How to write parentheses for binary tree?
<p>Here I am trying to combine the binary tree into expression. For instance </p>

<p>b1 = BinaryTree(3.0)</p>

<p>print(parenthesize(b1))</p>

<p>3.0</p>

<p>b2 = BinaryTree(4.0)</p>

<p>b3 = BinaryTree(7.0)</p>

<p>b4 = BinaryTree("*", b1, b2)</p>

<p>b5 = BinaryTree("+", b4, b3)</p>

<p>print(parenthesize(b5))`</p>

<p>((3.0 * 4.0) + 7.0)</p>

<p>The code I write for <code>parenthesize()</code> is at the bottom and the above are the Binary tree base code. But my code, instead of returning "somenumber", it returns 
("somenumber"). When I delete the  "(", the parenthesizes totally disappeared. Could someone help fill the code? </p>

<pre><code>class BinaryTree:
"""
A Binary Tree, i.e. arity 2.

=== Attributes ===
@param object data: data for this binary tree node
@param BinaryTree|None left: left child of this binary tree node
@param BinaryTree|None right: right child of this binary tree node
"""

def __init__(self, data, left=None, right=None):
    """
    Create BinaryTree self with data and children left and right.

    @param BinaryTree self: this binary tree
    @param object data: data of this node
    @param BinaryTree|None left: left child
    @param BinaryTree|None right: right child
    @rtype: None
    """
    self.data, self.left, self.right = data, left, right

def __eq__(self, other):
    """
    Return whether BinaryTree self is equivalent to other.

    @param BinaryTree self: this binary tree
    @param Any other: object to check equivalence to self
    @rtype: bool

    &gt;&gt;&gt; BinaryTree(7).__eq__("seven")
    False
    &gt;&gt;&gt; b1 = BinaryTree(7, BinaryTree(5))
    &gt;&gt;&gt; b1.__eq__(BinaryTree(7, BinaryTree(5), None))
    True
    """
    return (type(self) == type(other) and
            self.data == other.data and
            (self.left, self.right) == (other.left, other.right))

def __repr__(self):
    """
    Represent BinaryTree (self) as a string that can be evaluated to
    produce an equivalent BinaryTree.

    @param BinaryTree self: this binary tree
    @rtype: str

    &gt;&gt;&gt; BinaryTree(1, BinaryTree(2), BinaryTree(3))
    BinaryTree(1, BinaryTree(2, None, None), BinaryTree(3, None, None))
    """
    return "BinaryTree({}, {}, {})".format(repr(self.data),
                                           repr(self.left),
                                           repr(self.right))

def __str__(self, indent=""):
    """
    Return a user-friendly string representing BinaryTree (self)
    inorder.  Indent by indent.

    &gt;&gt;&gt; b = BinaryTree(1, BinaryTree(2, BinaryTree(3)), BinaryTree(4))
    &gt;&gt;&gt; print(b)
        4
    1
        2
            3
    &lt;BLANKLINE&gt;
    """
    right_tree = (self.right.__str__(
        indent + "    ") if self.right else "")
    left_tree = self.left.__str__(indent + "    ") if self.left else ""
    return (right_tree + "{}{}\n".format(indent, str(self.data)) +
            left_tree)

def __contains__(self, value):
    """
    Return whether tree rooted at node contains value.

    @param BinaryTree self: binary tree to search for value
    @param object value: value to search for
    @rtype: bool

    &gt;&gt;&gt; BinaryTree(5, BinaryTree(7), BinaryTree(9)).__contains__(7)
    True
    """
    return (self.data == value or
            (self.left and value in self.left) or
            (self.right and value in self.right))

def parenthesize(b):
"""
Return a parenthesized expression equivalent to the arithmetic
expression tree rooted at b.

Assume:  -- b is a binary tree
         -- interior nodes contain data in {'+', '-', '*', '/'}
         -- interior nodes always have two children
         -- leaves contain float data

@param BinaryTree b: arithmetic expression tree
@rtype: str

&gt;&gt;&gt; b1 = BinaryTree(3.0)
&gt;&gt;&gt; print(parenthesize(b1))
3.0
&gt;&gt;&gt; b2 = BinaryTree(4.0)
&gt;&gt;&gt; b3 = BinaryTree(7.0)
&gt;&gt;&gt; b4 = BinaryTree("*", b1, b2)
&gt;&gt;&gt; b5 = BinaryTree("+", b4, b3)
&gt;&gt;&gt; print(parenthesize(b5))
((3.0 * 4.0) + 7.0)
"""
if b is None:
    return ''
else:
    return "("+parenthesize(b.left)+str(b.data)+parenthesize(b.right)+")"
</code></pre>