Is there a way to assign vertex groups to all loose elements via python

Question

I have loose mesh elements within an object and I would like each loos element to be placed in its own vertex group.

Answer 1

Another take on this. Already had code that separated a mesh into vertex groups from seams,

import bpy

def island_verts(mesh):  
    import bmesh
    bpy.ops.object.mode_set(mode='EDIT')
    bpy.ops.mesh.select_all(action='DESELECT')

    bm = bmesh.from_edit_mesh(mesh)
    bm.verts.ensure_lookup_table()
    verts = [v.index for v in bm.verts]

    vgs = []
    while len(verts):        
        bm.verts[verts[0]].select = True
        #bpy.ops.mesh.select_linked(delimit={'SEAM'})
        bpy.ops.mesh.select_linked()
        sv = [v.index for v in bm.verts if v.select]
        vgs.append(sv)
        for v in sv:
            bm.verts[v].select = False
            verts.remove(v)
    bm.free() # prob not nec.        
    bpy.ops.object.mode_set(mode='OBJECT')
    return vgs      

# test run            
obj = bpy.context.object
mesh = obj.data
vgs = island_verts(mesh)

for vg in vgs:
    group = obj.vertex_groups.new()
    group.name = "Island"
    group.add(vg, 1.0, 'ADD')

Answer 2

Here's a script that iterates over each mesh island and assigns its vertices into a new vertex group.

EDIT - WARNING: After testing it appears that this solution is limited to around 1000 islands (due to Blender's max recursion limit). Use @batFINGER's solution if you have more vertex groups than that.

It's based on a recursive function since the blender API currently doesn't provide (as far as I know) any built in way to get all mesh islands.

import bpy, bmesh

def find_island_and_assign_vgroup( o, remaining ):
    ''' Recursive function that itertaes over mesh islands and assigns a new vertex group to each'''

    if len( remaining ) > 0:
        # Create bmesh object (must do this every time since vertex groups are created in object mode, which destroys the bm object
        bpy.ops.object.mode_set( mode = 'EDIT' )
        bm = bmesh.from_edit_mesh( o.data )
        bm.verts.ensure_lookup_table()

        bpy.ops.mesh.select_all( action = 'DESELECT' )
        bm.verts[ list(remaining)[0] ].select = True
        bm.select_flush( True )
        bpy.ops.mesh.select_linked()

        selected_verts = [ v.index for v in bm.verts if v.select ]

        # Add to a new vertex group
        bpy.ops.object.mode_set( mode = 'OBJECT' )
        vg = o.vertex_groups.new()
        vg.add( selected_verts, 1.0, 'ADD' )

        # Remove this island's verts from the vert list
        now_remaining = remaining - set( selected_verts )

        bm.free()
        find_island_and_assign_vgroup( o, now_remaining )

o         = bpy.data.objects[ bpy.context.object.name ]
all_verts = set( range( len( o.data.vertices ) ) )
find_island_and_assign_vgroup( o, all_verts )