二叉树判断子树问题

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Question:

You have two very 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.

Answer:

1) 分别求出T1和T2的前序和中序遍历的字符串，判断T2是否为T1的子串（利用KMP或者后缀树），复杂度O(n)。

2) 递归求解，复杂度O(m*n)

boolean containsTree(TreeNode t1, TreeNode t2) 
{
	if (t2 == null) return true; // The empty tree is always a subtree
	else return subTree(t1, t2);
}

boolean subTree(TreeNode r1, TreeNode r2) {
	if (r1 == null)
		return false; // big tree empty & subtree still not found.
	if (r1.data == r2.data) {
		if (matchTree(r1,r2)) return true;
	}
	return (subTree(r1.left, r2) || subTree(r1.right, r2));
}

boolean matchTree(TreeNode r1, TreeNode r2) {
	if (r2 == null && r1 == null)
		return true; // nothing left in the subtree
	if (r1 == null || r2 == null)
		return false; // big tree empty & subtree still not found
	if (r1.data != r2.data)
		return false; // data doesn’t match
	return (matchTree(r1.left, r2.left) && matchTree(r1.right, r2.right));
}