pygtrie.py

# -*- coding: utf-8 -*-
"""Implementation of a trie data structure.

`Trie data structure <http://en.wikipedia.org/wiki/Trie>`_, also known as radix
or prefix tree, is a tree associating keys to values where all the descendants
of a node have a common prefix (associated with that node).

The trie module contains :class:`pygtrie.Trie`, :class:`pygtrie.CharTrie` and
:class:`pygtrie.StringTrie` classes each implementing a mutable mapping
interface, i.e. :class:`dict` interface.  As such, in most circumstances,
:class:`pygtrie.Trie` could be used as a drop-in replacement for
a :class:`dict`, but the prefix nature of the data structure is trie’s real
strength.

The module also contains :class:`pygtrie.PrefixSet` class which uses a trie to
store a set of prefixes such that a key is contained in the set if it or its
prefix is stored in the set.

Features
--------

- A full mutable mapping implementation.

- Supports iterating over as well as deleting a subtrie.

- Supports prefix checking as well as shortest and longest prefix
  look-up.

- Extensible for any kind of user-defined keys.

- A PrefixSet supports “all keys starting with given prefix” logic.

- Can store any value including None.

For some simple examples see ``example.py`` file.
"""

__author__ = 'Michal Nazarewicz <mina86@mina86.com>'
__copyright__ = 'Copyright 2014 Google Inc.'


import collections as _collections

# Python 2.x and 3.x compatibility stuff
if hasattr(dict, 'iteritems'):
    # pylint: disable=invalid-name
    _iteritems = lambda d: d.iteritems()
    _iterkeys = lambda d: d.iterkeys()
    def _sorted_iteritems(d):
        """Returns d's items in sorted order."""
        items = d.items()
        items.sort()
        return iter(items)
else:
    _sorted_iteritems = lambda d: sorted(d.items())  # pylint: disable=invalid-name
    _iteritems = lambda d: iter(d.items())  # pylint: disable=invalid-name
    _iterkeys = lambda d: iter(d.keys())  # pylint: disable=invalid-name

try:
    _basestring = basestring
except NameError:
    _basestring = str


class ShortKeyError(KeyError):
    """Raised when given key is a prefix of a longer key."""
    pass


_SENTINEL = object()


class _Node(object):
    """A single node of a trie.

    Stores value associated with the node and dictionary of children.
    """
    __slots__ = ('children', 'value')

    def __init__(self):
        self.children = {}
        self.value = _SENTINEL

    def iterate(self, path, shallow, iteritems):
        """Yields all the nodes with values associated to them in the trie.

        Args:
            path: Path leading to this node.  Used to construct the key when
                returning value of this node and as a prefix for children.
            shallow: Perform a shallow traversal, i.e. do not yield nodes if
                their prefix has been yielded.
            iteritems: A function taking dictionary as argument and returning
                iterator over its items.  Something other than dict.iteritems
                may be given to enable sorting.

        Yields:
            ``(path, value)`` tuples.
        """
        # Use iterative function with stack on the heap so we don't hit Python's
        # recursion depth limits.
        node = self
        stack = []
        while True:
            if node.value is not _SENTINEL:
                yield path, node.value

            if (not shallow or node.value is _SENTINEL) and node.children:
                stack.append(iter(iteritems(node.children)))
                path.append(None)

            while True:
                try:
                    step, node = next(stack[-1])
                    path[-1] = step
                    break
                except StopIteration:
                    stack.pop()
                    path.pop()
                except IndexError:
                    return

    def traverse(self, node_factory, path_conv, path, iteritems):
        """Traverses the node and returns another type of node from factory.

        Args:
            node_factory: Callable function to construct new nodes.
            path_conv: Callable function to convert node path to a key.
            path: Current path for this node.
            iteritems: A function taking dictionary as argument and returning
                iterator over its items.  Something other than dict.iteritems
                may be given to enable sorting.

        Returns:
            An object constructed by calling node_factory(path_conv, path,
            children, value=...), where children are constructed by node_factory
            from the children of this node. There doesn't need to be 1:1
            correspondence between original nodes in the trie and constructed
            nodes (see make_test_node_and_compress in test.py).
        """
        def children():
            """Recursively traverses all of node's children."""
            for step, node in iteritems(self.children):
                yield node.traverse(node_factory, path_conv, path + [step],
                                    iteritems)

        args = [path_conv, tuple(path), children()]

        if self.value is not _SENTINEL:
            args.append(self.value)

        return node_factory(*args)

    def __eq__(self, other):
        # Like iterate, we don't recurse so this works on deep tries.
        a, b = self, other
        stack = []
        while True:
            if a.value != b.value or len(a.children) != len(b.children):
                return False
            if a.children:
                stack.append((_iteritems(a.children), b.children))

            while True:
                try:
                    key, a = next(stack[-1][0])
                    b = stack[-1][1].get(key)
                    if b is None:
                        return False
                    break
                except StopIteration:
                    stack.pop()
                except IndexError:
                    return True

        return self.value == other.value and self.children == other.children

    def __ne__(self, other):
        return not self.__eq__(other)

    def __bool__(self):
        return bool(self.value is not _SENTINEL or self.children)

    __nonzero__ = __bool__

    __hash__ = None

    def __getstate__(self):
        """Get state used for pickling.

