from __future__ import absolute_import, division, print_function

import math
import re
from operator import getitem

from . import config
from .compatibility import unicode
from .core import (istask, get_dependencies, subs, toposort,
                   flatten, reverse_dict, ishashable, _get_recursive)
from .utils_test import add, inc  # noqa: F401


def cull(dsk, keys):
    """ Return new dask with only the tasks required to calculate keys.

    In other words, remove unnecessary tasks from dask.
    ``keys`` may be a single key or list of keys.

    Examples
    --------
    >>> d = {'x': 1, 'y': (inc, 'x'), 'out': (add, 'x', 10)}
    >>> dsk, dependencies = cull(d, 'out')  # doctest: +SKIP
    >>> dsk  # doctest: +SKIP
    {'x': 1, 'out': (add, 'x', 10)}
    >>> dependencies  # doctest: +SKIP
    {'x': set(), 'out': set(['x'])}

    Returns
    -------
    dsk: culled dask graph
    dependencies: Dict mapping {key: [deps]}.  Useful side effect to accelerate
        other optimizations, notably fuse.
    """
    if not isinstance(keys, (list, set)):
        keys = [keys]
    out_keys = []
    seen = set()
    dependencies = dict()

    work = list(set(flatten(keys)))
    while work:
        new_work = []
        out_keys += work
        deps = [(k, get_dependencies(dsk, k, as_list=True))  # fuse needs lists
                for k in work]
        dependencies.update(deps)
        for _, deplist in deps:
            for d in deplist:
                if d not in seen:
                    seen.add(d)
                    new_work.append(d)
        work = new_work

    out = {k: dsk[k] for k in out_keys}

    return out, dependencies


def default_fused_linear_keys_renamer(keys):
    """Create new keys for fused tasks"""
    typ = type(keys[0])
    if typ is str or typ is unicode:
        names = [key_split(x) for x in keys[:0:-1]]
        names.append(keys[0])
        return '-'.join(names)
    elif (typ is tuple and len(keys[0]) > 0 and
          isinstance(keys[0][0], (str, unicode))):
        names = [key_split(x) for x in keys[:0:-1]]
        names.append(keys[0][0])
        return ('-'.join(names),) + keys[0][1:]
    else:
        return None


def fuse_linear(dsk, keys=None, dependencies=None, rename_keys=True):
    """ Return new dask graph with linear sequence of tasks fused together.

    If specified, the keys in ``keys`` keyword argument are *not* fused.
    Supply ``dependencies`` from output of ``cull`` if available to avoid
    recomputing dependencies.

    **This function is mostly superseded by ``fuse``**

    Parameters
    ----------
    dsk: dict
    keys: list
    dependencies: dict, optional
        {key: [list-of-keys]}.  Must be a list to provide count of each key
        This optional input often comes from ``cull``
    rename_keys: bool or func, optional
        Whether to rename fused keys with ``default_fused_linear_keys_renamer``
        or not.  Renaming fused keys can keep the graph more understandable
        and comprehensive, but it comes at the cost of additional processing.
        If False, then the top-most key will be used.  For advanced usage, a
        func is also accepted, ``new_key = rename_keys(fused_key_list)``.

    Examples
    --------
    >>> d = {'a': 1, 'b': (inc, 'a'), 'c': (inc, 'b')}
    >>> dsk, dependencies = fuse(d)
    >>> dsk # doctest: +SKIP
    {'a-b-c': (inc, (inc, 1)), 'c': 'a-b-c'}
    >>> dsk, dependencies = fuse(d, rename_keys=False)
    >>> dsk # doctest: +SKIP
    {'c': (inc, (inc, 1))}
    >>> dsk, dependencies = fuse(d, keys=['b'], rename_keys=False)
    >>> dsk  # doctest: +SKIP
    {'b': (inc, 1), 'c': (inc, 'b')}

    Returns
    -------
    dsk: output graph with keys fused
    dependencies: dict mapping dependencies after fusion.  Useful side effect
        to accelerate other downstream optimizations.
    """
    if keys is not None and not isinstance(keys, set):
        if not isinstance(keys, list):
            keys = [keys]
        keys = set(flatten(keys))

    if dependencies is None:
        dependencies = {k: get_dependencies(dsk, k, as_list=True)
                        for k in dsk}

