 1)
' Main logic
For i = 0 To n
p = i
ts = ""
For j = i To 0 Step -1
If ts = "" Then p = j
ts = ""
For k = 1 To Len(sets(p))
If j > 0 Then
If Instr(sets(j-1), Mid(sets(p), k, 1)) = 0 Then ts += Mid(sets(p), k, 1)
End If
Next k
If Len(ts) < Len(sets(p)) Then
If j > 0 Then
sets(j-1) += ts
sets(p) = "-"
ts = ""
End If
Else
p = i
End If
Next j
Next i
' Join the substrings into a string
temp = sets(0)
For i = 1 To n
temp += "," + sets(i)
Next i
Return s + " = " + temp
End Function
Dim As String test(3) = {"AB", "AB,CD", "AB,CD,DB", "HIK,AB,CD,DB,FGH"}
For t As Integer = Lbound(test) To Ubound(test)
Print Consolidate(test(t))
Next t
Sleep
- Output:
Same as Ring entry.
Gambas
Public test As String[] = ["AB", "AB,CD", "AB,CD,DB", "HIK,AB,CD,DB,FGH"]
Public Sub Main()
For t As Integer = 0 To test.Max
Print Consolidate(test[t])
Next
End
Public Function Consolidate(s As String) As String
Dim sets As New String[100]
Dim n As Integer, i As Integer, j As Integer, k As Integer, p As Integer
Dim ts As String, tmp As String
n = 0
For i = 1 To Len(s)
If Mid(s, i, 1) = "," Then
n += 1
Else
sets[n] = sets[n] & Mid(s, i, 1)
Endif
Next
For i = 0 To n
p = i
ts = ""
For j = i To 0 Step -1
If ts = "" Then p = j
ts = ""
For k = 1 To Len(sets[p])
If j > 0 Then
If InStr(sets[j - 1], Mid(sets[p], k, 1)) = 0 Then
ts &= Mid(sets[p], k, 1)
Endif
Endif
Next
If Len(ts) < Len(sets[p]) Then
If j > 0 Then
sets[j - 1] &= ts
sets[p] = "-"
ts = ""
Endif
Else
p = i
Endif
Next
Next
tmp = sets[0]
For i = 1 To n
tmp &= "," & sets[i]
Next
Return s & " = " & tmp
End
- Output:
Same as Ring entry.
GW-BASIC
100 CLS
110 S$ = "AB" : GOSUB 160
120 S$ = "AB,CD" : GOSUB 160
130 S$ = "AB,CD,DB" : GOSUB 160
140 S$ = "HIK,AB,CD,DB,FGH" : GOSUB 160
150 END
160 DIM R$(20)
170 N = 0
180 FOR I = 1 TO LEN(S$)
190 IF MID$(S$,I,1) = "," THEN N = N+1 : GOTO 210
200 R$(N) = R$(N)+MID$(S$,I,1)
210 NEXT I
220 FOR I = 0 TO N
230 P = I
240 TS$ = ""
250 FOR J = I TO 0 STEP -1
260 IF TS$ = "" THEN P = J
270 TS$ = ""
280 FOR K = 1 TO LEN(R$(P))
290 IF J > 0 THEN IF INSTR(R$(J-1),MID$(R$(P),K,1)) = 0 THEN TS$ = TS$+MID$(R$(P),K,1)
300 NEXT K
310 IF LEN(TS$) < LEN(R$(P)) THEN IF J > 0 THEN R$(J-1) = R$(J-1)+TS$ : R$(P) = "-" : TS$ = ""
320 NEXT J
330 NEXT I
340 T$ = R$(0)
350 FOR I = 1 TO N
360 T$ = T$+","+R$(I)
370 NEXT I
380 PRINT S$;" = ";T$
390 ERASE R$
400 RETURN
- Output:
AB = AB AB,CD = AB,CD AB,CD,DB = ABCD,-,- HIK,AB,CD,DB,FGH = HIKFG,ABCD,-,-,-
MSX Basic
Same code as GW-BASIC
PureBasic
Procedure.s Consolidate(s.s)
Dim sets.s(100)
Define.i n, i, j, k, p
Define.s ts.s, temp.s
n = 0
For i = 1 To Len(s)
If Mid(s, i, 1) = ",":
n + 1
Else
sets(n) = sets(n) + Mid(s, i, 1)
EndIf
Next i
For i = 0 To n
p = i
ts = ""
For j = i To 0 Step -1
If ts = "":
p = j
EndIf
ts = ""
For k = 1 To Len(sets(p))
If j > 0:
If FindString(sets(j-1), Mid(sets(p), k, 1)) = 0:
ts = ts + Mid(sets(p), k, 1)
EndIf
EndIf
Next k
If Len(ts) < Len(sets(p)):
If j > 0:
sets(j-1) = sets(j-1) + ts
sets(p) = "-"
ts = ""
EndIf
Else
p = i
EndIf
Next j
Next i
temp = sets(0)
For i = 1 To n
temp = temp + "," + sets(i)
Next i
ProcedureReturn s + " = " + temp
EndProcedure
OpenConsole()
Dim test.s(3) ;= {"AB","AB,CD","AB,CD,DB","HIK,AB,CD,DB,FGH"}
test(0) = "AB"
test(1) = "AB,CD"
test(2) = "AB,CD,DB"
test(3) = "HIK,AB,CD,DB,FGH"
For t.i = 0 To 3
PrintN(Consolidate(test(t)))
Next t
PrintN(#CRLF$ + "Press ENTER to exit"): Input()
CloseConsole()
- Output:
Same as Ring entry.
QBasic
SUB consolidate (s$)
DIM sets$(100)
n = 0
FOR i = 1 TO LEN(s$)
IF MID$(s$, i, 1) = "," THEN
n = n + 1
ELSE
sets$(n) = sets$(n) + MID$(s$, i, 1)
END IF
NEXT i
FOR i = 0 TO n
p = i
ts$ = ""
FOR j = i TO 0 STEP -1
IF ts$ = "" THEN
p = j
END IF
ts$ = ""
FOR k = 1 TO LEN(sets$(p))
IF j > 0 THEN
IF INSTR(sets$(j - 1), MID$(sets$(p), k, 1)) = 0 THEN
ts$ = ts$ + MID$(sets$(p), k, 1)
END IF
END IF
NEXT k
IF LEN(ts$) < LEN(sets$(p)) THEN
IF j > 0 THEN
sets$(j - 1) = sets$(j - 1) + ts$
sets$(p) = "-"
ts$ = ""
END IF
ELSE
p = i
END IF
NEXT j
NEXT i
temp$ = sets$(0)
FOR i = 1 TO n
temp$ = temp$ + "," + sets$(i)
NEXT i
PRINT s$; " = "; temp$
END SUB
DIM test$(3)
test$(0) = "AB"
test$(1) = "AB,CD"
test$(2) = "AB,CD,DB"
test$(3) = "HIK,AB,CD,DB,FGH"
FOR t = 0 TO 3
CALL consolidate(test$(t))
NEXT t
- Output:
Same as Ring entry.
