Implementing a binary tree

We will now create a binary tree (not a binary search tree). The key factor to have in a binary tree is that we must have two placeholders for the left child node and the right child node, along with the data we want to store in the node. A simple implementation of a binary node will look like this:

class BinaryNode { 

    public $data; 
    public $left; 
    public $right; 

    public function __construct(string $data = NULL) { 
      $this->data = $data; 
      $this->left = NULL; 
      $this->right = NULL; 
    } 

    public function addChildren(BinaryNode $left, BinaryNode $right) { 
      $this->left = $left;
      $this->right = $right;
    }

}

The preceding code shows that we have a class with tree properties to store data, left and right. When we are constructing a new node, we are adding the node value to the data property, and left and...