580 lines
24 KiB
Python
580 lines
24 KiB
Python
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# Natural Language Toolkit: Dependency Grammars
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#
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# Copyright (C) 2001-2018 NLTK Project
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# Author: Jason Narad <jason.narad@gmail.com>
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#
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# URL: <http://nltk.org/>
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# For license information, see LICENSE.TXT
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#
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from __future__ import print_function, unicode_literals
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from collections import defaultdict
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from itertools import chain
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from functools import total_ordering
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from nltk.grammar import (DependencyProduction, DependencyGrammar,
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ProbabilisticDependencyGrammar)
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from nltk.parse.dependencygraph import DependencyGraph
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from nltk.internals import raise_unorderable_types
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from nltk.compat import python_2_unicode_compatible
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#################################################################
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# Dependency Span
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#################################################################
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@total_ordering
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@python_2_unicode_compatible
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class DependencySpan(object):
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"""
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A contiguous span over some part of the input string representing
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dependency (head -> modifier) relationships amongst words. An atomic
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span corresponds to only one word so it isn't a 'span' in the conventional
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sense, as its _start_index = _end_index = _head_index for concatenation
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purposes. All other spans are assumed to have arcs between all nodes
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within the start and end indexes of the span, and one head index corresponding
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to the head word for the entire span. This is the same as the root node if
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the dependency structure were depicted as a graph.
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"""
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def __init__(self, start_index, end_index, head_index, arcs, tags):
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self._start_index = start_index
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self._end_index = end_index
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self._head_index = head_index
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self._arcs = arcs
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self._tags = tags
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self._comparison_key = (start_index, end_index, head_index, tuple(arcs))
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self._hash = hash(self._comparison_key)
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def head_index(self):
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"""
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:return: An value indexing the head of the entire ``DependencySpan``.
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:rtype: int
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"""
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return self._head_index
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def __repr__(self):
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"""
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:return: A concise string representatino of the ``DependencySpan``.
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:rtype: str.
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"""
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return 'Span %d-%d; Head Index: %d' % (self._start_index, self._end_index, self._head_index)
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def __str__(self):
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"""
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:return: A verbose string representation of the ``DependencySpan``.
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:rtype: str
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"""
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str = 'Span %d-%d; Head Index: %d' % (self._start_index, self._end_index, self._head_index)
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for i in range(len(self._arcs)):
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str += '\n%d <- %d, %s' % (i, self._arcs[i], self._tags[i])
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return str
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def __eq__(self, other):
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return (type(self) == type(other) and
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self._comparison_key == other._comparison_key)
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def __ne__(self, other):
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return not self == other
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def __lt__(self, other):
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if not isinstance(other, DependencySpan):
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raise_unorderable_types("<", self, other)
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return self._comparison_key < other._comparison_key
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def __hash__(self):
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"""
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:return: The hash value of this ``DependencySpan``.
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"""
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return self._hash
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#################################################################
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# Chart Cell
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#################################################################
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@python_2_unicode_compatible
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class ChartCell(object):
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"""
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A cell from the parse chart formed when performing the CYK algorithm.
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Each cell keeps track of its x and y coordinates (though this will probably
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be discarded), and a list of spans serving as the cell's entries.
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"""
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def __init__(self, x, y):
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"""
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:param x: This cell's x coordinate.
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:type x: int.
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:param y: This cell's y coordinate.
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:type y: int.
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"""
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self._x = x
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self._y = y
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self._entries = set([])
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def add(self, span):
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"""
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Appends the given span to the list of spans
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representing the chart cell's entries.
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:param span: The span to add.
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:type span: DependencySpan
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"""
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self._entries.add(span)
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def __str__(self):
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"""
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:return: A verbose string representation of this ``ChartCell``.
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:rtype: str.
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"""
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return 'CC[%d,%d]: %s' % (self._x, self._y, self._entries)
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def __repr__(self):
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"""
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:return: A concise string representation of this ``ChartCell``.
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:rtype: str.
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"""
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return '%s' % self
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#################################################################
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# Parsing with Dependency Grammars
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#################################################################
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class ProjectiveDependencyParser(object):
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"""
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A projective, rule-based, dependency parser. A ProjectiveDependencyParser
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is created with a DependencyGrammar, a set of productions specifying
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word-to-word dependency relations. The parse() method will then
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return the set of all parses, in tree representation, for a given input
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sequence of tokens. Each parse must meet the requirements of the both
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the grammar and the projectivity constraint which specifies that the
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branches of the dependency tree are not allowed to cross. Alternatively,
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this can be understood as stating that each parent node and its children
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in the parse tree form a continuous substring of the input sequence.