Run BASIC
function consolidate$(s$)
dim sets$(100)
n = 0
for i = 1 to len(s$)
if mid$(s$, i, 1) = "," then
n = n + 1
else
sets$(n) = sets$(n) + mid$(s$, i, 1)
end if
next i
for i = 0 to n
p = i
ts$ = ""
for j = i to 0 step -1
if ts$ = "" then p = j
ts$ = ""
for k = 1 to len(sets$(p))
if j > 0 then
if instr(sets$(j-1), mid$(sets$(p), k, 1)) = 0 then
ts$ = ts$ + mid$(sets$(p), k, 1)
end if
end if
next k
if len(ts$) < len(sets$(p)) then
if j > 0 then
sets$(j-1) = sets$(j-1) + ts$
sets$(p) = "-"
ts$ = ""
end if
else
p = i
end if
next j
next i
temp$ = sets$(0)
for i = 1 to n
temp$ = temp$ + "," + sets$(i)
next i
consolidate$ = s$ + " = " + temp$
end function
dim test$(3)
test$(0) = "AB"
test$(1) = "AB,CD"
test$(2) = "AB,CD,DB"
test$(3) = "HIK,AB,CD,DB,FGH"
for t = 0 to 3
print consolidate$(test$(t))
next t
XBasic
PROGRAM "Set consolidation"
VERSION "0.0001"
DECLARE FUNCTION Entry ()
DECLARE FUNCTION Consolidate$ (s$)
FUNCTION Entry ()
DIM test$[4]
test$[0] = "AB"
test$[1] = "AB,CD"
test$[2] = "AB,CD,DB"
test$[3] = "HIK,AB,CD,DB,FGH"
FOR t = 0 TO 3
PRINT Consolidate$(test$[t])
NEXT t
END FUNCTION
FUNCTION Consolidate$ (s$)
DIM sets$[100]
' Split the STRING into substrings
pio = 1
n = 0
FOR i = 1 TO LEN(s$)
IF MID$(s$, i, 1) = "," THEN
fin = i - 1
sets$[n] = MID$(s$, pio, fin - pio + 1)
pio = i + 1
INC n
END IF
NEXT i
sets$[n] = MID$(s$, pio, LEN(s$) - pio + 1)
' Main logic
FOR i = 0 TO n
p = i
ts$ = ""
FOR j = i TO 0 STEP -1
IF ts$ = "" THEN p = j
ts$ = ""
FOR k = 1 TO LEN(sets$[p])
IF j > 0 THEN
IF INSTR(sets$[j-1], MID$(sets$[p], k, 1)) = 0 THEN
ts$ = ts$ + MID$(sets$[p], k, 1)
END IF
END IF
NEXT k
IF LEN(ts$) < LEN(sets$[p]) THEN
IF j > 0 THEN
sets$[j-1] = sets$[j-1] + ts$
sets$[p] = "-"
ts$ = ""
END IF
ELSE
p = i
END IF
NEXT j
NEXT i
' Join the substrings into a STRING
temp$ = sets$[0]
FOR i = 1 TO n
temp$ = temp$ + "," + sets$[i]
NEXT i
RETURN s$ + " = " + temp$
END FUNCTION
END PROGRAM
- Output:
Same as BASIC256 entry.
Yabasic
dim test$(3)
test$(0) = "AB"
test$(1) = "AB,CD"
test$(2) = "AB,CD,DB"
test$(3) = "HIK,AB,CD,DB,FGH"
for t = 0 to arraysize(test$(), 1)
print Consolidate$(test$(t))
next t
end
sub Consolidate$(s$)
dim sets$(100)
// Split the string into substrings
pio = 1
n = 0
for i = 1 to len(s$)
if mid$(s$, i, 1) = "," then
fin = i - 1
sets$(n) = mid$(s$, pio, fin - pio + 1)
pio = i + 1
n = n + 1
fi
next i
sets$(n) = mid$(s$, pio, len(s$) - pio + 1)
// Main logic
for i = 0 to n
p = i
ts$ = ""
for j = i to 0 step -1
if ts$ = "" p = j
ts$ = ""
for k = 1 to len(sets$(p))
if j > 0 then
if instr(sets$(j-1), mid$(sets$(p), k, 1)) = 0 then
ts$ = ts$ + mid$(sets$(p), k, 1)
fi
fi
next k
if len(ts$) < len(sets$(p)) then
if j > 0 then
sets$(j-1) = sets$(j-1) + ts$
sets$(p) = "-"
ts$ = ""
fi
else
p = i
fi
next j
next i
// Join the substrings into a string
temp$ = sets$(0)
for i = 1 to n
temp$ = temp$ + "," + sets$(i)
next i
return s$ + " = " + temp$
end sub
- Output:
Same as FreeBASIC entry.
