LCA.java

package tree;

/**
 * Created by gouthamvidyapradhan on 21/03/2017.
 * Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree.
 * <p>
 * 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).”
 * <p>
 * _______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 LCA {
    public class TreeNode {
        int val;
        TreeNode left;
        TreeNode right;

        TreeNode(int x) {
            val = x;
        }
    }

    /**
     * Main method
     *
     * @param args
     * @throws Exception
     */
    public static void main(String[] args) throws Exception {

    }

    public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
        if (root != null) {
            if (root.equals(p) || root.equals(q)) return root;
            TreeNode left = lowestCommonAncestor(root.left, p, q);
            TreeNode right = lowestCommonAncestor(root.right, p, q);
            if (left != null && right != null) return root;
            else if (left != null) return left;
            else return right;
        }
        return null;
    }


}