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Merged
fingolfin merged 4 commits into from
Oct 14, 2025
Merged

Some quality of life improvements for PartitionDS #159

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57f3d33
Add string to PartitionDSFamily declaration
james-d-mitchell Oct 8, 2025
8d7ebca
Remove redundant code from union-find.gi
james-d-mitchell Oct 8, 2025
1551555
Replace constructors PartitionDS with operations
james-d-mitchell Oct 8, 2025
ce57e10
Add RootsOfPartitionDS
james-d-mitchell Oct 8, 2025
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39 changes: 36 additions & 3 deletions gap/union-find.gd
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Original file line number Diff line number Diff line change
Expand Up @@ -28,7 +28,7 @@ DeclareCategory("IsPartitionDS", IsObject);

#! @Description
#! Family containing all partition data structures
BindGlobal("PartitionDSFamily", NewFamily(IsPartitionDS));
BindGlobal("PartitionDSFamily", NewFamily("PartitionDSFamily", IsPartitionDS));

#
# Constructors. Given an integer return the trivial partition (n parts of size 1)
Expand All @@ -38,11 +38,37 @@ BindGlobal("PartitionDSFamily", NewFamily(IsPartitionDS));
#! @Description
#! Returns the trivial partition of the set <C>[1..n]</C>.
#! @Arguments filter, n
DeclareConstructor("PartitionDS",[IsPartitionDS, IsPosInt]);
DeclareConstructor("PartitionDSCons",[IsPartitionDS, IsPosInt]);

#! @Description
#! Returns the union find structure of <A>partition</A>.
#! @Arguments filter, partition
DeclareConstructor("PartitionDS",[IsPartitionDS, IsCyclotomicCollColl]);
DeclareConstructor("PartitionDSCons",[IsPartitionDS, IsCyclotomicCollColl]);

#
# Operations. Given an integer return the trivial partition (n parts of size 1)
# Given a list of disjoint sets, return that partition. Any points up to the maximum
# of any of the sets not included in a set are in singleton parts.
#
#! @Description
#! Returns the trivial partition of the set <C>[1..n]</C>.
#! @Arguments filter, n
DeclareOperation("PartitionDS",[IsFunction, IsPosInt]);

#! @Description
#! Returns the trivial partition of the set <C>[1..n]</C>.
#! @Arguments n
DeclareOperation("PartitionDS",[IsPosInt]);

#! @Description
#! Returns the union find structure of <A>partition</A>.
#! @Arguments filter, partition
DeclareOperation("PartitionDS",[IsFunction, IsCyclotomicCollColl]);

#! @Description
#! Returns the union find structure of <A>partition</A>.
#! @Arguments partition
DeclareOperation("PartitionDS",[IsCyclotomicCollColl]);

#
# Key operations
Expand All @@ -69,6 +95,13 @@ DeclareOperation("Unite",[IsPartitionDS and IsMutable, IsPosInt, IsPosInt]);
#! @Returns an iterator
DeclareOperation("RootsIteratorOfPartitionDS", [IsPartitionDS]);

#! @Description
#! Returns a list of the canonical representatives of the parts
#! of the partition <A>unionfind</A>.
#! @Arguments unionfind
#! @Returns A list.
DeclareOperation("RootsOfPartitionDS", [IsPartitionDS]);

#! @Description
#! Returns the number of parts of the partition <A>unionfind</A>.
#! @Arguments unionfind
Expand Down
109 changes: 42 additions & 67 deletions gap/union-find.gi
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Expand Up @@ -25,7 +25,7 @@ UF.setRank := UF.Bitfields.setters[1];
UF.setParent := UF.Bitfields.setters[2];


InstallMethod(PartitionDS, [IsPartitionDSRep and IsPartitionDS and IsMutable, IsPosInt],
InstallMethod(PartitionDSCons, [IsPartitionDSRep and IsPartitionDS and IsMutable, IsPosInt],
function(filt, n)
local r;
r := rec();
Expand All @@ -37,7 +37,7 @@ InstallMethod(PartitionDS, [IsPartitionDSRep and IsPartitionDS and IsMutable, Is
end);


InstallMethod(PartitionDS, [IsPartitionDSRep and IsPartitionDS and IsMutable, IsCyclotomicCollColl],
InstallMethod(PartitionDSCons, [IsPartitionDSRep and IsPartitionDS and IsMutable, IsCyclotomicCollColl],
function(filt, parts)
local r, n, seen, sp, sr, p, x;
if not (ForAll(parts, IsSet) and
Expand Down Expand Up @@ -66,76 +66,31 @@ InstallMethod(PartitionDS, [IsPartitionDSRep and IsPartitionDS and IsMutable, Is
return r;
end);