Bracmat
( ( 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
#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#
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)
{
var elements = new Dictionary<T, Node<T>>(comparer );
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<T> 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}
C++
#include <algorithm>
#include <iostream>
#include <unordered_map>
#include <unordered_set>
#include <vector>
using namespace std;
// Consolidation using a brute force approach
void SimpleConsolidate(vector<unordered_set<char>>& sets)
{
// Loop through the sets in reverse and consolidate them
for(auto last = sets.rbegin(); last != sets.rend(); ++last)
for(auto other = last + 1; other != sets.rend(); ++other)
{
bool hasIntersection = any_of(last->begin(), last->end(),
[&](auto val)
{ return other->contains(val); });
if(hasIntersection)
{
other->merge(*last);
sets.pop_back();
break;
}
}
}
// As a second approach, use the connected-component-finding-algorithm
// from the C# entry to consolidate
struct Node
{
char Value;
Node* Parent = nullptr;
};
Node* FindTop(Node& node)
{
auto top = &node;
while (top != top->Parent) top = top->Parent;
for(auto element = &node; element->Parent != top; )
{
// Point the elements to top to make it faster for the next time
auto parent = element->Parent;
element->Parent = top;
element = parent;
}
return top;
}
vector<unordered_set<char>> FastConsolidate(const vector<unordered_set<char>>& sets)
{
unordered_map<char, Node> elements;
for(auto& set : sets)
{
Node* top = nullptr;
for(auto val : set)
{
auto itr = elements.find(val);
if(itr == elements.end())
{
// A new value has been found
auto& ref = elements[val] = Node{val, nullptr};
if(!top) top = &ref;
ref.Parent = top;
}
else
{
auto newTop = FindTop(itr->second);
if(top)
{
top->Parent = newTop;
itr->second.Parent = newTop;
}
else
{
top = newTop;
}
}
}
}
unordered_map<char, unordered_set<char>> groupedByTop;
for(auto& e : elements)
{
auto& element = e.second;
groupedByTop[FindTop(element)->Value].insert(element.Value);
}
vector<unordered_set<char>> ret;
for(auto& itr : groupedByTop)
{
ret.push_back(move(itr.second));
}
return ret;
}
void PrintSets(const vector<unordered_set<char>>& sets)
{
for(const auto& set : sets)
{
cout << "{ ";
for(auto value : set){cout << value << " ";}
cout << "} ";
}
cout << "\n";
}
int main()
{
const unordered_set<char> AB{'A', 'B'}, CD{'C', 'D'}, DB{'D', 'B'},
HIJ{'H', 'I', 'K'}, FGH{'F', 'G', 'H'};
vector <unordered_set<char>> AB_CD {AB, CD};
vector <unordered_set<char>> AB_DB {AB, DB};
vector <unordered_set<char>> AB_CD_DB {AB, CD, DB};
vector <unordered_set<char>> HIJ_AB_CD_DB_FGH {HIJ, AB, CD, DB, FGH};
PrintSets(FastConsolidate(AB_CD));
PrintSets(FastConsolidate(AB_DB));
PrintSets(FastConsolidate(AB_CD_DB));
PrintSets(FastConsolidate(HIJ_AB_CD_DB_FGH));
SimpleConsolidate(AB_CD);
SimpleConsolidate(AB_DB);
SimpleConsolidate(AB_CD_DB);
SimpleConsolidate(HIJ_AB_CD_DB_FGH);
PrintSets(AB_CD);
PrintSets(AB_DB);
PrintSets(AB_CD_DB);
PrintSets(HIJ_AB_CD_DB_FGH);
}
- Output:
{ B A } { D C }
{ B A D }
{ B A D C }
{ B A D C } { I K H G F }
{ B A } { D C }
{ D A B }
{ D C A B }
{ F G H K I } { D C A B }
Clojure
(defn consolidate-linked-sets [sets]
(apply clojure.set/union sets))
(defn linked? [s1 s2]
(not (empty? (clojure.set/intersection s1 s2))))
(defn consolidate [& sets]
(loop [seeds sets
sets sets]
(if (empty? seeds)
sets
(let [s0 (first seeds)
linked (filter #(linked? s0 %) sets)
remove-used (fn [sets used]
(remove #(contains? (set used) %) sets))]
(recur (remove-used (rest seeds) linked)
(conj (remove-used sets linked)
(consolidate-linked-sets linked)))))))
- Output:
(consolidate #{:a :b} #{:c :d}) ; ==> (#{:c :d} #{:b :a})
(consolidate #{:a :b} #{:c :b}) ; ==> (#{:c :b :a})
(consolidate #{:a :b} #{:c :d} #{:d :b}) ; ==> (#{:c :b :d :a})
(consolidate #{:h :i :k} #{:a :b} #{:c :d} #{:d :b} #{:f :g :h})
; ==> (#{:c :b :d :a} #{:k :g :h :f :i})
Common Lisp
(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
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"]
Draco
type Set = word;
proc make_set(*char setdsc) Set:
Set set;
byte pos;
set := 0;
while setdsc* /= '\e' do
pos := setdsc* - 'A';
if pos < 16 then set := set | (1 << pos) fi;
setdsc := setdsc + 1
od;
set
corp
proc write_set(Set set) void:
char item;
write('(');
for item from 'A' upto ('A'+15) do
if set & 1 /= 0 then write(item) fi;
set := set >> 1
od;
write(')')
corp
proc consolidate([*]Set sets) word:
word i, j, n;
bool change;
n := dim(sets, 1);
change := true;
while change do
change := false;
for i from 0 upto n-1 do
for j from i+1 upto n-1 do
if sets[i] & sets[j] /= 0 then
sets[i] := sets[i] | sets[j];
sets[j] := 0;
change := true
fi
od
od
od;
for i from 1 upto n-1 do
if sets[i] = 0 then
for j from i+1 upto n-1 do
sets[j-1] := sets[j]
od
fi
od;
i := 0;
while i<n and sets[i] /= 0 do i := i+1 od;
i
corp
proc test([*]Set sets) void:
word i, n;
n := dim(sets, 1);
for i from 0 upto n-1 do write_set(sets[i]) od;
write(" -> ");
n := consolidate(sets);
for i from 0 upto n-1 do write_set(sets[i]) od;
writeln()
corp
proc main() void:
[2]Set ex1;
[2]Set ex2;
[3]Set ex3;
[5]Set ex4;
ex1[0]:=make_set("AB"); ex1[1]:=make_set("CD");
ex2[0]:=make_set("AB"); ex2[1]:=make_set("BC");
ex3[0]:=make_set("AB"); ex3[1]:=make_set("CD"); ex3[2]:=make_set("DB");
ex4[0]:=make_set("HIK"); ex4[1]:=make_set("AB"); ex4[2]:=make_set("CD");
ex4[3]:=make_set("DB"); ex4[4]:=make_set("FGH");
test(ex1);
test(ex2);
test(ex3);
test(ex4);
corp- Output:
(AB)(CD) -> (AB)(CD) (AB)(BC) -> (ABC) (AB)(CD)(BD) -> (ABCD) (HIK)(AB)(CD)(BD)(FGH) -> (FGHIK)(ABCD)
EchoLisp
;; 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
(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
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]) ysUsage:
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 yOutput:
[['K','I','F','G','H'],['A','C','D','B']] [['A','B','D']]
Elixir
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#
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"]]
Factor
USING: arrays kernel sequences sets ;
: comb ( x x -- x )
over empty? [ nip 1array ] [
dup pick first intersects?
[ [ unclip ] dip union comb ]
[ [ 1 cut ] dip comb append ] if
] if ;
: consolidate ( x -- x ) { } [ comb ] reduce ;
- Output:
IN: scratchpad USE: qw
IN: scratchpad qw{ AB CD } consolidate .
