Check if 2 tree nodes are related (ancestor/descendant) in O(1) with pre-processing

Question

Check if 2 tree nodes are related (i.e. ancestor-descendant)

• solve it in O(1) time, with O(N) space (N = # of nodes)
• pre-processing is allowed

Answer 1

if you consider a tree where a node in the tree has n/2 children (say), the running time of setting the labels will be as high as O(n*n). So this labeling scheme wont work ....