        The state is encoded as a list of simple commands which consist of an
        integer and some command-dependent number of arguments.  The commands
        modify what the current node is by navigating the trie up and down and
        setting node values.  Possible commands are:

        * [n, step0, step1, ..., stepn-1, value], for n >= 0, specifies step
          needed to reach the next current node as well as its new value.  There
          is no way to create a child node without setting its (or its
          descendant's) value.

        * [-n], for -n < 0, specifies to go up n steps in the trie.

        When encoded as a state, the commands are flattened into a single list.

        For example::

            [ 0, 'Root',
              2, 'Foo', 'Bar', 'Root/Foo/Bar Node',
             -1,
              1, 'Baz', 'Root/Foo/Baz Node',
             -2,
              1, 'Qux', 'Root/Qux Node' ]

        Creates the following hierarchy::

            -* value: Root
             +-- Foo --* no value
             |         +-- Bar -- * value: Root/Foo/Bar Node
             |         +-- Baz -- * value: Root/Foo/Baz Node
             +-- Qux -- * value: Root/Qux Node

        Returns:
            A pickable state which can be passed to :func:`_Node.__setstate__`
            to reconstruct the node and its full hierarchy.
        """
        # Like iterate, we don't recurse so pickling works on deep tries.
        state = [] if self.value is _SENTINEL else [0]
        last_cmd = 0
        node = self
        stack = []
        while True:
            if node.value is not _SENTINEL:
                last_cmd = 0
                state.append(node.value)
            stack.append(_iteritems(node.children))

            while True:
                try:
                    step, node = next(stack[-1])
                except StopIteration:
                    if last_cmd < 0:
                        state[-1] -= 1
                    else:
                        last_cmd = -1
                        state.append(-1)
                    stack.pop()
                    continue
                except IndexError:
                    if last_cmd < 0:
                        state.pop()
                    return state

                if last_cmd > 0:
                    last_cmd += 1
                    state[-last_cmd] += 1
                else:
                    last_cmd = 1
                    state.append(1)
                state.append(step)
                break

    def __setstate__(self, state):
        """Unpickles node.  See :func:`_Node.__getstate__`."""
        self.__init__()
        state = iter(state)
        stack = [self]
        for cmd in state:
            if cmd < 0:
                del stack[cmd:]
            else:
                while cmd > 0:
                    stack.append(type(self)())
                    stack[-2].children[next(state)] = stack[-1]
                    cmd -= 1
                stack[-1].value = next(state)


_NONE_PAIR = type('NonePair', (tuple,), {
    '__nonzero__': lambda _: False,
    '__bool__': lambda _: False,
    '__slots__': (),
})((None, None))


class Trie(_collections.MutableMapping):
    """A trie implementation with dict interface plus some extensions.

    Keys used with the :class:`pygtrie.Trie` must be iterable, yielding hashable
    objects.  In other words, for a given key, ``dict.fromkeys(key)`` must be
    valid.

    In particular, strings work fine as trie keys, however when getting keys
    back from iterkeys() method for example, instead of strings, tuples of
    characters are produced.  For that reason, :class:`pygtrie.CharTrie` or
    :class:`pygtrie.StringTrie` may be preferred when using
    :class:`pygtrie.Trie` with string keys.
    """

    def __init__(self, *args, **kwargs):
        """Initialises the trie.

        Arguments are interpreted the same way :func:`Trie.update` interprets
        them.
        """
        self._root = _Node()
        self._sorted = False
        self.update(*args, **kwargs)

    @property
    def _iteritems(self):
        """Returns function yielding over dict's items possibly in sorted order.

        Returns:
            A function iterating over items of a dictionary given as an
            argument. If child nodes sorting has been enabled (via
            :func:`Trie.enable_sorting` method), returned function will go
            through the items in sorted order..
        """
        return _sorted_iteritems if self._sorted else _iteritems

    def enable_sorting(self, enable=True):
        """Enables sorting of child nodes when iterating and traversing.

        Normally, child nodes are not sorted when iterating or traversing over
        the trie (just like dict elements are not sorted).  This method allows
        sorting to be enabled (which was the behaviour prior to pygtrie 2.0
        release).

        For Trie class, enabling sorting of children is identical to simply
        sorting the list of items since Trie returns keys as tuples.  However,
        for other implementations such as StringTrie the two may behove subtly
        different.  For example, sorting items might produce::

            root/foo-bar
            root/foo/baz

        even though foo comes before foo-bar.

        Args:
            enable: Whether to enable sorting of child nodes.
        """
        self._sorted = enable

    def clear(self):
        """Removes all the values from the trie."""
        self._root = _Node()

    def update(self, *args, **kwargs):
        """Updates stored values.  Works like :func:`dict.update`."""
        if len(args) > 1:
            raise ValueError('update() takes at most one positional argument, '
                             '%d given.' % len(args))
        # We have this here instead of just letting MutableMapping.update()
        # handle things because it will iterate over keys and for each key
        # retrieve the value.  With Trie, this may be expensive since the path
        # to the node would have to be walked twice.  Instead, we have our own
        # implementation where iteritems() is used avoiding the unnecessary
        # value look-up.
        if args and isinstance(args[0], Trie):
            for key, value in _iteritems(args[0]):
                self[key] = value
            args = ()
        super(Trie, self).update(*args, **kwargs)

    def copy(self):
        """Returns a shallow copy of the trie."""
        return self.__class__(self)

    @classmethod
    def fromkeys(cls, keys, value=None):
        """Creates a new trie with given keys set.