InstallMethod(PartitionDS, [IsPosInt],
n -> PartitionDSCons(IsPartitionDSRep, n));

InstallMethod(PartitionDS, [IsCyclotomicCollColl],
parts -> PartitionDSCons(IsPartitionDSRep, parts));

UF.RepresentativeTarjan :=
function(uf, x)
local gp, sp, p, y, z;
gp := UF.getParent;
sp := UF.setParent;
p := uf!.data;
while true do
y := gp(p[x]);
if y = x then
return x;
fi;
z := gp(p[y]);
if y = z then
return y;
fi;
p[x] := sp(p[x],z);
x := z;
od;
end;
InstallMethod(PartitionDS, [IsFunction, IsPosInt],
{filt, n} -> PartitionDSCons(filt, n));

if IsBound(DS_UF_FIND) then
UF.RepresentativeKernel := function(uf, x)
return DS_UF_FIND(x, uf!.data);
end;
InstallMethod(Representative, [IsPartitionDSRep and IsPartitionDS, IsPosInt],
UF.RepresentativeKernel);
else
InstallMethod(Representative, [IsPartitionDSRep and IsPartitionDS, IsPosInt],
UF.RepresentativeTarjan);
fi;
InstallMethod(PartitionDS, [IsFunction, IsCyclotomicCollColl],
{filt, parts} -> PartitionDSCons(filt, parts));

UF.UniteGAP := function(uf, x, y)
local r, rx, ry;
x := Representative(uf, x);
y := Representative(uf, y);
if x = y then
return;
fi;
r := uf!.data;
rx := UF.getRank(r[x]);
ry := UF.getRank(r[y]);
if rx > ry then
r[y] := UF.setParent(r[y],x);
elif ry > rx then
r[x] := UF.setParent(r[x],y);
else
r[x] := UF.setParent(r[x],y);
r[y] := UF.setRank(r[y],ry+1);
fi;
uf!.nparts := uf!.nparts -1;
return;
UF.RepresentativeKernel := function(uf, x)
return DS_UF_FIND(x, uf!.data);
end;


if IsBound(DS_UF_UNITE) then
InstallMethod(Unite, [IsPartitionDSRep and IsMutable and IsPartitionDS,
IsPosInt, IsPosInt],
function(uf, x, y)
if DS_UF_UNITE(x, y, uf!.data) then
uf!.nparts := uf!.nparts -1;
fi;
end);
else
InstallMethod(Unite, [IsPartitionDSRep and IsMutable and IsPartitionDS,
IsPosInt, IsPosInt],
UF.UniteGAP);
fi;

InstallMethod(Representative, [IsPartitionDSRep and IsPartitionDS, IsPosInt],
UF.RepresentativeKernel);

InstallMethod(Unite, [IsPartitionDSRep and IsMutable and IsPartitionDS,
IsPosInt, IsPosInt],
function(uf, x, y)
if DS_UF_UNITE(x, y, uf!.data) then
uf!.nparts := uf!.nparts -1;
fi;
end);

InstallMethod(\=, [IsPartitionDSRep and IsPartitionDS, IsPartitionDSRep and IsPartitionDS], IsIdenticalObj);

Expand Down Expand Up @@ -193,6 +148,26 @@ InstallMethod(RootsIteratorOfPartitionDS, [IsPartitionDSRep and IsPartitionDS],
end));
end);

InstallMethod(RootsOfPartitionDS, [IsPartitionDSRep and IsPartitionDS],
function(uf)
local pt, gp, data, n, result;
pt := 0;
gp := UF.getParent;
data := uf!.data;
n := SizeUnderlyingSetDS(uf);
result := [];
while pt <= n do
pt := pt + 1;
while pt <= n and gp(data[pt]) <> pt do
pt := pt + 1;
od;
if pt <= n then
Add(result, pt);
fi;
od;
return result;
end);

