Tree to DLL Conversion

Implement an in-place algorithm that converts a given binary tree into a doubly linked list (DLL). The left and right pointers in each node must be used as previous and next pointers respectively in the DLL. The order of the nodes in the doubly linked list should reflect the in-order traversal of the binary tree.

Requirements:

• Do not use any additional data structures (like auxiliary arrays or lists) to store nodes.
• The conversion should be done in-place, reusing the original node pointers.
• The head of the DLL should point to the smallest element (i.e., the first node in in-order traversal).
• Write a function or method that takes the root of the binary tree as input and returns the head of the resulting doubly linked list.

Example:

Given the binary tree:

      10
     /  \
    6    14
   / \   / \
  4   8 12  16

The resulting doubly linked list should have the nodes in the following order:

4 <-> 6 <-> 8 <-> 10 <-> 12 <-> 14 <-> 16

Assume that the tree nodes are defined with at least the following structure:

class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left  # Points to the previous node in DLL
        self.right = right  # Points to the next node in DLL

Your task is to write the conversion function and verify (through code or tests) that the resulting doubly linked list has the correct order and pointers.

Feel free to choose your preferred programming language and style. No additional libraries should be used unless absolutely necessary.