    # locate all members of linear chains
    child2parent = {}
    unfusible = set()
    for parent in dsk:
        deps = dependencies[parent]
        has_many_children = len(deps) > 1
        for child in deps:
            if keys is not None and child in keys:
                unfusible.add(child)
            elif child in child2parent:
                del child2parent[child]
                unfusible.add(child)
            elif has_many_children:
                unfusible.add(child)
            elif child not in unfusible:
                child2parent[child] = parent

    # construct the chains from ancestor to descendant
    chains = []
    parent2child = dict(map(reversed, child2parent.items()))
    while child2parent:
        child, parent = child2parent.popitem()
        chain = [child, parent]
        while parent in child2parent:
            parent = child2parent.pop(parent)
            del parent2child[parent]
            chain.append(parent)
        chain.reverse()
        while child in parent2child:
            child = parent2child.pop(child)
            del child2parent[child]
            chain.append(child)
        chains.append(chain)

    dependencies = {k: set(v) for k, v in dependencies.items()}

    if rename_keys is True:
        key_renamer = default_fused_linear_keys_renamer
    elif rename_keys is False:
        key_renamer = None
    else:
        key_renamer = rename_keys

    # create a new dask with fused chains
    rv = {}
    fused = set()
    aliases = set()
    is_renamed = False
    for chain in chains:
        if key_renamer is not None:
            new_key = key_renamer(chain)
            is_renamed = (new_key is not None and new_key not in dsk and
                          new_key not in rv)
        child = chain.pop()
        val = dsk[child]
        while chain:
            parent = chain.pop()
            dependencies[parent].update(dependencies.pop(child))
            dependencies[parent].remove(child)
            val = subs(dsk[parent], child, val)
            fused.add(child)
            child = parent
        fused.add(child)
        if is_renamed:
            rv[new_key] = val
            rv[child] = new_key
            dependencies[new_key] = dependencies[child]
            dependencies[child] = {new_key}
            aliases.add(child)
        else:
            rv[child] = val
    for key, val in dsk.items():
        if key not in fused:
            rv[key] = val
    if aliases:
        for key, deps in dependencies.items():
            for old_key in deps & aliases:
                new_key = rv[old_key]
                deps.remove(old_key)
                deps.add(new_key)
                rv[key] = subs(rv[key], old_key, new_key)
        if keys is not None:
            for key in aliases - keys:
                del rv[key]
                del dependencies[key]
    return rv, dependencies


def _flat_set(x):
    if x is None:
        return set()
    elif isinstance(x, set):
        return x
    elif not isinstance(x, (list, set)):
        x = [x]
    return set(x)


def inline(dsk, keys=None, inline_constants=True, dependencies=None):
    """ Return new dask with the given keys inlined with their values.

    Inlines all constants if ``inline_constants`` keyword is True. Note that
    the constant keys will remain in the graph, to remove them follow
    ``inline`` with ``cull``.

    Examples
    --------
    >>> d = {'x': 1, 'y': (inc, 'x'), 'z': (add, 'x', 'y')}
    >>> inline(d)  # doctest: +SKIP
    {'x': 1, 'y': (inc, 1), 'z': (add, 1, 'y')}

    >>> inline(d, keys='y')  # doctest: +SKIP
    {'x': 1, 'y': (inc, 1), 'z': (add, 1, (inc, 1))}

    >>> inline(d, keys='y', inline_constants=False)  # doctest: +SKIP
    {'x': 1, 'y': (inc, 1), 'z': (add, 'x', (inc, 'x'))}
    """
    if dependencies and isinstance(next(iter(dependencies.values())), list):
        dependencies = {k: set(v) for k, v in dependencies.items()}

    keys = _flat_set(keys)

    if dependencies is None:
        dependencies = {k: get_dependencies(dsk, k)
                        for k in dsk}

    if inline_constants:
        keys.update(k for k, v in dsk.items() if
                    (ishashable(v) and v in dsk) or
                    (not dependencies[k] and not istask(v)))