{ "AB" "CD" }
IN: scratchpad qw{ AB BC } consolidate .
{ "ABC" }
IN: scratchpad qw{ AB CD DB } consolidate .
{ "CDAB" }
IN: scratchpad qw{ HIK AB CD DB FGH } consolidate .
{ "CDAB" "HIKFG" }
Go
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
import Data.List (intersperse, intercalate)
import qualified Data.Set as S
consolidate
:: Ord a
=> [S.Set a] -> [S.Set a]
consolidate = foldr comb []
where
comb s_ [] = [s_]
comb s_ (s:ss)
| S.null (s `S.intersection` s_) = s : comb s_ ss
| otherwise = comb (s `S.union` s_) ss
-- TESTS -------------------------------------------------
main :: IO ()
main =
(putStrLn . unlines)
((intercalate ", and " . fmap showSet . consolidate) . fmap S.fromList <$>
[ ["ab", "cd"]
, ["ab", "bd"]
, ["ab", "cd", "db"]
, ["hik", "ab", "cd", "db", "fgh"]
])
showSet :: S.Set Char -> String
showSet = flip intercalate ["{", "}"] . intersperse ',' . S.elems
- Output:
{c,d}, and {a,b}
{a,b,d}
{a,b,c,d}
{a,b,c,d}, and {f,g,h,i,k}
J
consolidate=:4 :0/
b=. y 1&e.@e.&> x
(1,-.b)#(~.;x,b#y);y
)
In other words, fold each set into a growing list of consolidated sets. When there's any overlap between the newly considered set (x) and any of the list of previously considered sets (y), merge the unique values from all of those into a single set (any remaining sets remain as-is). Here, b selects the overlapping sets from y (and -.b selects the rest of those sets).
Examples:
consolidate 'ab';'cd'
┌──┬──┐
│ab│cd│
└──┴──┘
consolidate 'ab';'bd'
┌───┐
│abd│
└───┘
consolidate 'ab';'cd';'db'
┌────┐
│abcd│
└────┘
consolidate 'hij';'ab';'cd';'db';'fgh'
┌─────┬────┐
│hijfg│abcd│
└─────┴────┘
Java
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]
JavaScript
(() => {
'use strict';
// consolidated :: Ord a => [Set a] -> [Set a]
const consolidated = xs => {
const go = (s, xs) =>
0 !== xs.length ? (() => {
const h = xs[0];
return 0 === intersection(h, s).size ? (
[h].concat(go(s, tail(xs)))
) : go(union(h, s), tail(xs));
})() : [s];
return foldr(go, [], xs);
};
// TESTS ----------------------------------------------
const main = () =>
map(xs => intercalate(
', and ',
map(showSet, consolidated(xs))
),
map(x => map(
s => new Set(chars(s)),
x
),
[
['ab', 'cd'],
['ab', 'bd'],
['ab', 'cd', 'db'],
['hik', 'ab', 'cd', 'db', 'fgh']
]
)
).join('\n');
// GENERIC FUNCTIONS ----------------------------------
// chars :: String -> [Char]
const chars = s => s.split('');
// concat :: [[a]] -> [a]
// concat :: [String] -> String
const concat = xs =>
0 < xs.length ? (() => {
const unit = 'string' !== typeof xs[0] ? (
[]
) : '';
return unit.concat.apply(unit, xs);
})() : [];
// elems :: Dict -> [a]
// elems :: Set -> [a]
const elems = x =>
'Set' !== x.constructor.name ? (
Object.values(x)
) : Array.from(x.values());
// flip :: (a -> b -> c) -> b -> a -> c
const flip = f =>
1 < f.length ? (
(a, b) => f(b, a)
) : (x => y => f(y)(x));
// Note that that the Haskell signature of foldr differs from that of
// foldl - the positions of accumulator and current value are reversed
// foldr :: (a -> b -> b) -> b -> [a] -> b
const foldr = (f, a, xs) => xs.reduceRight(flip(f), a);
// intercalate :: [a] -> [[a]] -> [a]
// intercalate :: String -> [String] -> String
const intercalate = (sep, xs) =>
0 < xs.length && 'string' === typeof sep &&
'string' === typeof xs[0] ? (
xs.join(sep)
) : concat(intersperse(sep, xs));
// intersection :: Ord a => Set a -> Set a -> Set a
const intersection = (s, s1) =>
new Set([...s].filter(x => s1.has(x)));
// intersperse :: a -> [a] -> [a]
// intersperse :: Char -> String -> String
const intersperse = (sep, xs) => {
const bln = 'string' === typeof xs;
return xs.length > 1 ? (
(bln ? concat : x => x)(
(bln ? (
xs.split('')
) : xs)
.slice(1)
.reduce((a, x) => a.concat([sep, x]), [xs[0]])
)) : xs;
};
// map :: (a -> b) -> [a] -> [b]
const map = (f, xs) => xs.map(f);
// showSet :: Set -> String
const showSet = s =>
intercalate(elems(s), ['{', '}']);
// sort :: Ord a => [a] -> [a]
const sort = xs => xs.slice()
.sort((a, b) => a < b ? -1 : (a > b ? 1 : 0));
// tail :: [a] -> [a]
const tail = xs => 0 < xs.length ? xs.slice(1) : [];
// union :: Ord a => Set a -> Set a -> Set a
const union = (s, s1) =>
Array.from(s1.values())
.reduce(
(a, x) => (a.add(x), a),
new Set(s)
);
// MAIN ---
return main();
})();
- Output:
{c,d}, and {a,b}
{b,d,a}
{d,b,c,a}
{d,b,c,a}, and {f,g,h,i,k}
jq
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
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
// 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]]
Lua
-- SUPPORT:
function T(t) return setmetatable(t, {__index=table}) end
function S(t) local s=T{} for k,v in ipairs(t) do s[v]=v end return s end
table.each = function(t,f,...) for _,v in pairs(t) do f(v,...) end end
table.copy = function(t) local s=T{} for k,v in pairs(t) do s[k]=v end return s end
table.keys = function(t) local s=T{} for k,_ in pairs(t) do s[#s+1]=k end return s end
table.intersects = function(t1,t2) for k,_ in pairs(t1) do if t2[k] then return true end end return false end
table.union = function(t1,t2) local s=t1:copy() for k,_ in pairs(t2) do s[k]=k end return s end
table.dump = function(t) print('{ '..table.concat(t, ', ')..' }') end
-- TASK:
table.consolidate = function(t)
for a = #t, 1, -1 do
local seta = t[a]
for b = #t, a+1, -1 do
local setb = t[b]
if setb and seta:intersects(setb) then
t[a], t[b] = seta:union(setb), nil
end
end
end
return t
end
-- TESTING:
examples = {
T{ S{"A","B"}, S{"C","D"} },
T{ S{"A","B"}, S{"B","D"} },
T{ S{"A","B"}, S{"C","D"}, S{"D","B"} },
T{ S{"H","I","K"}, S{"A","B"}, S{"C","D"}, S{"D","B"}, S{"F","G","H"} },
}
for i,example in ipairs(examples) do
print("Given input sets:")
example:each(function(set) set:keys():dump() end)
print("Consolidated output sets:")
example:consolidate():each(function(set) set:keys():dump() end)
print("")
end
- Output:
Given input sets:
{ A, B }
{ C, D }
Consolidated output sets:
{ A, B }
{ C, D }
Given input sets:
{ A, B }
{ D, B }
Consolidated output sets:
{ A, D, B }
Given input sets:
{ A, B }
{ C, D }
{ B, D }
Consolidated output sets:
{ A, D, C, B }
Given input sets:
{ I, H, K }
{ A, B }
{ C, D }
{ B, D }
{ H, G, F }
Consolidated output sets:
{ I, H, K, G, F }
{ A, D, C, B }
Mathematica /Wolfram Language
reduce[x_] :=
Block[{pairs, unique},
pairs =
DeleteCases[
Subsets[Range@
Length@x, {2}], _?(Intersection @@ x[[#]] == {} &)];
unique = Complement[Range@Length@x, Flatten@pairs];
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}}
newLISP
Translated from the Common Lisp version.