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"""
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def __init__(self, dependency_grammar):
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"""
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Create a new ProjectiveDependencyParser, from a word-to-word
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dependency grammar ``DependencyGrammar``.
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:param dependency_grammar: A word-to-word relation dependencygrammar.
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:type dependency_grammar: DependencyGrammar
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"""
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self._grammar = dependency_grammar
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def parse(self, tokens):
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"""
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Performs a projective dependency parse on the list of tokens using
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a chart-based, span-concatenation algorithm similar to Eisner (1996).
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:param tokens: The list of input tokens.
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:type tokens: list(str)
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:return: An iterator over parse trees.
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:rtype: iter(Tree)
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"""
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self._tokens = list(tokens)
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chart = []
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for i in range(0, len(self._tokens) + 1):
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chart.append([])
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for j in range(0, len(self._tokens) + 1):
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chart[i].append(ChartCell(i,j))
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if i==j+1:
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chart[i][j].add(DependencySpan(i-1,i,i-1,[-1], ['null']))
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for i in range(1,len(self._tokens)+1):
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for j in range(i-2,-1,-1):
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for k in range(i-1,j,-1):
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for span1 in chart[k][j]._entries:
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for span2 in chart[i][k]._entries:
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for newspan in self.concatenate(span1, span2):
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chart[i][j].add(newspan)
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for parse in chart[len(self._tokens)][0]._entries:
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conll_format = ""
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# malt_format = ""
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for i in range(len(tokens)):
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# malt_format += '%s\t%s\t%d\t%s\n' % (tokens[i], 'null', parse._arcs[i] + 1, 'null')
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#conll_format += '\t%d\t%s\t%s\t%s\t%s\t%s\t%d\t%s\t%s\t%s\n' % (i+1, tokens[i], tokens[i], 'null', 'null', 'null', parse._arcs[i] + 1, 'null', '-', '-')
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# Modify to comply with the new Dependency Graph requirement (at least must have an root elements)
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conll_format += '\t%d\t%s\t%s\t%s\t%s\t%s\t%d\t%s\t%s\t%s\n' % (i+1, tokens[i], tokens[i], 'null', 'null', 'null', parse._arcs[i] + 1, 'ROOT', '-', '-')
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dg = DependencyGraph(conll_format)
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# if self.meets_arity(dg):
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yield dg.tree()
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def concatenate(self, span1, span2):
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"""
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Concatenates the two spans in whichever way possible. This
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includes rightward concatenation (from the leftmost word of the
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leftmost span to the rightmost word of the rightmost span) and
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leftward concatenation (vice-versa) between adjacent spans. Unlike
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Eisner's presentation of span concatenation, these spans do not
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share or pivot on a particular word/word-index.
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:return: A list of new spans formed through concatenation.
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:rtype: list(DependencySpan)
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"""
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spans = []
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if span1._start_index == span2._start_index:
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print('Error: Mismatched spans - replace this with thrown error')
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if span1._start_index > span2._start_index:
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temp_span = span1
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span1 = span2
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span2 = temp_span
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# adjacent rightward covered concatenation
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new_arcs = span1._arcs + span2._arcs
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new_tags = span1._tags + span2._tags
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if self._grammar.contains(self._tokens[span1._head_index], self._tokens[span2._head_index]):
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# print 'Performing rightward cover %d to %d' % (span1._head_index, span2._head_index)
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new_arcs[span2._head_index - span1._start_index] = span1._head_index
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spans.append(DependencySpan(span1._start_index, span2._end_index, span1._head_index, new_arcs, new_tags))
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# adjacent leftward covered concatenation
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new_arcs = span1._arcs + span2._arcs
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if self._grammar.contains(self._tokens[span2._head_index], self._tokens[span1._head_index]):
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# print 'performing leftward cover %d to %d' % (span2._head_index, span1._head_index)
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new_arcs[span1._head_index - span1._start_index] = span2._head_index
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spans.append(DependencySpan(span1._start_index, span2._end_index, span2._head_index, new_arcs, new_tags))
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return spans
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#################################################################
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# Parsing with Probabilistic Dependency Grammars
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#################################################################
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class ProbabilisticProjectiveDependencyParser(object):
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"""A probabilistic, projective dependency parser.