        This is roughly equivalent to calling the constructor with a ``(key,
        value) for key in keys`` generator.

        Args:
            keys: An iterable of keys that should be set in the new trie.
            value: Value to associate with given keys.

        Returns:
            A new trie where each key from ``keys`` has been set to the given
            value.
        """
        trie = cls()
        for key in keys:
            trie[key] = value
        return trie

    def _get_node(self, key, create=False):
        """Returns node for given key.  Creates it if requested.

        Args:
            key: A key to look for.
            create: Whether to create the node if it does not exist.

        Returns:
            ``(node, trace)`` tuple where ``node`` is the node for given key and
            ``trace`` is a list specifying path to reach the node including all
            the encountered nodes.  Each element of trace is a ``(step, node)``
            tuple where ``step`` is a step from parent node to given node and
            ``node`` is node on the path.  The first element of the path is
            always ``(None, self._root)``.

        Raises:
            KeyError: If there is no node for the key and ``create`` is
                ``False``.
        """
        node = self._root
        trace = [(None, node)]
        for step in self.__path_from_key(key):
            if create:
                node = node.children.setdefault(step, _Node())
            else:
                node = node.children.get(step)
                if not node:
                    raise KeyError(key)
            trace.append((step, node))
        return node, trace

    def __iter__(self):
        return self.iterkeys()

    # pylint: disable=arguments-differ

    def iteritems(self, prefix=_SENTINEL, shallow=False):
        """Yields all nodes with associated values with given prefix.

        Only nodes with values are output.  For example::

            >>> import pygtrie
            >>> t = pygtrie.StringTrie()
            >>> t['foo'] = 'Foo'
            >>> t['foo/bar/baz'] = 'Baz'
            >>> t['qux'] = 'Qux'
            >>> t.items()
            [('qux', 'Qux'), ('foo', 'Foo'), ('foo/bar/baz', 'Baz')]

        Items are generated in topological order but the order of siblings is
        unspecified by default.  In other words, in the above example, the
        ``('qux', 'Qux')`` pair might have been at the end of the list. At an
        expense of efficiency, this can be changed via
        :func:`Trie.enable_sorting`.

        With ``prefix`` argument, only items with specified prefix are generated
        (i.e. only given subtrie is traversed) as demonstrated by::

            >>> t.items(prefix='foo/bar')
            [('foo/bar/baz', 'Baz')]

        With ``shallow`` argument, if a node has value associated with it, it's
        children are not traversed even if they exist which can be seen in::

            >>> t.items(shallow=True)
            [('qux', 'Qux'), ('foo', 'Foo')]

        Args:
            prefix: Prefix to limit iteration to.
            shallow: Perform a shallow traversal, i.e. do not yield items if
                their prefix has been yielded.

        Yields:
            ``(key, value)`` tuples.

        Raises:
            KeyError: If ``prefix`` does not match any node.
        """
        node, _ = self._get_node(prefix)
        for path, value in node.iterate(list(self.__path_from_key(prefix)),
                                        shallow, self._iteritems):
            yield (self._key_from_path(path), value)

    def iterkeys(self, prefix=_SENTINEL, shallow=False):
        """Yields all keys having associated values with given prefix.

        This is equivalent to taking first element of tuples generated by
        :func:`Trie.iteritems` which see for more detailed documentation.

        Args:
            prefix: Prefix to limit iteration to.
            shallow: Perform a shallow traversal, i.e. do not yield keys if
                their prefix has been yielded.

        Yields:
            All the keys (with given prefix) with associated values in the trie.

        Raises:
            KeyError: If ``prefix`` does not match any node.
        """
        for key, _ in self.iteritems(prefix=prefix, shallow=shallow):
            yield key

    def itervalues(self, prefix=_SENTINEL, shallow=False):
        """Yields all values associated with keys with given prefix.

        This is equivalent to taking second element of tuples generated by
        :func:`Trie.iteritems` which see for more detailed documentation.

        Args:
            prefix: Prefix to limit iteration to.
            shallow: Perform a shallow traversal, i.e. do not yield values if
                their prefix has been yielded.

        Yields:
            All the values associated with keys (with given prefix) in the trie.

        Raises:
            KeyError: If ``prefix`` does not match any node.
        """
        node, _ = self._get_node(prefix)
        for _, value in node.iterate(list(self.__path_from_key(prefix)),
                                     shallow, self._iteritems):
            yield value

    def items(self, prefix=_SENTINEL, shallow=False):
        """Returns a list of ``(key, value)`` pairs in given subtrie.

        This is equivalent to constructing a list from generator returned by
        :func:`Trie.iteritems` which see for more detailed documentation.
        """
        return list(self.iteritems(prefix=prefix, shallow=shallow))

    def keys(self, prefix=_SENTINEL, shallow=False):
        """Returns a list of all the keys, with given prefix, in the trie.

        This is equivalent to constructing a list from generator returned by
        :func:`Trie.iterkeys` which see for more detailed documentation.
        """
        return list(self.iterkeys(prefix=prefix, shallow=shallow))

    def values(self, prefix=_SENTINEL, shallow=False):
        """Returns a list of values in given subtrie.