    # Keys may depend on other keys, so determine replace order with toposort.
    # The values stored in `keysubs` do not include other keys.
    replaceorder = toposort(dict((k, dsk[k]) for k in keys if k in dsk),
                            dependencies=dependencies)
    keysubs = {}
    for key in replaceorder:
        val = dsk[key]
        for dep in keys & dependencies[key]:
            if dep in keysubs:
                replace = keysubs[dep]
            else:
                replace = dsk[dep]
            val = subs(val, dep, replace)
        keysubs[key] = val

    # Make new dask with substitutions
    dsk2 = keysubs.copy()
    for key, val in dsk.items():
        if key not in dsk2:
            for item in keys & dependencies[key]:
                val = subs(val, item, keysubs[item])
            dsk2[key] = val
    return dsk2


def inline_functions(dsk, output, fast_functions=None, inline_constants=False,
                     dependencies=None):
    """ Inline cheap functions into larger operations

    Examples
    --------
    >>> dsk = {'out': (add, 'i', 'd'),  # doctest: +SKIP
    ...        'i': (inc, 'x'),
    ...        'd': (double, 'y'),
    ...        'x': 1, 'y': 1}
    >>> inline_functions(dsk, [], [inc])  # doctest: +SKIP
    {'out': (add, (inc, 'x'), 'd'),
     'd': (double, 'y'),
     'x': 1, 'y': 1}

    Protect output keys.  In the example below ``i`` is not inlined because it
    is marked as an output key.

    >>> inline_functions(dsk, ['i', 'out'], [inc, double])  # doctest: +SKIP
    {'out': (add, 'i', (double, 'y')),
     'i': (inc, 'x'),
     'x': 1, 'y': 1}
    """
    if not fast_functions:
        return dsk

    output = set(output)

    fast_functions = set(fast_functions)

    if dependencies is None:
        dependencies = {k: get_dependencies(dsk, k)
                        for k in dsk}
    dependents = reverse_dict(dependencies)

    def inlinable(v):
        try:
            return functions_of(v).issubset(fast_functions)
        except TypeError:
            return False

    keys = [k for k, v in dsk.items()
            if istask(v) and dependents[k] and k not in output and inlinable(v)]

    if keys:
        dsk = inline(dsk, keys, inline_constants=inline_constants,
                     dependencies=dependencies)
        for k in keys:
            del dsk[k]
    return dsk


def unwrap_partial(func):
    while hasattr(func, 'func'):
        func = func.func
    return func


def functions_of(task):
    """ Set of functions contained within nested task

    Examples
    --------
    >>> task = (add, (mul, 1, 2), (inc, 3))  # doctest: +SKIP
    >>> functions_of(task)  # doctest: +SKIP
    set([add, mul, inc])
    """
    funcs = set()

    work = [task]
    sequence_types = {list, tuple}

    while work:
        new_work = []
        for task in work:
            if type(task) in sequence_types:
                if istask(task):
                    funcs.add(unwrap_partial(task[0]))
                    new_work += task[1:]
                else:
                    new_work += task
        work = new_work

    return funcs


def fuse_selections(dsk, head1, head2, merge):
    """Fuse selections with lower operation.

    Handles graphs of the form:
    ``{key1: (head1, key2, ...), key2: (head2, ...)}``

    Parameters
    ----------
    dsk : dict
        dask graph
    head1 : function
        The first element of task1
    head2 : function
        The first element of task2
    merge : function
        Takes ``task1`` and ``task2`` and returns a merged task to
        replace ``task1``.