(macro (reduce Func List (Init-Val nil))
(apply
Func
(append (if (= nil Init-Val) '() (list Init-Val)) List)
2))
(define (consol ss)
(let (comb
(lambda (cs s)
(cond ((empty? s) cs)
((empty? cs) (list s))
((empty? (intersect s (first cs)))
(cons (first cs) (comb (rest cs) s)))
(true (consol (cons (union s (cs 0)) (rest cs)))))))
(reduce comb ss '())))
(consol '((a b) (c d)))
((a b) (c d))
(consol '((a b) (b c)))
((b c a))
(consol '((a b) (c d) (d b)))
((c d b a))
(consol '((h i k) (a b) (c d) (d b) (f g h)))
((f g h i k) (c d b a))
Nim
proc consolidate(sets: varargs[set[char]]): seq[set[char]] =
if len(sets) < 2:
return @sets
var (r, b) = (@[sets[0]], consolidate(sets[1..^1]))
for x in b:
if len(r[0] * x) != 0:
r[0] = r[0] + x
else:
r.add(x)
r
echo consolidate({'A', 'B'}, {'C', 'D'})
echo consolidate({'A', 'B'}, {'B', 'D'})
echo consolidate({'A', 'B'}, {'C', 'D'}, {'D', 'B'})
echo consolidate({'H', 'I', 'K'}, {'A', 'B'}, {'C', 'D'}, {'D', 'B'}, {'F', 'G', 'H'})
- Output:
@[{'A', 'B'}, {'C', 'D'}]
@[{'A', 'B', 'D'}]
@[{'A', 'B', 'C', 'D'}]
@[{'F', 'G', 'H', 'I', 'K'}, {'A', 'B', 'C', 'D'}]
OCaml
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
/* 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
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
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' ### ] ### ]
Phix
Using strings to represent sets of characters
with javascript_semantics function has_intersection(sequence set1, set2) for i=1 to length(set1) do if find(set1[i],set2) then return true end if end for return false end function function get_union(sequence set1, set2) for i=1 to length(set2) do if not find(set2[i],set1) then set1 = append(set1,set2[i]) end if end for return set1 end function function consolidate(sequence sets) for i=length(sets) to 1 by -1 do for j=length(sets) to i+1 by -1 do if has_intersection(sets[i],sets[j]) then sets[i] = get_union(sets[i],sets[j]) sets[j..j] = {} end if end for end for return sets end function ?consolidate({"AB","CD"}) ?consolidate({"AB","BD"}) ?consolidate({"AB","CD","DB"}) ?consolidate({"HIK","AB","CD","DB","FGH"})
- Output:
{"AB","CD"}
{"ABD"}
{"ABCD"}
{"HIKFG","ABCD"}
PicoLisp
(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
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}
PL/M
100H:
BDOS: PROCEDURE (F,A); DECLARE F BYTE, A ADDRESS; GO TO 5; END BDOS;
EXIT: PROCEDURE; GO TO 0; END EXIT;
PUTC: PROCEDURE (C); DECLARE C BYTE; CALL BDOS(2, C); END PUTC;
PUTS: PROCEDURE (S); DECLARE S ADDRESS; CALL BDOS(9, S); END PUTS;
BIT: PROCEDURE (I) ADDRESS;
DECLARE I BYTE;
IF I=0 THEN RETURN 1;
RETURN SHL(DOUBLE(1), I);
END BIT;
PRINT$SET: PROCEDURE (SET);
DECLARE SET ADDRESS, I BYTE;
CALL PUTC('(');
DO I=0 TO 15;
IF (BIT(I) AND SET) <> 0 THEN CALL PUTC('A' + I);
END;
CALL PUTC(')');
END PRINT$SET;
MAKE$SET: PROCEDURE (SETSTR) ADDRESS;
DECLARE SETSTR ADDRESS, ITEM BASED SETSTR BYTE;
DECLARE SET ADDRESS, POS ADDRESS;
SET = 0;
DO WHILE ITEM <> '$';
POS = ITEM - 'A';
IF POS < 16 THEN SET = SET OR BIT(POS);
SETSTR = SETSTR + 1;
END;
RETURN SET;
END MAKE$SET;
CONSOLIDATE: PROCEDURE (SETS, N) BYTE;
DECLARE (SETS, S BASED SETS) ADDRESS;
DECLARE (N, I, J, CHANGE) BYTE;
STEP:
CHANGE = 0;
DO I=0 TO N-1;
DO J=I+1 TO N-1;
IF (S(I) AND S(J)) <> 0 THEN DO;
S(I) = S(I) OR S(J);
S(J) = 0;
CHANGE = 1;
END;
END;
END;
IF CHANGE THEN GO TO STEP;
DO I=0 TO N-1;
IF S(I)=0 THEN
DO J=I+1 TO N-1;
S(J-1) = S(J);
END;
END;
DO I=0 TO N-1;
IF S(I)=0 THEN RETURN I;
END;
RETURN N;
END CONSOLIDATE;
TEST: PROCEDURE (SETS, N);
DECLARE (SETS, S BASED SETS) ADDRESS;
DECLARE (N, I) BYTE;
DO I=0 TO N-1;
CALL PRINT$SET(S(I));
END;
CALL PUTS(.' -> $');
N = CONSOLIDATE(SETS, N);
DO I=0 TO N-1;
CALL PRINT$SET(S(I));
END;
CALL PUTS(.(13,10,'$'));
END TEST;
DECLARE S (5) ADDRESS;
S(0) = MAKE$SET(.'AB$'); S(1) = MAKE$SET(.'CD$');
CALL TEST(.S, 2);
S(0) = MAKE$SET(.'AB$'); S(1) = MAKE$SET(.'BD$');
CALL TEST(.S, 2);
S(0) = MAKE$SET(.'AB$'); S(1) = MAKE$SET(.'CD$');
S(2) = MAKE$SET(.'DB$');
CALL TEST(.S, 3);
S(0) = MAKE$SET(.'HIK$'); S(1) = MAKE$SET(.'AB$');
S(2) = MAKE$SET(.'CD$'); S(3) = MAKE$SET(.'DB$');
S(4) = MAKE$SET(.'FGH$');
CALL TEST(.S, 5);
CALL EXIT;
EOF- Output:
(AB)(CD) -> (AB)(CD) (AB)(BD) -> (ABD) (AB)(CD)(BD) -> (ABCD) (HIK)(AB)(CD)(BD)(FGH) -> (FGHIK)(ABCD)
Python
Python: Iterative
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
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
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
Python: Functional
As a fold (catamorphism), using union in preference to mutation:
'''Set consolidation'''
from functools import (reduce)
# consolidated :: Ord a => [Set a] -> [Set a]
def consolidated(sets):
'''A consolidated list of sets.'''
def go(xs, s):
if xs:
h = xs[0]
return go(xs[1:], h.union(s)) if (
h.intersection(s)
) else [h] + go(xs[1:], s)
else:
return [s]
return reduce(go, sets, [])
# TESTS ---------------------------------------------------
# main :: IO ()
def main():
'''Illustrative consolidations.'''
print(
tabulated('Consolidation of sets of characters:')(
lambda x: str(list(map(compose(concat)(list), x)))
)(str)(
consolidated
)(list(map(lambda xs: list(map(set, xs)), [
['ab', 'cd'],
['ab', 'bd'],
['ab', 'cd', 'db'],
['hik', 'ab', 'cd', 'db', 'fgh']
])))
)
# DISPLAY OF RESULTS --------------------------------------
# compose (<<<) :: (b -> c) -> (a -> b) -> a -> c
def compose(g):
'''Right to left function composition.'''
return lambda f: lambda x: g(f(x))
# concat :: [String] -> String
def concat(xs):
'''Concatenation of strings in xs.'''
return ''.join(xs)
# tabulated :: String -> (a -> String) ->
# (b -> String) ->
# (a -> b) -> [a] -> String
def tabulated(s):
'''Heading -> x display function -> fx display function ->
f -> value list -> tabular string.'''
def go(xShow, fxShow, f, xs):
w = max(map(compose(len)(xShow), xs))
return s + '\n' + '\n'.join([
xShow(x).rjust(w, ' ') + ' -> ' + fxShow(f(x)) for x in xs
])
return lambda xShow: lambda fxShow: (
lambda f: lambda xs: go(
xShow, fxShow, f, xs
)
)
# MAIN ---
if __name__ == '__main__':
main()
- Output:
Consolidation of sets of characters:
['ba', 'cd'] -> [{'b', 'a'}, {'c', 'd'}]
['ba', 'bd'] -> [{'b', 'd', 'a'}]
['ba', 'cd', 'db'] -> [{'d', 'a', 'c', 'b'}]
['ikh', 'ba', 'cd', 'db', 'gfh'] -> [{'d', 'a', 'c', 'b'}, {'i', 'k', 'g', 'h', 'f'}]
Quackery
[ 0 swap witheach [ bit | ] ] is ->set ( $ --> { )
[ say "{" 0 swap
[ dup 0 != while
dup 1 & if [ over emit ]
1 >> dip 1+ again ]
2drop say "} " ] is echoset ( { --> )
[ [] swap dup size 1 - times
[ behead over witheach
[ 2dup & iff
[ | swap i^ poke
[] conclude ]
else drop ]
swap dip join ]
join ] is consolidate ( [ --> [ )
[ dup witheach echoset
say "--> "
consolidate witheach echoset
cr ] is task ( [ --> )
$ "AB" ->set
$ "CD" ->set join
task
$ "AB" ->set
$ "BD" ->set join
task
$ "AB" ->set
$ "CD" ->set join
$ "DB" ->set join
task
$ "HIK" ->set
$ "AB" ->set join
$ "CD" ->set join
$ "DB" ->set join
$ "FGH" ->set join
task- Output:
{AB} {CD} --> {AB} {CD}
{AB} {BD} --> {ABD}
{AB} {CD} {BD} --> {ABCD}
{HIK} {AB} {CD} {BD} {FGH} --> {ABCD} {FGHIK}
Racket
#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))
Raku
(formerly Perl 6)
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)
Refal
$ENTRY Go {
= <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)>;
};
Test {
e.S = <Prout e.S ' -> ' <Consolidate e.S>>;
};
Consolidate {
e.SS, <Consolidate1 () e.SS>: {
e.SS = e.SS;
e.SS2 = <Consolidate e.SS2>;
};
};
Consolidate1 {
(e.CSS) = e.CSS;
(e.CSS) (e.S) e.SS,
<Consolidate2 (e.CSS) (e.S)>: e.CSS2 =
<Consolidate1 (e.CSS2) e.SS>;
};
Consolidate2 {
() (e.S) = (e.S);
((e.S1) e.SS) (e.S), <Overlap (e.S1) (e.S)>: {
True = (<Set e.S1 e.S>) e.SS;
False = (e.S1) <Consolidate2 (e.SS) (e.S)>;
};
};
Overlap {
(e.S1) () = False;
(e.S1) (s.I e.S2), e.S1: {
e.L s.I e.R = True;
e.S1 = <Overlap (e.S1) (e.S2)>;
};
};
Set {
= ;
s.I e.S, e.S: {
e.L s.I e.R = <Set e.S>;
e.S = s.I <Set e.S>;
};
};- Output:
(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 ) -> (I K F G H )(A B C D )
REXX
/*REXX program demonstrates a method of set consolidating using 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 0 /*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)
_= 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}
Ring
# Project : Set consolidation
load "stdlib.ring"
test = ["AB","AB,CD","AB,CD,DB","HIK,AB,CD,DB,FGH"]
for t in test
see consolidate(t) + nl
next
func consolidate(s)
sets = split(s,",")
n = len(sets)
for i = 1 to n
p = i
ts = ""
for j = i to 1 step -1
if ts = ""
p = j
ok
ts = ""
for k = 1 to len(sets[p])
if j > 1
if substring(sets[j-1],substr(sets[p],k,1),1) = 0
ts = ts + substr(sets[p],k,1)
ok
ok
next
if len(ts) < len(sets[p])
if j > 1
sets[j-1] = sets[j-1] + ts
sets[p] = "-"
ts = ""
ok
else
p = i
ok
next
next
consolidate = s + " = " + substr(list2str(sets),nl,",")
return consolidateOutput:
AB = AB AB,CD = AB,CD AB,CD,DB = ABCD,-,- HIK,AB,CD,DB,FGH = HIKFG,ABCD,-,-,-
RPL
« DUP SIZE 1 + → a b j
« { }
WHILE 'j' DECR REPEAT
b j GET
IF a OVER POS THEN 'a' LASTARG ? PUT + ELSE DROP END
END
» » 'INTER' STO @ ( { set_a } { set_b } } → { set_a ∩ set_b } )
