[Nonlinear.ReverseAd.Coloring] fix acyclic coloring algorithm

src/Nonlinear/ReverseAD/Coloring/Coloring.jl

@@ -171,14 +171,9 @@ function _grow_star(v, w, e_idx, firstNeighbor, color, S)
     @inbounds if p != v
         firstNeighbor[color[w]] = _Edge(e_idx, v, w)
     else
-        _root_union!(S, e_idx, e.index)
-    end
-    return
-end
-
-function _merge_trees(S::_IntDisjointSet, eg::Int, eg1::Int)
-    if _find_root!(S, eg) != _find_root!(S, eg1)
-        _root_union!(S, eg, eg1)
+        root1 = _find_root!(S, e_idx)
+        root2 = _find_root!(S, e.index)
+        _root_union!(S, root1, root2)
     end
     return
 end
@@ -280,7 +275,7 @@ function acyclic_coloring(g::UndirectedGraph)
                     continue
                 end
                 if color[x] == color[v]
-                    _merge_trees(S, e_idx, e2_idx)
+                    _union!(S, e_idx, e2_idx)
                 end
             end
         end

src/Nonlinear/ReverseAD/Coloring/IntDisjointSet.jl

@@ -45,3 +45,12 @@ function _root_union!(S::_IntDisjointSet, x::Int, y::Int)
     S.number_of_trees -= 1
     return
 end
+
+function _union!(S, x::Int, y::Int)
+    root_x = _find_root!(S, x)
+    root_y = _find_root!(S, y)
+    if root_x != root_y
+        _root_union!(S, root_x, root_y)
+    end
+    return
+end

test/Nonlinear/ReverseAD.jl

@@ -1448,6 +1448,16 @@ function test_IntDisjointSet()
     return
 end
 
+function test_issue_2897()
+    I = [4, 5, 4, 6, 5, 6]
+    J = [2, 1, 1, 2, 3, 3]
+    g = Coloring.UndirectedGraph(I, J, length(I))
+    color, num_colors = Coloring.acyclic_coloring(g)
+    @test color == [1, 1, 1, 2, 2, 3]
+    @test num_colors == 3
+    return
+end
+
 end  # module
 
 TestReverseAD.runtests()