    Examples
    --------
    >>> def load(store, partition, columns):
    ...     pass
    >>> dsk = {'x': (load, 'store', 'part', ['a', 'b']),
    ...        'y': (getitem, 'x', 'a')}
    >>> merge = lambda t1, t2: (load, t2[1], t2[2], t1[2])
    >>> dsk2 = fuse_selections(dsk, getitem, load, merge)
    >>> cull(dsk2, 'y')[0]
    {'y': (<function load at ...>, 'store', 'part', 'a')}
    """
    dsk2 = dict()
    for k, v in dsk.items():
        try:
            if (istask(v) and v[0] == head1 and v[1] in dsk and
                    istask(dsk[v[1]]) and dsk[v[1]][0] == head2):
                dsk2[k] = merge(v, dsk[v[1]])
            else:
                dsk2[k] = v
        except TypeError:
            dsk2[k] = v
    return dsk2


def fuse_getitem(dsk, func, place):
    """ Fuse getitem with lower operation

    Parameters
    ----------
    dsk: dict
        dask graph
    func: function
        A function in a task to merge
    place: int
        Location in task to insert the getitem key

    Examples
    --------
    >>> def load(store, partition, columns):
    ...     pass
    >>> dsk = {'x': (load, 'store', 'part', ['a', 'b']),
    ...        'y': (getitem, 'x', 'a')}
    >>> dsk2 = fuse_getitem(dsk, load, 3)  # columns in arg place 3
    >>> cull(dsk2, 'y')[0]
    {'y': (<function load at ...>, 'store', 'part', 'a')}
    """
    return fuse_selections(dsk, getitem, func,
                           lambda a, b: tuple(b[:place]) + (a[2], ) + tuple(b[place + 1:]))


def default_fused_keys_renamer(keys):
    """Create new keys for ``fuse`` tasks"""
    it = reversed(keys)
    first_key = next(it)
    typ = type(first_key)
    if typ is str or typ is unicode:
        first_name = key_split(first_key)
        names = {key_split(k) for k in it}
        names.discard(first_name)
        names = sorted(names)
        names.append(first_key)
        return '-'.join(names)
    elif (typ is tuple and len(first_key) > 0 and
          isinstance(first_key[0], (str, unicode))):
        first_name = key_split(first_key)
        names = {key_split(k) for k in it}
        names.discard(first_name)
        names = sorted(names)
        names.append(first_key[0])
        return ('-'.join(names),) + first_key[1:]


def fuse(dsk, keys=None, dependencies=None, ave_width=None, max_width=None,
         max_height=None, max_depth_new_edges=None, rename_keys=None,
         fuse_subgraphs=None):
    """ Fuse tasks that form reductions; more advanced than ``fuse_linear``

    This trades parallelism opportunities for faster scheduling by making tasks
    less granular.  It can replace ``fuse_linear`` in optimization passes.

    This optimization applies to all reductions--tasks that have at most one
    dependent--so it may be viewed as fusing "multiple input, single output"
    groups of tasks into a single task.  There are many parameters to fine
    tune the behavior, which are described below.  ``ave_width`` is the
    natural parameter with which to compare parallelism to granularity, so
    it should always be specified.  Reasonable values for other parameters
    with be determined using ``ave_width`` if necessary.

    Parameters
    ----------
    dsk: dict
        dask graph
    keys: list or set, optional
        Keys that must remain in the returned dask graph
    dependencies: dict, optional
        {key: [list-of-keys]}.  Must be a list to provide count of each key
        This optional input often comes from ``cull``
    ave_width: float (default 2)
        Upper limit for ``width = num_nodes / height``, a good measure of
        parallelizability
    max_width: int
        Don't fuse if total width is greater than this
    max_height: int
        Don't fuse more than this many levels
    max_depth_new_edges: int
        Don't fuse if new dependencies are added after this many levels
    rename_keys: bool or func, optional
        Whether to rename the fused keys with ``default_fused_keys_renamer``
        or not.  Renaming fused keys can keep the graph more understandable
        and comprehensive, but it comes at the cost of additional processing.
        If False, then the top-most key will be used.  For advanced usage, a
        function to create the new name is also accepted.
    fuse_subgraphs : bool, optional
        Whether to fuse multiple tasks into ``SubgraphCallable`` objects.

