O(1) algorithm to determine if node is descendant of another node in a multiway tree?

Question

Imagine the following tree:

    A
   / \\
  B   C
 / \\   \\
D   E   F

I\'m looking for a way to query if for example F is a descendant of A (n

Answer 1

In a pre-order traversal, every set of descendants is contiguous. For your example,

A B D E C F
+---------+ A
  +---+ B
    + D
      + E
        +-+ C
          + F

If you can preprocess, then all you need to do is number each node and compute the descendant interval.

If you can't preprocess, then a link/cut tree offers O(log n) performance for both updates and queries.