graph_drawing/line.py

from traverse import traverse_depth_first
from node import Node


all_parens = ('()', '[]', '||', '{}')
OPERATORS = (
    ('left', ('vv', )),
    ('left', ('^^', )),
    ('left', ('=', )),
    ('left', ('+', '-')),
    ('nonassoc', ('int', 'd/d')),
    ('left', ('*', 'mod')),
    ('left', ('/', )),
    ('nonassoc', ('\'', )),
    ('nonassoc', ('neg', )),
    ('nonassoc', ('function', )),
    ('right', ('^', '_')),
    ('nonassoc', all_parens),
)

assocs = {}
preds = {}

for i, (assoc, ops) in enumerate(OPERATORS):
    for op in ops:
        assocs[op] = assoc
        preds[op] = i

NEG_PRED = preds['neg']
FUNC_PRED = preds['function']
MAX_PRED = len(OPERATORS)


def is_function(node):
    """
    Check if a given node is a function. A node is considered a function if it
    is not a leaf, and is not known in the precedences list above.
    """
    return not node.is_leaf and node.title() not in preds


def pred(node):
    """
    Get the operator precedence of a node. Leaf nodes have the highest
    precedence for practical reasons.
    """
    # Check known operators
    if not node.is_leaf:
        op = node.title()

        if node.is_negation():
            if node[0].title() in '*/':
                return preds['-']

            return NEG_PRED

        #if node.is_postfix() and not node[0].is_leaf \
        #        and node[0].title() in all_parens:
        #    return preds['()']

        if op in preds:
            return preds[op]

        return FUNC_PRED

    # Unary operator and leaves have highest precedence
    return MAX_PRED


def rightmost_node(node):
    if node.is_leaf or not len(node):
        return node

    return rightmost_node(node[-1])


def is_unary_prefix(node):
    """
    Check if a node is a unary operator that is placed before the operand.
    """
    return not node.is_leaf and len(node) == 1 and node.title() == '-'


def is_left_assoc(op):
    return op in assocs and assocs[op] == 'left'


def is_right_assoc(op):
    return op in assocs and assocs[op] == 'right'


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 preprocess_node(node):
    node = node.clone()
    node.preprocess_str_exp()

    if node.negated:
        node.negated -= 1
        return Node('-', preprocess_node(node))

    if not node.is_leaf:
        for i, child in enumerate(node):
            node[i] = preprocess_node(child)

        if node.title() == '+' and node[1].is_negation():
            return Node('-', node[0], node[1][0])

    return node


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

    >>> 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 mult_sign(left, right, lparens, rparens):
        # Get the previous multiplication element in an nary multiplication
        if left.title() == '*':
            left = rightmost_node(left)

        # a * b -> ab
        # a * 2 -> a * 2
        # a * (b) -> a(b)
        # (a) * b -> (a)b
        # (a) * (b) -> (a)(b)
        # 2 * a -> 2a
        # a * sin(b) -> a sin(b)
        left_char = content[left][-1]
        right_char = content[right][0]
        left_paren = lparens or left_char in ')]}'
        right_paren = rparens or right_char in '([{'
        right_alpha = right_char.isalpha()
        left_simple = is_id(left) or is_int(left)

        if left_paren or (right_paren and left_simple) \
                or (is_id(left) and is_id(right)) \
                or (is_int(left) and right_alpha):
            return ''

        if is_id(left) and right_alpha:
            return ' '

        return ' * '

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

        if op in ('()', '[]', '||', '{}'):
            return op[0] + strval + op[1]

        parens = False

        if pred(value) < pred(node):
            parens = not value.is_negation()
        elif pred(value) == pred(node):
            parens = len(value) > 1

        if parens:
            strval = '(' + strval + ')'

        if node.is_postfix():
            return strval + node.operator()

        prefix = node.operator()

        if prefix != '-' and not (strval[0] in '([|{' and is_function(node)):
            prefix += ' '

        return prefix + strval

    def construct_binary(node):
        op = node.title()
        op_pred = pred(node)

        if node.no_spacing:
            sep = node.operator()
        else:
            sep = ' ' + node.operator() + ' '

        left, right = node
        lstr = content[left]
        rstr = content[right]
        lpred = pred(left)
        rpred = pred(right)
        lparens = rparens = False
        unary_right = is_unary_prefix(right)

        if lpred < op_pred or (op in '*/' and left.is_negation()):
            lparens = True
        elif lpred == op_pred:
            lparens = is_right_assoc(left.title()) or is_right_assoc(op)

        if rpred < op_pred:
            rparens = not unary_right
        elif rpred == op_pred and len(right) > 1:
            if right.title() == op:
                rparens = not is_right_assoc(op)
            elif is_left_assoc(right.title()):
                rparens = True

        # Check if multiplication sig is necessary
        if op == '*' and not unary_right:
            sep = mult_sign(left, right, lparens, rparens)

        if lparens:
            lstr = '(' + lstr + ')'

        if rparens:
            rstr = '(' + rstr + ')'

        return lstr + sep + rstr

    def construct_nary_mult(node):
        op_pred = pred(node)
        lstr = content[node[0]]
        lparens = pred(node[0]) < op_pred or node[0].is_negation()

        if lparens:
            lstr = '(' + lstr + ')'

        for i, right in enumerate(node[1:]):
            rparens = pred(right) < op_pred
            rstr = content[right]

            if rparens:
                rstr = '(' + rstr + ')'

            sign = mult_sign(node[i], right, lparens, rparens)
            lstr += sign + rstr
            lparens = rparens

        return lstr

    def construct_nary(node):
        if node.title() == '*':
            return construct_nary_mult(node)

        op_pred = pred(node)
        e = []

        for child in node:
            exp = content[child]

            if pred(child) < op_pred:
                exp = '(' + exp + ')'

            e.append(exp)

        return (' ' + node.operator() + ' ').join(e)

    def construct_function(node):
        children = [content[child] for child in node]
        return '%s(%s)' % (node.operator(), ', '.join(children))

    # Convert negations to unary nodes to be able to account for operator
    # precedence
    root = preprocess_node(root.clone())

    # 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):
        custom = node.custom_line()

        if custom is not None:
            content[node] = custom
            continue

        if node.is_leaf:
            nodestr = str(node.value)
        else:
            arity = node.arity()

            if arity == 1:
                nodestr = construct_unary(node)
            elif is_function(node):
                nodestr = construct_function(node)
            elif arity == 2:
                nodestr = construct_binary(node)
            else:
                nodestr = construct_nary(node)

        content[node] = node.postprocess_str(nodestr)

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