        This is equivalent to constructing a list from generator returned by
        :func:`Trie.iterivalues` which see for more detailed documentation.
        """
        return list(self.itervalues(prefix=prefix, shallow=shallow))

    # pylint: enable=arguments-differ

    def __len__(self):
        """Returns number of values in a trie.

        Note that this method is expensive as it iterates over the whole trie.
        """
        return sum(1 for _ in self.itervalues())

    def __nonzero__(self):
        return bool(self._root)

    HAS_VALUE = 1
    HAS_SUBTRIE = 2

    def has_node(self, key):
        """Returns whether given node is in the trie.

        Return value is a bitwise or of ``HAS_VALUE`` and ``HAS_SUBTRIE``
        constants indicating node has a value associated with it and that it is
        a prefix of another existing key respectively.  Both of those are
        independent of each other and all of the four combinations are possible.
        For example::

            >>> import pygtrie
            >>> t = pygtrie.StringTrie()
            >>> t['foo/bar'] = 'Bar'
            >>> t['foo/bar/baz'] = 'Baz'
            >>> t.has_node('qux') == 0
            True
            >>> t.has_node('foo/bar/baz') == pygtrie.Trie.HAS_VALUE
            True
            >>> t.has_node('foo') == pygtrie.Trie.HAS_SUBTRIE
            True
            >>> t.has_node('foo/bar') == (pygtrie.Trie.HAS_VALUE |
            ...                           pygtrie.Trie.HAS_SUBTRIE)
            True

        There are two higher level methods built on top of this one which give
        easier interface for the information. :func:`Trie.has_key` and returns
        whether node has a value associated with it and :func:`Trie.has_subtrie`
        checks whether node is a prefix.  Continuing previous example::

            >>> t.has_key('qux'), t.has_subtrie('qux')
            False, False
            >>> t.has_key('foo/bar/baz'), t.has_subtrie('foo/bar/baz')
            True, False
            >>> t.has_key('foo'), t.has_subtrie('foo')
            False, True
            >>> t.has_key('foo/bar'), t.has_subtrie('foo/bar')
            True, True

        Args:
            key: A key to look for.

        Returns:
            Non-zero if node exists and if it does a bit-field denoting whether
            it has a value associated with it and whether it has a subtrie.
        """
        try:
            node, _ = self._get_node(key)
        except KeyError:
            return 0
        return ((self.HAS_VALUE * int(node.value is not _SENTINEL)) |
                        (self.HAS_SUBTRIE * int(bool(node.children))))

    def has_key(self, key):
        """Indicates whether given key has value associated with it.

        See :func:`Trie.has_node` for more detailed documentation.
        """
        return bool(self.has_node(key) & self.HAS_VALUE)

    def has_subtrie(self, key):
        """Returns whether given key is a prefix of another key in the trie.

        See :func:`Trie.has_node` for more detailed documentation.
        """
        return bool(self.has_node(key) & self.HAS_SUBTRIE)

    @staticmethod
    def _slice_maybe(key_or_slice):
        """Checks whether argument is a slice or a plain key.

        Args:
            key_or_slice: A key or a slice to test.

        Returns:
            ``(key, is_slice)`` tuple.  ``is_slice`` indicates whether
            ``key_or_slice`` is a slice and ``key`` is either ``key_or_slice``
            itself (if it's not a slice) or slice's start position.

        Raises:
            TypeError: If ``key_or_slice`` is a slice whose stop or step are not
                ``None`` In other words, only ``[key:]`` slices are valid.
        """
        if isinstance(key_or_slice, slice):
            if key_or_slice.stop is not None or key_or_slice.step is not None:
                raise TypeError(key_or_slice)
            return key_or_slice.start, True
        return key_or_slice, False

    def __getitem__(self, key_or_slice):
        """Returns value associated with given key or raises KeyError.

        When argument is a single key, value for that key is returned (or
        :class:`KeyError` exception is thrown if the node does not exist or has
        no value associated with it).

        When argument is a slice, it must be one with only `start` set in which
        case the access is identical to :func:`Trie.itervalues` invocation with
        prefix argument.

        Example:

            >>> import pygtrie
            >>> t = pygtrie.StringTrie()
            >>> t['foo/bar'] = 'Bar'
            >>> t['foo/baz'] = 'Baz'
            >>> t['qux'] = 'Qux'
            >>> t['foo/bar']
            'Bar'
            >>> list(t['foo':])
            ['Baz', 'Bar']
            >>> t['foo']
            Traceback (most recent call last):
                ...
            pygtrie.ShortKeyError: 'foo'

        Args:
            key_or_slice: A key or a slice to look for.

        Returns:
            If a single key is passed, a value associated with given key.  If
            a slice is passed, a generator of values in specified subtrie.

        Raises:
            ShortKeyError: If the key has no value associated with it but is
                a prefix of some key with a value.  Note that
                :class:`ShortKeyError` is subclass of :class:`KeyError`.
            KeyError: If key has no value associated with it nor is a prefix of
                an existing key.
            TypeError: If ``key_or_slice`` is a slice but it's stop or step are
                not ``None``.
        """
        if self._slice_maybe(key_or_slice)[1]:
            return self.itervalues(key_or_slice.start)
        node, _ = self._get_node(key_or_slice)
        if node.value is _SENTINEL:
            raise ShortKeyError(key_or_slice)
        return node.value

    def _set(self, key, value, only_if_missing=False, clear_children=False):
        """Sets value for a given key.