« DUP2 + UNROT INTER DUP SIZE 1 +
→ inter j
« WHILE 'j' DECR REPEAT
DUP inter j GET POS
IF DUP 1 == THEN DROP TAIL
ELSE
1 SWAP 1 - SUB
LASTARG 2 + NIP OVER SIZE SUB +
END END
SORT @ optional
» » 'UPDATE' STO @ ( { set_a } { set_b } } → { set_a + set_b } )
« DUP SIZE DUP → times length
« EVAL @ put the sets in the stack
WHILE 'times' DECR REPEAT
2 length FOR j
j PICK
IF DUP2 INTER SIZE THEN
UPDATE j ROLL DROP
length 'j' STO 'length' DECR
END
DROP
NEXT
length ROLL
END
length →LIST
» » 'CONSO' STO @ ( { set } .. } → { { set } .. )
{{ A B } { C D }} CONSO
{{ A B } { B D }} CONSO
{{ A B } { C D } { D B }} CONSO
{{ H I K } { A B } { C D } { D B } { F G H }} CONSO
- Output:
4: { { C D } { A B } }
3: { { A B D } }
2; { { A B C D } }
1: { { F G H I K } { C A D B } }
This implementation can handle sets with duplicate elements:
{ { A A B } { B B C C } } CONSO
- Output:
1: { { A A B B C C } }
Ruby
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
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}
SETL
program set_consolidation;
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'}}
];
loop for t in tests do
print(consolidate(t));
end loop;
proc consolidate(sets);
outp := {};
loop while sets /= {} do
set_ from sets;
loop until overlap = {} do
overlap := {s : s in sets | exists el in s | el in set_};
set_ +:= {} +/ overlap;
sets -:= overlap;
end loop;
outp with:= set_;
end loop;
return outp;
end proc;
end program;- Output:
{{A B} {C D}}
{{A B D}}
{{A B C D}}
{{A B C D} {F G H I K}}
Sidef
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)
SQL
This is not a particularly efficient solution, but it gets the job done.
/*
This code is an implementation of "Set consolidation" in SQL ORACLE 19c
p_list_of_sets -- input string
delimeter by default "|"
*/
with
function set_consolidation(p_list_of_sets in varchar2)
return varchar2 is
--
v_list_of_sets varchar2(32767) := p_list_of_sets;
v_output varchar2(32767) ;
v_set_1 varchar2(2000) ;
v_set_2 varchar2(2000) ;
v_pos_set_1 pls_integer;
v_pos_set_2 pls_integer;
--
function remove_duplicates(p_set varchar2)
return varchar2 is
v_set varchar2(1000) := p_set;
begin
for i in 1..length(v_set)
loop
v_set := regexp_replace(v_set, substr(v_set, i, 1), '', i+1, 0) ;
end loop;
return v_set;
end;
--
begin
--cleaning
v_list_of_sets := ltrim(v_list_of_sets, '{') ;
v_list_of_sets := rtrim(v_list_of_sets, '}') ;
v_list_of_sets := replace(v_list_of_sets, ' ', '') ;
v_list_of_sets := replace(v_list_of_sets, ',', '') ;
--set delimeter "|"
v_list_of_sets := replace(v_list_of_sets, '}{', '|') ;
--
<<loop_through_sets>>
while regexp_count(v_list_of_sets, '[^|]+') > 0
loop
v_set_1 := regexp_substr(v_list_of_sets, '[^|]+', 1, 1) ;
v_pos_set_1 := regexp_instr(v_list_of_sets, '[^|]+', 1, 1) ;
--
<<loop_for>>
for i in 1..regexp_count(v_list_of_sets, '[^|]+')-1
loop
--
v_set_2 := regexp_substr(v_list_of_sets, '[^|]+', 1, i+1) ;
v_pos_set_2 := regexp_instr(v_list_of_sets, '[^|]+', 1, i+1) ;
--
if regexp_count(v_set_2, '['||v_set_1||']') > 0 then
v_list_of_sets := regexp_replace(v_list_of_sets, v_set_1, remove_duplicates(v_set_1||v_set_2), v_pos_set_1, 1) ;
v_list_of_sets := regexp_replace(v_list_of_sets, v_set_2, '', v_pos_set_2, 1) ;
continue loop_through_sets;
end if;
--
end loop loop_for;
--
v_output := v_output||'{'||rtrim(regexp_replace(v_set_1, '([A-Z])', '\1,'), ',') ||'}';
v_list_of_sets := regexp_replace(v_list_of_sets, v_set_1, '', 1, 1) ;
--
end loop loop_through_sets;
--
return replace(nvl(v_output,'{}'),'}{','},{') ;
end;
--Test
select lpad('{}',50) || ' ==> ' || set_consolidation('{}') as output from dual
union all
select lpad('{},{}',50) || ' ==> ' || set_consolidation('{},{}') as output from dual
union all
select lpad('{},{B}',50) || ' ==> ' || set_consolidation('{},{B}') as output from dual
union all
select lpad('{D}',50) || ' ==> ' || set_consolidation('{D}') as output from dual
union all
select lpad('{F},{A},{A}',50) || ' ==> ' || set_consolidation('{F},{A},{A}') as output from dual
union all
select lpad('{A,B},{B}',50) || ' ==> ' || set_consolidation('{A,B},{B}') as output from dual
union all
select lpad('{A,D},{D,A}',50) || ' ==> ' || set_consolidation('{A,D},{D,A}') as output from dual
union all
--Test RosettaCode
select '-- Test RosettaCode' as output from dual
union all
select lpad('{A,B},{C,D}',50) || ' ==> ' || set_consolidation('{A,B},{C,D}') as output from dual
union all
select lpad('{A,B},{B,D}',50) || ' ==> ' || set_consolidation('{A,B},{B,D}') as output from dual
union all
