PseudoDistances within a depthdetermination problem
I was given the following problem description for a depthdetermination problem, however I am completly unable to figure out how this "pseudodistance" feature works, if anyone has any clues and can provide a ubersimple example it would be much appreciated  I just can't see how it works/applies.
[Problem]
In the depthdetermination problem, we maintain a forest F = {Ti} of rooted trees. We use the disjointset forest S=Si, where each set Si (which is itself a tree) corresponds to a tree Ti in the forest F. The tree structure within a set Si, however, does not necessarily correspond to that of Ti. In fact, the implementation of Si does not record the exact parentchild relationships but nevertheless allows us to determine any node’s depth in Ti.
The key idea is to maintain each node v a ”pseudodistance” d[v], which is defined so that the sum of the pseudodistances along the path from v to the root of its set Si equals the depth of v in Ti. That is, if the path from v to its root in v0 , v1 , . . . , vk , where v0 = v and vk is Si’s root, then the depth of v in Ti is the sum of d[vj] where j=0 to j=k.