    Returns
    -------
    dsk: output graph with keys fused
    dependencies: dict mapping dependencies after fusion.  Useful side effect
        to accelerate other downstream optimizations.
    """
    if keys is not None and not isinstance(keys, set):
        if not isinstance(keys, list):
            keys = [keys]
        keys = set(flatten(keys))

    # Assign reasonable, not too restrictive defaults
    if ave_width is None:
        if config.get('fuse_ave_width', None) is None:
            ave_width = 1
        else:
            ave_width = config.get('fuse_ave_width', None)

    if max_height is None:
        if config.get('fuse_max_height', None) is None:
            max_height = len(dsk)
        else:
            max_height = config.get('fuse_max_height', None)

    max_depth_new_edges = (
        max_depth_new_edges or
        config.get('fuse_max_depth_new_edges', None) or
        ave_width + 1.5
    )
    max_width = (
        max_width or
        config.get('fuse_max_width', None) or
        1.5 + ave_width * math.log(ave_width + 1)
    )

    if fuse_subgraphs is None:
        fuse_subgraphs = config.get('fuse_subgraphs', False)

    if not ave_width or not max_height:
        return dsk, dependencies

    if rename_keys is None:
        rename_keys = config.get('fuse_rename_keys', True)
    if rename_keys is True:
        key_renamer = default_fused_keys_renamer
    elif rename_keys is False:
        key_renamer = None
    else:
        key_renamer = rename_keys
    rename_keys = key_renamer is not None

    if dependencies is None:
        deps = {k: get_dependencies(dsk, k, as_list=True) for k in dsk}
    else:
        deps = dict(dependencies)

    rdeps = {}
    for k, vals in deps.items():
        for v in vals:
            if v not in rdeps:
                rdeps[v] = [k]
            else:
                rdeps[v].append(k)
        deps[k] = set(vals)

    reducible = {k for k, vals in rdeps.items() if len(vals) == 1}
    if keys:
        reducible -= keys
    if (not reducible and
            (not fuse_subgraphs or all(len(set(v)) != 1 for v in rdeps.values()))):
        # Quick return if there's nothing to do. Only progress if there's tasks
        # fusible by the main `fuse`, or by `fuse_subgraphs` if enabled.
        return dsk, deps

    rv = dsk.copy()
    fused_trees = {}
    # These are the stacks we use to store data as we traverse the graph
    info_stack = []
    children_stack = []
    # For speed
    deps_pop = deps.pop
    reducible_add = reducible.add
    reducible_pop = reducible.pop
    reducible_remove = reducible.remove
    fused_trees_pop = fused_trees.pop
    info_stack_append = info_stack.append
    info_stack_pop = info_stack.pop
    children_stack_append = children_stack.append
    children_stack_extend = children_stack.extend
    children_stack_pop = children_stack.pop
    while reducible:
        parent = reducible_pop()
        reducible_add(parent)
        while parent in reducible:
            # Go to the top
            parent = rdeps[parent][0]
        children_stack_append(parent)
        children_stack_extend(reducible & deps[parent])
        while True:
            child = children_stack[-1]
            if child != parent:
                children = reducible & deps[child]
                while children:
                    # Depth-first search
                    children_stack_extend(children)
                    parent = child
                    child = children_stack[-1]
                    children = reducible & deps[child]
                children_stack_pop()
                # This is a leaf node in the reduction region
                # key, task, fused_keys, height, width, number of nodes, fudge, set of edges
                info_stack_append((child, rv[child], [child] if rename_keys else None,
                                   1, 1, 1, 0, deps[child] - reducible))
            else:
                children_stack_pop()
                # Calculate metrics and fuse as appropriate
                deps_parent = deps[parent]
                edges = deps_parent - reducible
                children = deps_parent - edges
                num_children = len(children)

                if num_children == 1:
                    (child_key, child_task, child_keys, height, width, num_nodes, fudge,
                     children_edges) = info_stack_pop()
                    num_children_edges = len(children_edges)

                    if fudge > num_children_edges - 1 >= 0:
                        fudge = num_children_edges - 1
                    edges |= children_edges
                    no_new_edges = len(edges) == num_children_edges
                    if not no_new_edges:
                        fudge += 1
                    if (
                        (num_nodes + fudge) / height <= ave_width and
                        # Sanity check; don't go too deep if new levels introduce new edge dependencies
                        (no_new_edges or height < max_depth_new_edges)
                    ):
                        # Perform substitutions as we go
                        val = subs(dsk[parent], child_key, child_task)
                        deps_parent.remove(child_key)
                        deps_parent |= deps_pop(child_key)
                        del rv[child_key]
                        reducible_remove(child_key)
                        if rename_keys:
                            child_keys.append(parent)
                            fused_trees[parent] = child_keys
                            fused_trees_pop(child_key, None)