        Args:
            key: Key to set value of.
            value: Value to set to.
            only_if_missing: If ``True``, value won't be changed if the key is
                    already associated with a value.
            clear_children: If ``True``, all children of the node, if any, will
                    be removed.

        Returns:
            Value of the node.
        """
        node, _ = self._get_node(key, create=True)
        if not only_if_missing or node.value is _SENTINEL:
            node.value = value
        if clear_children:
            node.children.clear()
        return node.value

    def __setitem__(self, key_or_slice, value):
        """Sets value associated with given key.

        If `key_or_slice` is a key, simply associate it with given value.  If it
        is a slice (which must have `start` set only), it in addition clears any
        subtrie that might have been attached to particular key.  For example::

            >>> import pygtrie
            >>> t = pygtrie.StringTrie()
            >>> t['foo/bar'] = 'Bar'
            >>> t['foo/baz'] = 'Baz'
            >>> t.keys()
            ['foo/baz', 'foo/bar']
            >>> t['foo':] = 'Foo'
            >>> t.keys()
            ['foo']

        Args:
            key_or_slice: A key to look for or a slice.  If it is a slice, the
                whole subtrie (if present) will be replaced by a single node
                with given value set.
            value: Value to set.

        Raises:
            TypeError: If key is a slice whose stop or step are not None.
        """
        key, is_slice = self._slice_maybe(key_or_slice)
        self._set(key, value, clear_children=is_slice)

    def setdefault(self, key, value=None):
        """Sets value of a given node if not set already.  Also returns it.

        In contrast to :func:`Trie.__setitem__`, this method does not accept
        slice as a key.
        """
        return self._set(key, value, only_if_missing=True)

    @staticmethod
    def _cleanup_trace(trace):
        """Removes empty nodes present on specified trace.

        Args:
            trace: Trace to the node to cleanup as returned by
                :func:`Trie._get_node`.
        """
        i = len(trace) - 1  # len(path) >= 1 since root is always there
        step, node = trace[i]
        while i and not node:
            i -= 1
            parent_step, parent = trace[i]
            del parent.children[step]
            step, node = parent_step, parent

    def _pop_from_node(self, node, trace, default=_SENTINEL):
        """Removes a value from given node.

        Args:
            node: Node to get value of.
            trace: Trace to that node as returned by :func:`Trie._get_node`.
            default: A default value to return if node has no value set.

        Returns:
            Value of the node or ``default``.

        Raises:
            ShortKeyError: If the node has no value associated with it and
                ``default`` has not been given.
        """
        if node.value is not _SENTINEL:
            value = node.value
            node.value = _SENTINEL
            self._cleanup_trace(trace)
            return value
        elif default is _SENTINEL:
            raise ShortKeyError()
        else:
            return default

    def pop(self, key, default=_SENTINEL):
        """Deletes value associated with given key and returns it.

        Args:
            key: A key to look for.
            default: If specified, value that will be returned if given key has
                no value associated with it.  If not specified, method will
                throw KeyError in such cases.

        Returns:
            Removed value, if key had value associated with it, or ``default``
            (if given).

        Raises:
            ShortKeyError: If ``default`` has not been specified and the key has
                no value associated with it but is a prefix of some key with
                a value.  Note that :class:`ShortKeyError` is subclass of
                :class:`KeyError`.
            KeyError: If default has not been specified and key has no value
                associated with it nor is a prefix of an existing key.
        """
        try:
            return self._pop_from_node(*self._get_node(key))
        except KeyError:
            if default is not _SENTINEL:
                return default
            raise

    def popitem(self):
        """Deletes an arbitrary value from the trie and returns it.

        There is no guarantee as to which item is deleted and returned.  Neither
        in respect to its lexicographical nor topological order.

        Returns:
            ``(key, value)`` tuple indicating deleted key.

        Raises:
            KeyError: If the trie is empty.
        """
        if not self:
            raise KeyError()
        node = self._root
        trace = [(None, node)]
        while node.value is _SENTINEL:
            step = next(_iterkeys(node.children))
            node = node.children[step]
            trace.append((step, node))
        return (self._key_from_path((step for step, _ in trace[1:])),
                        self._pop_from_node(node, trace))

    def __delitem__(self, key_or_slice):
        """Deletes value associated with given key or raises KeyError.

        If argument is a key, value associated with it is deleted.  If the key
        is also a prefix, its descendents are not affected.  On the other hand,
        if the argument is a slice (in which case it must have only start set),
        the whole subtrie is removed.  For example::

            >>> import pygtrie
            >>> t = pygtrie.StringTrie()
            >>> t['foo'] = 'Foo'
            >>> t['foo/bar'] = 'Bar'
            >>> t['foo/bar/baz'] = 'Baz'
            >>> del t['foo/bar']
            >>> t.keys()
            ['foo', 'foo/bar/baz']
            >>> del t['foo':]
            >>> t.keys()
            []

        Args:
            key_or_slice: A key to look for or a slice.  If key is a slice, the
                    whole subtrie will be removed.

