# Subtree

## Problem

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

## Note

A tree T2 is a subtree of T1 if there exists a node n in T1 such that the subtree of n is identical to T2. That is, if you cut off the tree at node n, the two trees would be identical.

## Code - Java

/**
* Definition of TreeNode:
* public class TreeNode {
*   public int val;
*   public TreeNode left, right;
*   public TreeNode(int val) {
*     this.val = val;
*     this.left = this.right = null;
*   }
* }
*/
public class Solution {
/**
* @param T1, T2: The roots of binary tree.
* @return: True if T2 is a subtree of T1, or false.
*/
public boolean isSubtree(TreeNode T1, TreeNode T2) {
if (T2 == null) {
return true;
}

if (T1 == null) {
return false;
}

return same(T1, T2) || isSubtree(T1.left, T2) || isSubtree(T1.right, T2);
}

private boolean same(TreeNode T1, TreeNode T2) {
if (T1 == null && T2 == null) return true;
if (T1 == null || T2 == null || T1.val != T2.val) return false;
return same(T1.left, T2.left) && same(T1.right, T2.right);
}
}