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This parser returns the most probable projective parse derived from the
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probabilistic dependency grammar derived from the train() method. The
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probabilistic model is an implementation of Eisner's (1996) Model C, which
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conditions on head-word, head-tag, child-word, and child-tag. The decoding
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uses a bottom-up chart-based span concatenation algorithm that's identical
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to the one utilized by the rule-based projective parser.
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Usage example
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-------------
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>>> from nltk.parse.dependencygraph import conll_data2
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>>> graphs = [
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... DependencyGraph(entry) for entry in conll_data2.split('\\n\\n') if entry
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... ]
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>>> ppdp = ProbabilisticProjectiveDependencyParser()
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>>> ppdp.train(graphs)
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>>> sent = ['Cathy', 'zag', 'hen', 'wild', 'zwaaien', '.']
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>>> list(ppdp.parse(sent))
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[Tree('zag', ['Cathy', 'hen', Tree('zwaaien', ['wild', '.'])])]
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"""
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def __init__(self):
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"""
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Create a new probabilistic dependency parser. No additional
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operations are necessary.
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"""
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def parse(self, tokens):
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"""
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Parses the list of tokens subject to the projectivity constraint
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and the productions in the parser's grammar. This uses a method
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similar to the span-concatenation algorithm defined in Eisner (1996).
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It returns the most probable parse derived from the parser's
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probabilistic dependency grammar.
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"""
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self._tokens = list(tokens)
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chart = []
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for i in range(0, len(self._tokens) + 1):
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chart.append([])
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for j in range(0, len(self._tokens) + 1):
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chart[i].append(ChartCell(i,j))
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if i==j+1:
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if tokens[i-1] in self._grammar._tags:
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for tag in self._grammar._tags[tokens[i-1]]:
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chart[i][j].add(DependencySpan(i-1,i,i-1,[-1], [tag]))
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else:
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print('No tag found for input token \'%s\', parse is impossible.' % tokens[i-1])
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return []
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for i in range(1,len(self._tokens)+1):
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for j in range(i-2,-1,-1):
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for k in range(i-1,j,-1):
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for span1 in chart[k][j]._entries:
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for span2 in chart[i][k]._entries:
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for newspan in self.concatenate(span1, span2):
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chart[i][j].add(newspan)
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trees = []
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max_parse = None
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max_score = 0
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for parse in chart[len(self._tokens)][0]._entries:
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conll_format = ""
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malt_format = ""
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for i in range(len(tokens)):
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malt_format += '%s\t%s\t%d\t%s\n' % (tokens[i], 'null', parse._arcs[i] + 1, 'null')
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#conll_format += '\t%d\t%s\t%s\t%s\t%s\t%s\t%d\t%s\t%s\t%s\n' % (i+1, tokens[i], tokens[i], parse._tags[i], parse._tags[i], 'null', parse._arcs[i] + 1, 'null', '-', '-')
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# Modify to comply with recent change in dependency graph such that there must be a ROOT element.
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conll_format += '\t%d\t%s\t%s\t%s\t%s\t%s\t%d\t%s\t%s\t%s\n' % (i+1, tokens[i], tokens[i], parse._tags[i], parse._tags[i], 'null', parse._arcs[i] + 1, 'ROOT', '-', '-')
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dg = DependencyGraph(conll_format)
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score = self.compute_prob(dg)
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trees.append((score, dg.tree()))
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trees.sort()
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return (tree for (score, tree) in trees)
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def concatenate(self, span1, span2):
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"""
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Concatenates the two spans in whichever way possible. This
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includes rightward concatenation (from the leftmost word of the
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leftmost span to the rightmost word of the rightmost span) and
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leftward concatenation (vice-versa) between adjacent spans. Unlike
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Eisner's presentation of span concatenation, these spans do not
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share or pivot on a particular word/word-index.
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:return: A list of new spans formed through concatenation.
