/*
Problem 236: Lowest Common Ancestor of a Binary

Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree.

According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined
between two nodes v and w as the lowest node in T that has both v and w as descendants
(where we allow a node to be a descendant of itself).”

        _______3______
       /              \
    ___5__          ___1__
   /      \        /      \
   6      _2       0       8
         /  \
         7   4
For example, the lowest common ancestor (LCA) of nodes 5 and 1 is 3.
Another example is LCA of nodes 5 and 4 is 5, since a node can be a descendant of
itself according to the LCA definition.
*/

public class LowestCommonAncestor {

  public class TreeNode {
    int val;
    TreeNode left, right;
    TreeNode(int x) {
      val = x;
    }
  }

  public static TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {

    if (root == null || root == p || root == q)
      return root;


    TreeNode left = lowestCommonAncestor(root.left, p, q);
    TreeNode right = lowestCommonAncestor(root.right, p, q);

    if (left != null && right != null)
      return root;

    return (left == null) ? right : left;

  }
}