!!! USING C++ !!!!

Given a binary tree, determine if it is a valid binary search tree (BST).

Assume a BST is defined as follows:

The left subtree of a node contains only nodes with keys less than the node's key.

The right subtree of a node contains only nodes with keys greater than the node's key.

Both the left and right subtrees must also be binary search trees.

Here's an example: ('#' represents path terminator)

 1 / \ 2 3 / 4 \ 5 

The above binary tree is serialized as "{1,2,3,#,#,4,#,#,5}".