/**
 * 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 p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself).”
 *
 * Given the following binary tree:  root = [3,5,1,6,2,0,8,null,null,7,4]
 *
 * Example 1:
 *
 * Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1
 * Output: 3
 * Explanation: The LCA of nodes 5 and 1 is 3.
 * Example 2:
 *
 * Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 4
 * Output: 5
 * Explanation: The LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.
 *
 *
 * Note:
 *
 * All of the nodes' values will be unique.
 * p and q are different and both values will exist in the binary tree.
 */
public class LowestCommonAncestor {
    public class TreeNode {
        int val;
        TreeNode left;
        TreeNode right;
        TreeNode(int x) { val = x; }
    }
    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        if (root == null) return null;
        TreeNode result = null;
        int mid = 0;
        TreeNode left = lowestCommonAncestor(root.left, p, q);
        if (left != null) {
            mid++;
            result = left;
        }
        TreeNode right = lowestCommonAncestor(root.right, p, q);
        if (right != null) {
            mid++;
            result = right;
        }
        if (root.val == p.val || root.val == q.val || mid == 2) {
            result = root;
        }
        return result;
    }
}
