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

I don't know if this would fit your problem, but one way to store hierarchies in databases, with quick "give me everything from this node and downwards" features is to store a "path".

For instance, for a tree that looks like this:

    +-- b
    |
a --+       +-- d
    |       |
    +-- c --+
            |
            +-- e

you would store the rows as follows, assuming the letter in the above tree is the "id" of each row:

id    path
a     a
b     a*b
c     a*c
d     a*c*d
e     a*c*e

To find all descendants of a particular node, you would do a "STARTSWITH" query on the path column, ie. all nodes with a path that starts with a*c*

To find out if a particular node is a descendant of another node, you would see if the longest path started with the shortest path.

So for instance:

• e is a descendant of a since a*c*e starts with a
• d is a descendant of c since a*c*d starts with a*c

Would that be useful in your instance?