graph_drawing/line.py

from traverse import traverse_depth_first


OPERATORS = (
    ('vv', ),
    ('^^', ),
    ('=', ),
    ('+', '-'),
    ('*', 'mod'),
    ('/', ),
    ('^', '_'),
)

NEG_PRED = 3
MAX_PRED = len(OPERATORS)


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

    return any(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 node.is_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 is_id(node):
    return node.is_leaf and not node.title().isdigit()


def is_int(node):
    return node.is_leaf and node.title().isdigit()


def is_power(node):
    return not node.is_leaf and node.title() == '^'


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)
    >>> print generate_line(l0)
    1

    >>> 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)

    >>> minus = Node('-', Leaf(2), Node('-', Node('*', Leaf(15), Leaf('x'))))
    >>> print generate_line(minus)
    2 - -15x

    >>> left = Node('/', Leaf(22), Leaf(77))
    >>> right = Node('/', Leaf(28), Leaf(77))
    >>> minus = Node('-', left, right)
    >>> print generate_line(minus)
    22 / 77 - 28 / 77

    >>> plus = Node('+', left, Node('-', right))
    >>> print generate_line(plus)
    22 / 77 - 28 / 77
    """

    if not root:
        return '<empty expression>'

    if root.is_leaf:
        return str(root)

    content = {}

    def construct_unary(node):
        op = node.title()
        value = node[0]

        # -a
        # -3 * 4
        # --a
        if value.is_leaf \
                or not ' ' in content[value] or pred(value) > NEG_PRED:
            return op + content[value]

        # -(a + b)
        return '%s(%s)' % (op, content[value])


    def construct_nary(node):
        op = node.title()

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

        for i, child in enumerate(node):
            exp = content[child]

            #if i and op == '+' and exp[:2] == '-(':
            #    exp = '-' + exp[2:-1]
            #    print 'exp:', exp

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

            if child.negated:
                # (-a) ^ b
                # -a ^ -b
                # (-a) * b
                # a * -b
                # (-a) / b
                if node_pred > NEG_PRED:
                    exp = '(' + exp + ')'
            elif child_pred < node_pred:
                exp = '(' + exp + ')'
            elif child_pred == node_pred:
                if i and (op != child.title() or op == '/' \
                          or (op == '+' and child[1].negated)):
                    exp = '(' + exp + ')'
                elif not i and op == '^':
                    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
            l = e[0][-1]
            r = e[1][0]
            left_simple = is_id(left) or is_int(left)

            if (r in ('(', '[') and left_simple) or (l == ')' and r != '-') \
                    or (left_simple and r.isalpha()):
                sep = ''

        exp = sep.join(e)

        if node.negated and op not in ('*', '/', '^'):
            exp = '(' + exp + ')'

        return exp

    def construct_function(node):
        buf = []

        for child in node:
            buf.append(content[child])

        return '%s(%s)' % (node.title(), ', '.join(buf))

    # Traverse the expression tree and construct the mathematical expression in
    # the leafs and nodes in depth first order.
    for node in traverse_depth_first(root):
        if node.is_leaf:
            content[node] = str(node)
        else:
            arity = len(node)

            if is_operator(node):
                if arity == 1:
                    content[node] = construct_unary(node)
                else:
                    content[node] = construct_nary(node)
            else:
                result = None

                if hasattr(node, 'construct_function'):
                    children = [content[c] for c in node]
                    result = node.construct_function(children)

                if result == None:
                    result = construct_function(node)

                content[node] = result

            # Add negations
            content[node] = '-' * node.negated + content[node]

    # Merge binary plus and unary minus signs into binary minus.
    return content[root].replace('+ -', '- ')