        Raises:
            ShortKeyError: If the key has no value associated with it but is
                a prefix of some key with a value.  This is not thrown is
                key_or_slice is a slice -- in such cases, the whole subtrie is
                removed.  Note that :class:`ShortKeyError` is subclass of
                :class:`KeyError`.
            KeyError: If key has no value associated with it nor is a prefix of
                an existing key.
            TypeError: If key is a slice whose stop or step are not ``None``.
        """
        key, is_slice = self._slice_maybe(key_or_slice)
        node, trace = self._get_node(key)
        if is_slice:
            node.children.clear()
        elif node.value is _SENTINEL:
            raise ShortKeyError(key)
        node.value = _SENTINEL
        self._cleanup_trace(trace)

    def prefixes(self, key):
        """Walks towards the node specified by key and yields all found items.

        Example:

            >>> import pygtrie
            >>> t = pygtrie.StringTrie()
            >>> t['foo'] = 'Foo'
            >>> t['foo/bar/baz'] = 'Baz'
            >>> list(t.prefixes('foo/bar/baz/qux'))
            [('foo', 'Foo'), ('foo/bar/baz', 'Baz')]
            >>> list(t.prefixes('does/not/exist'))
            []

        Args:
            key: Key to look for.

        Yields:
            ``(k, value)`` pairs denoting keys with associated values
            encountered on the way towards the specified key.
        """
        node = self._root
        path = self.__path_from_key(key)
        pos = 0
        while True:
            if node.value is not _SENTINEL:
                yield self._key_from_path(path[:pos]), node.value
            if pos == len(path):
                break
            node = node.children.get(path[pos])
            if not node:
                break
            pos += 1

    def shortest_prefix(self, key):
        """Finds the shortest prefix of a key with a value.

        This is equivalent to taking the first object yielded by
        :func:`Trie.prefixes` with a default of `(None, None)` if said method
        yields no items.  As an added bonus, the pair in that case will be
        a falsy value (as opposed to regular two-element tuple of ``None``
        values).

        Example:

            >>> import pygtrie
            >>> t = pygtrie.StringTrie()
            >>> t['foo'] = 'Foo'
            >>> t['foo/bar/baz'] = 'Baz'
            >>> t.shortest_prefix('foo/bar/baz/qux')
            ('foo', 'Foo')
            >>> t.shortest_prefix('does/not/exist')
            (None, None)
            >>> bool(t.shortest_prefix('does/not/exist'))
            False

        Args:
            key: Key to look for.

        Returns:
            ``(k, value)`` where ``k`` is the shortest prefix of ``key`` (it may
            equal ``key``) and ``value`` is a value associated with that key.
            If no node is found, ``(None, None)`` is returned.
        """
        return next(self.prefixes(key), _NONE_PAIR)

    def longest_prefix(self, key):
        """Finds the longest prefix of a key with a value.

        This is equivalent to taking the last object yielded by
        :func:`Trie.prefixes` with a default of `(None, None)` if said method
        yields no items.  As an added bonus, the pair in that case will be
        a falsy value (as opposed to regular two-element tuple of ``None``
        values).

        Example:

            >>> import pygtrie
            >>> t = pygtrie.StringTrie()
            >>> t['foo'] = 'Foo'
            >>> t['foo/bar/baz'] = 'Baz'
            >>> t.longest_prefix('foo/bar/baz/qux')
            ('foo/bar/baz', 'Baz')
            >>> t.longest_prefix('does/not/exist')
            (None, None)
            >>> bool(t.longest_prefix('does/not/exist'))
            False

        Args:
            key: Key to look for.

        Returns:
            ``(k, value)`` where ``k`` is the longest prefix of ``key`` (it may
            equal ``key``) and ``value`` is a value associated with that key.
            If no node is found, ``(None, None)`` is returned.
        """
        ret = _NONE_PAIR
        for ret in self.prefixes(key):
            pass
        return ret

    def __eq__(self, other):
        return self._root == other._root  # pylint: disable=protected-access

    def __ne__(self, other):
        return self._root != other._root  # pylint: disable=protected-access

    def __str__(self):
        return 'Trie(%s)' % (
                ', '.join('%s: %s' % item for item in self.iteritems()))

    def __repr__(self):
        if self:
            return  'Trie((%s,))' % (
                    ', '.join('(%r, %r)' % item for item in self.iteritems()))
        else:
            return 'Trie()'

    def __path_from_key(self, key):
        """Converts a user visible key object to internal path representation.

        Args:
            key: User supplied key or ``_SENTINEL``.

        Returns:
            An empty tuple if ``key`` was ``_SENTINEL``, otherwise whatever
            :func:`Trie._path_from_key` returns.

        Raises:
            TypeError: If ``key`` is of invalid type.
        """
        return () if key is _SENTINEL else self._path_from_key(key)

    def _path_from_key(self, key):  # pylint: disable=no-self-use
        """Converts a user visible key object to internal path representation.

        The default implementation simply returns key.

        Args:
            key: User supplied key.

        Returns:
            A path, which is an iterable of steps.  Each step must be hashable.

        Raises:
            TypeError: If key is of invalid type.
        """
        return key

    def _key_from_path(self, path):  # pylint: disable=no-self-use
        """Converts an internal path into a user visible key object.