                        if children_stack:
                            if no_new_edges:
                                # Linear fuse
                                info_stack_append((parent, val, child_keys, height, width, num_nodes, fudge, edges))
                            else:
                                info_stack_append((parent, val, child_keys, height + 1, width, num_nodes + 1, fudge,
                                                   edges))
                        else:
                            rv[parent] = val
                            break
                    else:
                        rv[child_key] = child_task
                        reducible_remove(child_key)
                        if children_stack:
                            # Allow the parent to be fused, but only under strict circumstances.
                            # Ensure that linear chains may still be fused.
                            if fudge > int(ave_width - 1):
                                fudge = int(ave_width - 1)
                            # This task *implicitly* depends on `edges`
                            info_stack_append((parent, rv[parent], [parent] if rename_keys else None,
                                               1, width, 1, fudge, edges))
                        else:
                            break
                else:
                    child_keys = []
                    height = 1
                    width = 0
                    num_single_nodes = 0
                    num_nodes = 0
                    fudge = 0
                    children_edges = set()
                    max_num_edges = 0
                    children_info = info_stack[-num_children:]
                    del info_stack[-num_children:]
                    for cur_key, cur_task, cur_keys, cur_height, cur_width, cur_num_nodes, cur_fudge, \
                            cur_edges in children_info:
                        if cur_height == 1:
                            num_single_nodes += 1
                        elif cur_height > height:
                            height = cur_height
                        width += cur_width
                        num_nodes += cur_num_nodes
                        fudge += cur_fudge
                        if len(cur_edges) > max_num_edges:
                            max_num_edges = len(cur_edges)
                        children_edges |= cur_edges
                    # Fudge factor to account for possible parallelism with the boundaries
                    num_children_edges = len(children_edges)
                    fudge += min(num_children - 1, max(0, num_children_edges - max_num_edges))

                    if fudge > num_children_edges - 1 >= 0:
                        fudge = num_children_edges - 1
                    edges |= children_edges
                    no_new_edges = len(edges) == num_children_edges
                    if not no_new_edges:
                        fudge += 1
                    if (
                        (num_nodes + fudge) / height <= ave_width and
                        num_single_nodes <= ave_width and
                        width <= max_width and
                        height <= max_height and
                        # Sanity check; don't go too deep if new levels introduce new edge dependencies
                        (no_new_edges or height < max_depth_new_edges)
                    ):
                        # Perform substitutions as we go
                        val = dsk[parent]
                        children_deps = set()
                        for child_info in children_info:
                            cur_child = child_info[0]
                            val = subs(val, cur_child, child_info[1])
                            del rv[cur_child]
                            children_deps |= deps_pop(cur_child)
                            reducible_remove(cur_child)
                            if rename_keys:
                                fused_trees_pop(cur_child, None)
                                child_keys.extend(child_info[2])
                        deps_parent -= children
                        deps_parent |= children_deps

                        if rename_keys:
                            child_keys.append(parent)
                            fused_trees[parent] = child_keys

                        if children_stack:
                            info_stack_append((parent, val, child_keys, height + 1, width, num_nodes + 1, fudge, edges))
                        else:
                            rv[parent] = val
                            break
                    else:
                        for child_info in children_info:
                            rv[child_info[0]] = child_info[1]
                            reducible_remove(child_info[0])
                        if children_stack:
                            # Allow the parent to be fused, but only under strict circumstances.
                            # Ensure that linear chains may still be fused.
                            if width > max_width:
                                width = max_width
                            if fudge > int(ave_width - 1):
                                fudge = int(ave_width - 1)
                            # key, task, height, width, number of nodes, fudge, set of edges
                            # This task *implicitly* depends on `edges`
                            info_stack_append((parent, rv[parent], [parent] if rename_keys else None,
                                               1, width, 1, fudge, edges))
                        else:
                            break
                # Traverse upwards
                parent = rdeps[parent][0]

    if fuse_subgraphs:
        _inplace_fuse_subgraphs(rv, keys, deps, fused_trees, rename_keys)

    if rename_keys:
        for root_key, fused_keys in fused_trees.items():
            alias = key_renamer(fused_keys)
            if alias is not None and alias not in rv:
                rv[alias] = rv[root_key]
                rv[root_key] = alias
                deps[alias] = deps[root_key]
                deps[root_key] = {alias}

    return rv, deps


def _inplace_fuse_subgraphs(dsk, keys, dependencies, fused_trees, rename_keys):
    """Subroutine of fuse.