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:rtype: list(DependencySpan)
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"""
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spans = []
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if span1._start_index == span2._start_index:
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print('Error: Mismatched spans - replace this with thrown error')
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if span1._start_index > span2._start_index:
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temp_span = span1
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span1 = span2
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span2 = temp_span
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# adjacent rightward covered concatenation
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new_arcs = span1._arcs + span2._arcs
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new_tags = span1._tags + span2._tags
|
||
|
|
if self._grammar.contains(self._tokens[span1._head_index], self._tokens[span2._head_index]):
|
||
|
|
new_arcs[span2._head_index - span1._start_index] = span1._head_index
|
||
|
|
spans.append(DependencySpan(span1._start_index, span2._end_index, span1._head_index, new_arcs, new_tags))
|
||
|
|
# adjacent leftward covered concatenation
|
||
|
|
new_arcs = span1._arcs + span2._arcs
|
||
|
|
new_tags = span1._tags + span2._tags
|
||
|
|
if self._grammar.contains(self._tokens[span2._head_index], self._tokens[span1._head_index]):
|
||
|
|
new_arcs[span1._head_index - span1._start_index] = span2._head_index
|
||
|
|
spans.append(DependencySpan(span1._start_index, span2._end_index, span2._head_index, new_arcs, new_tags))
|
||
|
|
return spans
|
||
|
|
|
||
|
|
def train(self, graphs):
|
||
|
|
"""
|
||
|
|
Trains a ProbabilisticDependencyGrammar based on the list of input
|
||
|
|
DependencyGraphs. This model is an implementation of Eisner's (1996)
|
||
|
|
Model C, which derives its statistics from head-word, head-tag,
|
||
|
|
child-word, and child-tag relationships.
|
||
|
|
|
||
|
|
:param graphs: A list of dependency graphs to train from.
|
||
|
|
:type: list(DependencyGraph)
|
||
|
|
"""
|
||
|
|
productions = []
|
||
|
|
events = defaultdict(int)
|
||
|
|
tags = {}
|
||
|
|
for dg in graphs:
|
||
|
|
for node_index in range(1, len(dg.nodes)):
|
||
|
|
#children = dg.nodes[node_index]['deps']
|
||
|
|
children = list(chain(*dg.nodes[node_index]['deps'].values()))
|
||
|
|
|
||
|
|
nr_left_children = dg.left_children(node_index)
|
||
|
|
nr_right_children = dg.right_children(node_index)
|
||
|
|
nr_children = nr_left_children + nr_right_children
|
||
|
|
for child_index in range(0 - (nr_left_children + 1), nr_right_children + 2):
|
||
|
|
head_word = dg.nodes[node_index]['word']
|
||
|
|
head_tag = dg.nodes[node_index]['tag']
|
||
|
|
if head_word in tags:
|
||
|
|
tags[head_word].add(head_tag)
|
||
|
|
else:
|
||
|
|
tags[head_word] = set([head_tag])
|
||
|
|
child = 'STOP'
|
||
|
|
child_tag = 'STOP'
|
||
|
|
prev_word = 'START'
|
||
|
|
prev_tag = 'START'
|
||
|
|
if child_index < 0:
|
||
|
|
array_index = child_index + nr_left_children
|
||
|
|
if array_index >= 0:
|
||
|
|
child = dg.nodes[children[array_index]]['word']
|
||
|
|
child_tag = dg.nodes[children[array_index]]['tag']
|
||
|
|
if child_index != -1:
|
||
|
|
prev_word = dg.nodes[children[array_index + 1]]['word']
|
||
|
|
prev_tag = dg.nodes[children[array_index + 1]]['tag']
|
||
|
|
if child != 'STOP':
|
||
|
|
productions.append(DependencyProduction(head_word, [child]))
|
||
|
|
head_event = '(head (%s %s) (mods (%s, %s, %s) left))' % (child, child_tag, prev_tag, head_word, head_tag)
|
||
|
|
mod_event = '(mods (%s, %s, %s) left))' % (prev_tag, head_word, head_tag)
|
||
|
|
events[head_event] += 1
|
||
|
|
events[mod_event] += 1
|
||
|
|
elif child_index > 0:
|
||
|
|
array_index = child_index + nr_left_children - 1
|
||
|
|
if array_index < nr_children:
|
||
|
|
child = dg.nodes[children[array_index]]['word']
|
||
|
|
child_tag = dg.nodes[children[array_index]]['tag']
|
||
|
|
if child_index != 1:
|
||
|
|
prev_word = dg.nodes[children[array_index - 1]]['word']
|
||
|
|
prev_tag = dg.nodes[children[array_index - 1]]['tag']
|
||
|
|
if child != 'STOP':
|
||
|
|
productions.append(DependencyProduction(head_word, [child]))
|
||
|
|
head_event = '(head (%s %s) (mods (%s, %s, %s) right))' % (child, child_tag, prev_tag, head_word, head_tag)
|
||
|
|
mod_event = '(mods (%s, %s, %s) right))' % (prev_tag, head_word, head_tag)
|
||
|
|
events[head_event] += 1
|
||
|
|
events[mod_event] += 1
|
||
|
|
self._grammar = ProbabilisticDependencyGrammar(productions, events, tags)
|
||
|
|
|
||
|
|
def compute_prob(self, dg):
|
||
|
|
"""
|
||
|
|
Computes the probability of a dependency graph based
|
||
|
|
on the parser's probability model (defined by the parser's
|
||
|
|
statistical dependency grammar).
