Subtree

You have two every large binary trees: T1, with millions of nodes, and T2, with hundreds of nodes. Create an algorithm to decide if T2 is a subtree of T1.

Example

T2 is a subtree of T1 in the following case:

       1                3
      / \              / 
T1 = 2   3      T2 =  4
        /
       4

T2 isn't a subtree of T1 in the following case:

       1               3
      / \               \
T1 = 2   3       T2 =    4
        /
       4

/**
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left, right;
 *     public TreeNode(int val) {
 *         this.val = val;
 *         this.left = this.right = null;
 *     }
 * }
 */

//time:O(mn), space:O(1)

public class Solution {
    public boolean isSubtree(TreeNode T1, TreeNode T2) {
        if (T2 == null) {
            return true;
        }
        if (T1 == null) {
            return false;
        }
        if (identical(T1, T2)) {
            return true;
        }
        if (isSubtree(T1.left, T2) || isSubtree(T1.right, T2)) {
            return true;
        }
        return false;
    }
    
    public boolean identical(TreeNode root1, TreeNode root2) {
        if (root1 == null || root2 == null) {
            return root1 == root2;
        }
        if (root1.val != root2.val) {
            return false;
        }
        return identical(root1.left, root2.left) && 
               identical(root1.right, root2.right);
    }
}