Lowest Common Ancestor of Binary Tree(Not Binary Search Tree)

Question

I tried working out the problem using Tarjan\'s Algorithm and one algorithm from the website: http://discuss.techinterview.org/default.asp?interview.11.532716.6, but none is

Answer 1

The LCA algorithm tries to do a simple thing: Figure out paths from the two nodes in question to the root. Now, these two paths would have a common suffix (assuming that the path ends at the root). The LCA is the first node where the suffix begins.

Consider the following tree:

              r * 
               / \
            s *   *
             / \
          u *   * t
           /   / \
          * v *   *
             / \
            *   *

In order to find the LCA(u, v) we proceed as follows:

• Path from u to root: Path(u, r) = usr
• Path from v to root: Path(v, r) = vtsr

Now, we check for the common suffix:

• Common suffix: 'sr'
• Therefore LCA(u, v) = first node of the suffix = s

Note the actual algorithms do not go all the way up to the root. They use Disjoint-Set data structures to stop when they reach s.

An excellent set of alternative approaches are explained here.