|
||
|
|
|
||
|
|
:param dg: A dependency graph to score.
|
||
|
|
:type dg: DependencyGraph
|
||
|
|
:return: The probability of the dependency graph.
|
||
|
|
:rtype: int
|
||
|
|
"""
|
||
|
|
prob = 1.0
|
||
|
|
for node_index in range(1, len(dg.nodes)):
|
||
|
|
#children = dg.nodes[node_index]['deps']
|
||
|
|
children = list(chain(*dg.nodes[node_index]['deps'].values()))
|
||
|
|
|
||
|
|
nr_left_children = dg.left_children(node_index)
|
||
|
|
nr_right_children = dg.right_children(node_index)
|
||
|
|
nr_children = nr_left_children + nr_right_children
|
||
|
|
for child_index in range(0 - (nr_left_children + 1), nr_right_children + 2):
|
||
|
|
head_word = dg.nodes[node_index]['word']
|
||
|
|
head_tag = dg.nodes[node_index]['tag']
|
||
|
|
child = 'STOP'
|
||
|
|
child_tag = 'STOP'
|
||
|
|
prev_word = 'START'
|
||
|
|
prev_tag = 'START'
|
||
|
|
if child_index < 0:
|
||
|
|
array_index = child_index + nr_left_children
|
||
|
|
if array_index >= 0:
|
||
|
|
child = dg.nodes[children[array_index]]['word']
|
||
|
|
child_tag = dg.nodes[children[array_index]]['tag']
|
||
|
|
if child_index != -1:
|
||
|
|
prev_word = dg.nodes[children[array_index + 1]]['word']
|
||
|
|
prev_tag = dg.nodes[children[array_index + 1]]['tag']
|
||
|
|
head_event = '(head (%s %s) (mods (%s, %s, %s) left))' % (child, child_tag, prev_tag, head_word, head_tag)
|
||
|
|
mod_event = '(mods (%s, %s, %s) left))' % (prev_tag, head_word, head_tag)
|
||
|
|
h_count = self._grammar._events[head_event]
|
||
|
|
m_count = self._grammar._events[mod_event]
|
||
|
|
|
||
|
|
# If the grammar is not covered
|
||
|
|
if m_count != 0:
|
||
|
|
prob *= (h_count / m_count)
|
||
|
|
else:
|
||
|
|
prob = 0.00000001 # Very small number
|
||
|
|
|
||
|
|
elif child_index > 0:
|
||
|
|
array_index = child_index + nr_left_children - 1
|
||
|
|
if array_index < nr_children:
|
||
|
|
child = dg.nodes[children[array_index]]['word']
|
||
|
|
child_tag = dg.nodes[children[array_index]]['tag']
|
||
|
|
if child_index != 1:
|
||
|
|
prev_word = dg.nodes[children[array_index - 1]]['word']
|
||
|
|
prev_tag = dg.nodes[children[array_index - 1]]['tag']
|
||
|
|
head_event = '(head (%s %s) (mods (%s, %s, %s) right))' % (child, child_tag, prev_tag, head_word, head_tag)
|
||
|
|
mod_event = '(mods (%s, %s, %s) right))' % (prev_tag, head_word, head_tag)
|
||
|
|
h_count = self._grammar._events[head_event]
|
||
|
|
m_count = self._grammar._events[mod_event]
|
||
|
|
|
||
|
|
if m_count != 0:
|
||
|
|
prob *= (h_count / m_count)
|
||
|
|
else:
|
||
|
|
prob = 0.00000001 # Very small number
|
||
|
|
|
||
|
|
return prob
|
||
|
|
|
||
|
|
|
||
|
|
#################################################################
|
||
|
|
# Demos
|
||
|
|
#################################################################
|
||
|
|
|
||
|
|
def demo():
|
||
|
|
projective_rule_parse_demo()
|
||
|
|
# arity_parse_demo()
|
||
|
|
projective_prob_parse_demo()
|
||
|
|
|
||
|
|
|
||
|
|
def projective_rule_parse_demo():
|
||
|
|
"""
|
||
|
|
A demonstration showing the creation and use of a
|
||
|
|
``DependencyGrammar`` to perform a projective dependency
|
||
|
|
parse.