select lpad('{A,B},{C,D},{D,B}',50) || ' ==> ' || set_consolidation('{A,B},{C,D},{D,B}') as output from dual
union all
select lpad('{H, I, K}, {A,B}, {C,D}, {D,B}, {F,G,H}',50) || ' ==> ' || set_consolidation('{H, I, K}, {A,B}, {C,D}, {D,B}, {F,G,H}') as output from dual
union all
select lpad('HIK|AB|CD|DB|FGH',50) || ' ==> ' || set_consolidation('HIK|AB|CD|DB|FGH') as output from dual
;
/
- Output:
{} ==> {}
{},{} ==> {}
{},{B} ==> {B}
{D} ==> {D}
{F},{A},{A} ==> {F},{A}
{A,B},{B} ==> {A,B}
{A,D},{D,A} ==> {A,D}
-- Test RosettaCode
{A,B},{C,D} ==> {A,B},{C,D}
{A,B},{B,D} ==> {A,B,D}
{A,B},{C,D},{D,B} ==> {A,B,D,C}
{H, I, K}, {A,B}, {C,D}, {D,B}, {F,G,H} ==> {H,I,K,F,G},{A,B,D,C}
HIK|AB|CD|DB|FGH ==> {H,I,K,F,G},{A,B,D,C}
Tcl
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
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)
(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))
VBA
This solutions uses collections as sets. The first three coroutines are based on the Phix solution. Two coroutines are written to create the example sets as collections, and another coroutine to show the consolidated set.
Private Function has_intersection(set1 As Collection, set2 As Collection) As Boolean
For Each element In set1
On Error Resume Next
tmp = set2(element)
If tmp = element Then
has_intersection = True
Exit Function
End If
Next element
End Function
Private Sub union(set1 As Collection, set2 As Collection)
For Each element In set2
On Error Resume Next
tmp = set1(element)
If tmp <> element Then
set1.Add element, element
End If
Next element
End Sub
Private Function consolidate(sets As Collection) As Collection
For i = sets.Count To 1 Step -1
For j = sets.Count To i + 1 Step -1
If has_intersection(sets(i), sets(j)) Then
union sets(i), sets(j)
sets.Remove j
End If
Next j
Next i
Set consolidate = sets
End Function
Private Function mc(s As Variant) As Collection
Dim res As New Collection
For i = 1 To Len(s)
res.Add Mid(s, i, 1), Mid(s, i, 1)
Next i
Set mc = res
End Function
Private Function ms(t As Variant) As Collection
Dim res As New Collection
Dim element As Collection
For i = LBound(t) To UBound(t)
Set element = t(i)
res.Add t(i)
Next i
Set ms = res
End Function
Private Sub show(x As Collection)
Dim t() As String
Dim u() As String
ReDim t(1 To x.Count)
For i = 1 To x.Count
ReDim u(1 To x(i).Count)
For j = 1 To x(i).Count
u(j) = x(i)(j)
Next j
t(i) = "{" & Join(u, ", ") & "}"
Next i
Debug.Print "{" & Join(t, ", ") & "}"
End Sub
Public Sub main()
show consolidate(ms(Array(mc("AB"), mc("CD"))))
show consolidate(ms(Array(mc("AB"), mc("BD"))))
show consolidate(ms(Array(mc("AB"), mc("CD"), mc("DB"))))
show consolidate(ms(Array(mc("HIK"), mc("AB"), mc("CD"), mc("DB"), mc("FGH"))))
End Sub
- Output:
{{A, B}, {C, D}}
{{A, B, D}}
{{A, B, C, D}}
{{H, I, K, F, G}, {A, B, C, D}}
VBScript
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 , - , - , -
Wren
Note that (as implemented in the above module) it is not possible to have a 'Set of Sets' because Set elements can only be certain primitives which can act as Map keys. However, you can have a List of Sets and so that's what we use here.
As Sets are Map-based, iteration (and hence printing) order are undefined.
import "./set" for Set
var consolidateSets = Fn.new { |sets|
var size = sets.count
var consolidated = List.filled(size, false)
var i = 0
while (i < size - 1) {
if (!consolidated[i]) {
while (true) {
var intersects = 0
for (j in i+1...size) {
if (!consolidated[j]) {
if (!sets[i].intersect(sets[j]).isEmpty) {
sets[i].addAll(sets[j])
consolidated[j] = true
intersects = intersects + 1
}
}
}
if (intersects == 0) break
}
}
i = i + 1
}
return (0...size).where { |i| !consolidated[i] }.map { |i| sets[i] }.toList
}
var unconsolidatedSets = [
[Set.new(["A", "B"]), Set.new(["C", "D"])],
[Set.new(["A", "B"]), Set.new(["B", "D"])],
[Set.new(["A", "B"]), Set.new(["C", "D"]), Set.new(["D", "B"])],
[Set.new(["H", "I", "K"]), Set.new(["A", "B"]), Set.new(["C", "D"]),
Set.new(["D", "B"]), Set.new(["F", "G", "H"])]
]
for (sets in unconsolidatedSets) {
System.print("Unconsolidated: %(sets)")
System.print("Cosolidated : %(consolidateSets.call(sets))\n")
}
- Output:
Unconsolidated: [<B, A>, <C, D>] Cosolidated : [<B, A>, <C, D>] Unconsolidated: [<B, A>, <D, B>] Cosolidated : [<D, B, A>] Unconsolidated: [<B, A>, <C, D>, <D, B>] Cosolidated : [<C, D, B, A>] Unconsolidated: [<I, H, K>, <B, A>, <C, D>, <D, B>, <G, H, F>] Cosolidated : [<I, G, H, F, K>, <C, D, B, A>]
zkl
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)
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