InstallMethod(PartsOfPartitionDS, [IsPartitionDS],
function(u)
local p, i, r, x;
Expand Down
44 changes: 24 additions & 20 deletions tst/uf.tst
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Original file line number Diff line number Diff line change
Expand Up @@ -5,7 +5,7 @@ gap> START_TEST("uf.tst");
# Test the union-find data structure
#
#
gap> u := PartitionDS(IsPartitionDS,10);
gap> u := PartitionDS(10);
<union find 10 parts on 10 points>
gap> NumberParts(u);
10
Expand Down Expand Up @@ -36,7 +36,7 @@ gap> Unite(u,1,3);
gap> u;
<union find 8 parts on 10 points>
gap> Print(u,"\n");
PartitionDS( IsPartitionDS, [ [ 1, 2, 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ], \
PartitionDS(IsPartitionDS, [ [ 1, 2, 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ], \
[ 9 ], [ 10 ] ])
gap> PartitionDS( IsPartitionDS, [ [ 1, 2, 3 ], [ 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ],
> [ 9 ], [ 10 ] ]);
Expand All @@ -57,6 +57,8 @@ gap> for x in i do Print(x,"\n"); od;
8
9
10
gap> RootsOfPartitionDS(u);
[ 2, 4, 5, 6, 7, 8, 9, 10 ]
gap> for x in i2 do Print(x,"\n"); od;
4
5
Expand All @@ -65,21 +67,21 @@ gap> for x in i2 do Print(x,"\n"); od;
8
9
10
gap> UF.RepresentativeTarjan(u,3);
gap> Representative(u,3);
2
gap> UF.UniteGAP(u,4,5);
gap> Unite(u,4,5);
gap> u;
<union find 7 parts on 10 points>
gap> PartitionDS(IsPartitionDS,[[2,1]]);
gap> PartitionDS([[2,1]]);
Error, PartitionDS: supplied partition must be a list of disjoint sets of posi\
tive integers
gap> PartitionDS(IsPartitionDS,[[-2,1]]);
gap> PartitionDS([[-2,1]]);
Error, PartitionDS: supplied partition must be a list of disjoint sets of posi\
tive integers
gap> PartitionDS(IsPartitionDS,[[1,2,3],[3,4,5]]);
gap> PartitionDS([[1,2,3],[3,4,5]]);
Error, PartitionDS: supplied partition must be a list of disjoint sets of posi\
tive integers
gap> u := PartitionDS(IsPartitionDS, 16);
gap> u := PartitionDS(16);
<union find 16 parts on 16 points>
gap> for i in [1,3..15] do Unite(u,i, i+1); od;
gap> for i in [1,5..13] do Unite(u,i, i+2); od;
Expand All @@ -89,28 +91,30 @@ gap> Representative(u,1);
16
gap> Representative(u,15);
16
gap> u := PartitionDS(IsPartitionDS, 16);
gap> u := PartitionDS(16);
<union find 16 parts on 16 points>
gap> for i in [1,3..15] do UF.UniteGAP(u,i, i+1); od;
gap> for i in [1,5..13] do UF.UniteGAP(u,i, i+2); od;
gap> for i in [1,9] do UF.UniteGAP(u,i, i+4); od;
gap> UF.UniteGAP(u,1,9);
gap> UF.RepresentativeTarjan(u,1);
gap> for i in [1,3..15] do Unite(u,i, i+1); od;
gap> for i in [1,5..13] do Unite(u,i, i+2); od;
gap> for i in [1,9] do Unite(u,i, i+4); od;
gap> Unite(u,1,9);
gap> Representative(u,1);
16
gap> UF.RepresentativeTarjan(u,15);
gap> Representative(u,15);
16
gap> u := PartitionDS(IsPartitionDS, 16);;
gap> u := PartitionDS(16);;
gap> Unite(u,1,2);
gap> Unite(u,2,3);
gap> Unite(u,4,2);
gap> Unite(u,5,5);
gap> UF.UniteGAP(u,9,10);
gap> UF.UniteGAP(u,10,11);
gap> UF.UniteGAP(u,12,10);
gap> UF.UniteGAP(u,9,12);
gap> Unite(u,9,10);
gap> Unite(u,10,11);
gap> Unite(u,12,10);
gap> Unite(u,9,12);
gap> PartsOfPartitionDS(u);
[ [ 1, 2, 3, 4 ], [ 5 ], [ 6 ], [ 7 ], [ 8 ], [ 9, 10, 11, 12 ], [ 13 ],
[ 14 ], [ 15 ], [ 16 ] ]
gap> RootsOfPartitionDS(u);
[ 2, 5, 6, 7, 8, 10, 13, 14, 15, 16 ]

#
gap> STOP_TEST( "uf.tst", 1);