|
||
|
|
"""
|
||
|
|
grammar = DependencyGrammar.fromstring("""
|
||
|
|
'scratch' -> 'cats' | 'walls'
|
||
|
|
'walls' -> 'the'
|
||
|
|
'cats' -> 'the'
|
||
|
|
""")
|
||
|
|
print(grammar)
|
||
|
|
pdp = ProjectiveDependencyParser(grammar)
|
||
|
|
trees = pdp.parse(['the', 'cats', 'scratch', 'the', 'walls'])
|
||
|
|
for tree in trees:
|
||
|
|
print(tree)
|
||
|
|
|
||
|
|
def arity_parse_demo():
|
||
|
|
"""
|
||
|
|
A demonstration showing the creation of a ``DependencyGrammar``
|
||
|
|
in which a specific number of modifiers is listed for a given
|
||
|
|
head. This can further constrain the number of possible parses
|
||
|
|
created by a ``ProjectiveDependencyParser``.
|
||
|
|
"""
|
||
|
|
print()
|
||
|
|
print('A grammar with no arity constraints. Each DependencyProduction')
|
||
|
|
print('specifies a relationship between one head word and only one')
|
||
|
|
print('modifier word.')
|
||
|
|
grammar = DependencyGrammar.fromstring("""
|
||
|
|
'fell' -> 'price' | 'stock'
|
||
|
|
'price' -> 'of' | 'the'
|
||
|
|
'of' -> 'stock'
|
||
|
|
'stock' -> 'the'
|
||
|
|
""")
|
||
|
|
print(grammar)
|
||
|
|
|
||
|
|
print()
|
||
|
|
print('For the sentence \'The price of the stock fell\', this grammar')
|
||
|
|
print('will produce the following three parses:')
|
||
|
|
pdp = ProjectiveDependencyParser(grammar)
|
||
|
|
trees = pdp.parse(['the', 'price', 'of', 'the', 'stock', 'fell'])
|
||
|
|
for tree in trees:
|
||
|
|
print(tree)
|
||
|
|
|
||
|
|
print()
|
||
|
|
print('By contrast, the following grammar contains a ')
|
||
|
|
print('DependencyProduction that specifies a relationship')
|
||
|
|
print('between a single head word, \'price\', and two modifier')
|
||
|
|
print('words, \'of\' and \'the\'.')
|
||
|
|
grammar = DependencyGrammar.fromstring("""
|
||
|
|
'fell' -> 'price' | 'stock'
|
||
|
|
'price' -> 'of' 'the'
|
||
|
|
'of' -> 'stock'
|
||
|
|
'stock' -> 'the'
|
||
|
|
""")
|
||
|
|
print(grammar)
|
||
|
|
|
||
|
|
print()
|
||
|
|
print('This constrains the number of possible parses to just one:') # unimplemented, soon to replace
|
||
|
|
pdp = ProjectiveDependencyParser(grammar)
|
||
|
|
trees = pdp.parse(['the', 'price', 'of', 'the', 'stock', 'fell'])
|
||
|
|
for tree in trees:
|
||
|
|
print(tree)
|
||
|
|
|
||
|
|
|
||
|
|
def projective_prob_parse_demo():
|
||
|
|
"""
|
||
|
|
A demo showing the training and use of a projective
|
||
|
|
dependency parser.
|
||
|
|
"""
|
||
|
|
from nltk.parse.dependencygraph import conll_data2
|
||
|
|
|
||
|
|
graphs = [DependencyGraph(entry)
|
||
|
|
for entry in conll_data2.split('\n\n') if entry]
|
||
|
|
ppdp = ProbabilisticProjectiveDependencyParser()
|
||
|
|
print('Training Probabilistic Projective Dependency Parser...')
|
||
|
|
ppdp.train(graphs)
|
||
|
|
|
||
|
|
sent = ['Cathy', 'zag', 'hen', 'wild', 'zwaaien', '.']
|
||
|
|
print('Parsing \'', " ".join(sent), '\'...')
|
||
|
|
print('Parse:')
|
||
|
|
for tree in ppdp.parse(sent):
|
||
|
|
print(tree)
|
||
|
|
|
||
|
|
if __name__ == '__main__':
|
||
|
|
demo()
|