        The default implementation creates a tuple from the path.

        Args:
            path: Internal path representation.
        Returns:
            A user visible key object.
        """
        return tuple(path)

    def traverse(self, node_factory, prefix=_SENTINEL):
        """Traverses the tree using node_factory object.

        node_factory is a callable function which accepts (path_conv, path,
        children, value=...) arguments, where path_conv is a lambda converting
        path representation to key, path is the path to this node, children is
        an iterable of children nodes constructed by node_factory, optional
        value is the value associated with the path.

        node_factory's children argument is a generator which has a few
        consequences:

        * To traverse into node's children, the generator must be iterated over.
          This can by accomplished by a simple "children = list(children)"
          statement.
        * Ignoring the argument allows node_factory to stop the traversal from
          going into the children of the node.  In other words, whole subtrie
          can be removed from traversal if node_factory chooses so.
        * If children is stored as is (i.e. as a generator) when it is iterated
          over later on it will see state of the trie as it is during the
          iteration and not when traverse method was called.

        :func:`Trie.traverse` has two advantages over :func:`Trie.iteritems` and
        similar methods:

        1. it allows subtries to be skipped completely when going through the
           list of nodes based on the property of the parent node; and

        2. it represents structure of the trie directly making it easy to
           convert structure into a different representation.

        For example, the below snippet prints all files in current directory
        counting how many HTML files were found but ignores hidden files and
        directories (i.e. those whose names start with a dot)::

            import os
            import pygtrie

            t = pygtrie.StringTrie(separator=os.sep)

            # Construct a trie with all files in current directory and all
            # of its sub-directories.  Files get set a True value.
            # Directories are represented implicitly by being prefixes of
            # files.
            for root, _, files in os.walk('.'):
                for name in files: t[os.path.join(root, name)] = True

            def traverse_callback(path_conv, path, children, is_file=False):
                if path and path[-1] != '.' and path[-1][0] == '.':
                    # Ignore hidden directory (but accept root node and '.')
                    return 0
                elif is_file:
                    print path_conv(path)
                    return int(path[-1].endswith('.html'))
                else:
                    # Otherwise, it's a directory.  Traverse into children.
                    return sum(int(is_html) for is_html in children)

            print t.traverse(traverse_callback)

        As documented, ignoring the children argument causes subtrie to be
        omitted and not walked into.

        In the next example, the trie is converted to a tree representation
        where child nodes include a pointer to their parent.  As before, hidden
        files and directories are ignored::

            import os
            import pygtrie

            t = pygtrie.StringTrie(separator=os.sep)
            for root, _, files in os.walk('.'):
                for name in files: t[os.path.join(root, name)] = True

            class File(object):
                def __init__(self, name):
                    self.name = name
                    self.parent = None

            class Directory(File):
                def __init__(self, name, children):
                    super(Directory, self).__init__(name)
                    self._children = children
                    for child in children:
                        child.parent = self

            def traverse_callback(path_conv, path, children, is_file=False):
                if not path or path[-1] == '.' or path[-1][0] != '.':
                    if is_file:
                        return File(path[-1])
                    children = filter(None, children)
                    return Directory(path[-1] if path else '', children)

            root = t.traverse(traverse_callback)

        Note: Unlike iterators, traverse method uses stack recursion which means
        that using it on deep tries may lead to a RuntimeError exception thrown
        once Python's maximum recursion depth is reached.

        Args:
            node_factory: Makes opaque objects from the keys and values of the
                trie.
            prefix: Prefix for node to start traversal, by default starts at
                root.

        Returns:
            Node object constructed by node_factory corresponding to the root
            node.

        """
        node, _ = self._get_node(prefix)
        return node.traverse(node_factory, self._key_from_path,
                             list(self.__path_from_key(prefix)),
                             self._iteritems)

class CharTrie(Trie):
    """A variant of a :class:`pygtrie.Trie` which accepts strings as keys.

    The only difference between :class:`pygtrie.CharTrie` and
    :class:`pygtrie.Trie` is that when :class:`pygtrie.CharTrie` returns keys
    back to the client (for instance in keys() method is called), those keys are
    returned as strings.

    Canonical example where this class can be used is a dictionary of words in
    a natural language.  For example::

        >>> import pygtrie
        >>> t = pygtrie.CharTrie()
        >>> t['wombat'] = True
        >>> t['woman'] = True
        >>> t['man'] = True
        >>> t['manhole'] = True
        >>> t.has_subtrie('wo')
        True
        >>> t.has_key('man')
        True
        >>> t.has_subtrie('man')
        True
        >>> t.has_subtrie('manhole')
        False
    """

    def _key_from_path(self, path):
        return ''.join(path)


class StringTrie(Trie):
    """:class:`pygtrie.Trie` variant accepting strings with a separator as keys.

    The trie accepts strings as keys which are split into components using
    a separator specified during initialisation ("/" by default).

    Canonical example where this class can be used is when keys are paths.  For
    example, it could map from a path to a request handler::

        import pygtrie

        def handle_root(): pass
        def handle_admin(): pass
        def handle_admin_images(): pass

        handlers = pygtrie.StringTrie()
        handlers[''] = handle_root
        handlers['/admin'] = handle_admin
        handlers['/admin/images'] = handle_admin_images

        request_path = '/admin/images/foo'

        handler = handlers.longest_prefix(request_path)
    """

    def __init__(self, *args, **kwargs):
        """Initialises the trie.

