Symmetric Tree

/**
 * Definition for binary tree
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public boolean isSymmetric(TreeNode root) {
        // Note: The Solution object is instantiated only once and is reused by each test case.
        if(root == null) return true;  //{} is symmetric
        return checkChild(root.left, root.right);
    }
    private boolean checkChild(TreeNode x, TreeNode y){
        if(x == null && y == null)  return true;    // traverse to the leaf nodes
        else if(x == null || y == null) return false;   //not complete binary tree
        else if(x.val != y.val) return false;
        else return (checkChild(x.left, y.right) & checkChild(x.right, y.left));
    }
}