from node import Leaf


def generate_line(root):
    """
    Print an expression tree in a single text line. Where needed, add
    parentheses.

    >>> from node import Node, Leaf
    >>> l0, l1 = Leaf(1), Leaf(2)
    >>> plus = Node('+', l0, l1)
    >>> print generate_line(plus)
    1 + 2

    >>> plus2 = Node('+', l0, l1)
    >>> times = Node('*', plus, plus2)
    >>> print generate_line(times)
    (1 + 2)(1 + 2)

    >>> l2 = Leaf(3)
    >>> uminus = Node('-', l2)
    >>> times = Node('*', plus, uminus)
    >>> print generate_line(times)
    (1 + 2) * -3

    >>> exp = Leaf('x')
    >>> inf = Leaf('oo')
    >>> minus_inf = Node('-', inf)
    >>> integral = Node('int', exp, minus_inf, inf)
    >>> print generate_line(integral)
    int(x, -oo, oo)
    """

    operators = [
            ('+', '-'),
            ('*', '/', 'mod'),
            ('^', )
            ]

    max_pred = len(operators)

    def is_operator(node):
        """
        Check if a given node is an operator (otherwise, it's a function).
        """
        label = node.title()
        either = lambda a, b: a or b

        return reduce(either, map(lambda x: label in x, operators))

    def pred(node):
        """
        Get the precedence of an operator node.
        """
        # Check binary and n-ary operators
        if not isinstance(node, Leaf) and len(node) > 1:
            op = node.title()

            for i, group in enumerate(operators):
                if op in group:
                    return i

        # Unary operator and leaves have highest precedence
        return max_pred

    def traverse(node):
        """
        The expression tree is traversed using preorder traversal:
        1. Visit the root
        2. Traverse the subtrees in left-to-right order
        """
        if not node:
            return '<empty expression>'

        op = node.title()

        if not node.nodes:
            return op

        arity = len(node)

        if is_operator(node):
            if arity == 1:
                # Unary operator
                sub = node[0]
                sub_exp = traverse(sub)

                # Negated sub-expressions with spaces in them should be
                # enclosed in parentheses, unless they have a higher precedence
                # than subtraction are rewritten to a factor of a subtraction:
                # -(1 + 2)
                # -(1 - 2)
                # -4a
                # -(4 * 5)
                # 1 - 4 * 5
                # 1 + -(4 * 5)  ->  1 - 4 * 5
                if ' ' in sub_exp and not (not isinstance(sub, Leaf) \
                        and hasattr(node, 'marked_negation')
                        and pred(sub) > 0):
                    sub_exp = '(' + sub_exp + ')'

                result = op + sub_exp
            else:
                # N-ary operator
                node_pred = pred(node)
                result = ''
                sep = ' ' + op + ' '
                e = []

                # Mark added and subtracted negations for later use when adding
                # parentheses
                if op in ('+', '-'):
                    for child in node:
                        if child.title() == '-' and len(child) == 1:
                            child.marked_negation = True

                for i, child in enumerate(node):
                    exp = traverse(child)

                    # Check if there is a precedence conflict
                    # If so, add parentheses
                    child_pred = pred(child)

                    if child_pred < node_pred or \
                            (i and child_pred == node_pred \
                             and op != child.title()):
                        exp = '(' + exp + ')'

                    e.append(exp)

                if op == '*':
                    # Check if an explicit multiplication sign is nessecary
                    left, right = node

                    # Get the previous multiplication element if the arity is
                    # greater than 2
                    if left.title() == '*':
                        left = left[1]

                    # a * b -> ab
                    # a * 2 -> a * 2
                    # a * (b) -> a(b)
                    # (a) * b -> (a)b
                    # (a) * (b) -> (a)(b)
                    # 2 * a -> 2a
                    left_id = is_id(left)
                    right_id = is_id(right)
                    left_paren = e[0][-1] == ')'
                    right_paren = e[1][0] == '('
                    left_int = is_int(left)

                    if (left_id or left_paren or left_int) \
                            and (right_id or right_paren):
                        sep = ''

                result += sep.join(e)
        else:
            # Function call
            result = op + '(' + ', '.join(map(traverse, node)) + ')'

        # An addition with negation can be written as a subtraction, e.g.:
        # 1 + -2  ->  1 - 2
        return result.replace('+ -', '- ')

    return traverse(root)


def is_negation(node):
    if isinstance(node, Leaf):
        return False

    return node.title() == '-' and len(node) == 1


def is_id(node):
    if is_negation(node):
        return is_id(node[0])

    return isinstance(node, Leaf) and not node.title().isdigit()


def is_int(node):
    if is_negation(node):
        return is_int(node[0])

    return isinstance(node, Leaf) and node.title().isdigit()