        Except for a ``separator`` named argument, all other arguments are
        interpreted the same way :func:`Trie.update` interprets them.

        Args:
            *args: Passed to super class initialiser.
            **kwargs: Passed to super class initialiser.
            separator: A separator to use when splitting keys into paths used by
                the trie.  "/" is used if this argument is not specified.  This
                named argument is not specified on the function's prototype
                because of Python's limitations.
        """
        separator = kwargs.pop('separator', '/')
        if not isinstance(separator, _basestring):
            raise TypeError('separator must be a string')
        if not separator:
            raise ValueError('separator can not be empty')
        self._separator = separator
        super(StringTrie, self).__init__(*args, **kwargs)

    @classmethod
    def fromkeys(cls, keys, value=None, separator='/'):  # pylint: disable=arguments-differ
        trie = cls(separator=separator)
        for key in keys:
            trie[key] = value
        return trie

    def _path_from_key(self, key):
        return key.split(self._separator)

    def _key_from_path(self, path):
        return self._separator.join(path)


class PrefixSet(_collections.MutableSet):  # pylint: disable=abstract-class-not-used
    """A set of prefixes.

    :class:`pygtrie.PrefixSet` works similar to a normal set except it is said
    to contain a key if the key or it's prefix is stored in the set.  For
    instance, if "foo" is added to the set, the set contains "foo" as well as
    "foobar".

    The set supports addition of elements but does *not* support removal of
    elements.  This is because there's no obvious consistent and intuitive
    behaviour for element deletion.
    """

    def __init__(self, iterable=None, factory=Trie, **kwargs):
        """Initialises the prefix set.

        Args:
            iterable: A sequence of keys to add to the set.
            factory: A function used to create a trie used by the
                    :class:`pygtrie.PrefixSet`.
            kwargs: Additional keyword arguments passed to the factory function.
        """
        super(PrefixSet, self).__init__()
        trie = factory(**kwargs)
        if iterable:
            trie.update((key, True) for key in iterable)
        self._trie = trie

    def copy(self):
        """Returns a copy of the prefix set."""
        return self.__class__(self._trie)

    def clear(self):
        """Removes all keys from the set."""
        self._trie.clear()

    def __contains__(self, key):
        """Checks whether set contains key or its prefix."""
        return bool(self._trie.shortest_prefix(key)[1])

    def __iter__(self):
        """Return iterator over all prefixes in the set.

        See :func:`PrefixSet.iter` method for more info.
        """
        return self._trie.iterkeys()

    def iter(self, prefix=_SENTINEL):
        """Iterates over all keys in the set optionally starting with a prefix.

        Since a key does not have to be explicitly added to the set to be an
        element of the set, this method does not iterate over all possible keys
        that the set contains, but only over the shortest set of prefixes of all
        the keys the set contains.

        For example, if "foo" has been added to the set, the set contains also
        "foobar", but this method will *not* iterate over "foobar".

        If ``prefix`` argument is given, method will iterate over keys with
        given prefix only.  The keys yielded from the function if prefix is
        given does not have to be a subset (in mathematical sense) of the keys
        yielded when there is not prefix.  This happens, if the set contains
        a prefix of the given prefix.

        For example, if only "foo" has been added to the set, iter method called
        with no arguments will yield "foo" only.  However, when called with
        "foobar" argument, it will yield "foobar" only.
        """
        if prefix is _SENTINEL:
            return iter(self)
        elif self._trie.has_node(prefix):
            return self._trie.iterkeys(prefix=prefix)
        elif prefix in self:
            # Make sure the type of returned keys is consistent.
            # pylint: disable=protected-access
            return self._trie._key_from_path(self._trie._path_from_key(prefix)),
        else:
            return ()

    def __len__(self):
        """Returns number of keys stored in the set.

        Since a key does not have to be explicitly added to the set to be an
        element of the set, this method does not count over all possible keys
        that the set contains (since that would be infinity), but only over the
        shortest set of prefixes of all the keys the set contains.

        For example, if "foo" has been added to the set, the set contains also
        "foobar", but this method will *not* count "foobar".

        """
        return len(self._trie)

    def add(self, key):
        """Adds given key to the set.

        If the set already contains prefix of the key being added, this
        operation has no effect.  If the key being added is a prefix of some
        existing keys in the set, those keys are deleted and replaced by
        a single entry for the key being added.

        For example, if the set contains key "foo" adding a key "foobar" does
        not change anything.  On the other hand, if the set contains keys
        "foobar" and "foobaz", adding a key "foo" will replace those two keys
        with a single key "foo".

        This makes a difference when iterating over the keys or counting number
        of keys.  Counter intuitively, adding of a key can *decrease* size of
        the set.

        Args:
            key: Key to add.
        """
        if key not in self:
            self._trie[key:] = True

    def discard(self, key):
        raise NotImplementedError(
            'Removing keys from PrefixSet is not implemented.')

    def remove(self, key):
        raise NotImplementedError(
            'Removing keys from PrefixSet is not implemented.')

    def pop(self):
        raise NotImplementedError(
            'Removing keys from PrefixSet is not implemented.')