[Tree]..Is parent or grandparent?

There are two nodes given in a tree(not binary tree). Find whether one node
is parent/grand parent of other.
order should be O(1).

tag root as 0 , tag left child as 00 , right child as 01.
left child's left child as 000 , left's child's right child as
001 ... and so on.
now
let input be tags t1 and t2
if( (t1 == (t2>>1)) || (t2==(t1>>1)))
return child parent relationship
if( (t1 == (t2>>2)) || (t2==(t1>>2)))
return child grand-parent relationship ...


This solution can take a lot of space as the three grows.

We can tag the node by number ..
Root -0
1 -2-3-4

SO given two node get their tags..
Get Max of both t1, t2.
Go for parent of that node if other node then return or check for parent of parent and check again for other node.

With 2^32 value avaialable for indexing ..u wont run out of values.