    Mutates dsk, depenencies, and fused_trees inplace"""
    # locate all members of linear chains
    child2parent = {}
    unfusible = set()
    for parent in dsk:
        deps = dependencies[parent]
        has_many_children = len(deps) > 1
        for child in deps:
            if keys is not None and child in keys:
                unfusible.add(child)
            elif child in child2parent:
                del child2parent[child]
                unfusible.add(child)
            elif has_many_children:
                unfusible.add(child)
            elif child not in unfusible:
                child2parent[child] = parent

    # construct the chains from ancestor to descendant
    chains = []
    parent2child = {v: k for k, v in child2parent.items()}
    while child2parent:
        child, parent = child2parent.popitem()
        chain = [child, parent]
        while parent in child2parent:
            parent = child2parent.pop(parent)
            del parent2child[parent]
            chain.append(parent)
        chain.reverse()
        while child in parent2child:
            child = parent2child.pop(child)
            del child2parent[child]
            chain.append(child)
        # Skip chains with < 2 executable tasks
        ntasks = 0
        for key in chain:
            ntasks += istask(dsk[key])
            if ntasks > 1:
                chains.append(chain)
                break

    # Mutate dsk fusing chains into subgraphs
    for chain in chains:
        subgraph = {k: dsk[k] for k in chain}
        outkey = chain[0]

        # Update dependencies and graph
        inkeys_set = dependencies[outkey] = dependencies[chain[-1]]
        for k in chain[1:]:
            del dependencies[k]
            del dsk[k]

        # Create new task
        inkeys = tuple(inkeys_set)
        dsk[outkey] = (SubgraphCallable(subgraph, outkey, inkeys),) + inkeys

        # Mutate `fused_trees` if key renaming is needed (renaming done in fuse)
        if rename_keys:
            chain2 = []
            for k in chain:
                subchain = fused_trees.pop(k, False)
                if subchain:
                    chain2.extend(subchain)
                else:
                    chain2.append(k)
            fused_trees[outkey] = chain2


# Defining `key_split` (used by key renamers in `fuse`) in utils.py
# results in messy circular imports, so define it here instead.
hex_pattern = re.compile('[a-f]+')


def key_split(s):
    """
    >>> key_split('x')
    'x'
    >>> key_split('x-1')
    'x'
    >>> key_split('x-1-2-3')
    'x'
    >>> key_split(('x-2', 1))
    'x'
    >>> key_split("('x-2', 1)")
    'x'
    >>> key_split('hello-world-1')
    'hello-world'
    >>> key_split(b'hello-world-1')
    'hello-world'
    >>> key_split('ae05086432ca935f6eba409a8ecd4896')
    'data'
    >>> key_split('<module.submodule.myclass object at 0xdaf372')
    'myclass'
    >>> key_split(None)
    'Other'
    >>> key_split('x-abcdefab')  # ignores hex
    'x'
    >>> key_split('_(x)')  # strips unpleasant characters
    'x'
    """
    if type(s) is bytes:
        s = s.decode()
    if type(s) is tuple:
        s = s[0]
    try:
        words = s.split('-')
        if not words[0][0].isalpha():
            result = words[0].strip("_'()\"")
        else:
            result = words[0]
        for word in words[1:]:
            if word.isalpha() and not (len(word) == 8 and
                                       hex_pattern.match(word) is not None):
                result += '-' + word
            else:
                break
        if len(result) == 32 and re.match(r'[a-f0-9]{32}', result):
            return 'data'
        else:
            if result[0] == '<':
                result = result.strip('<>').split()[0].split('.')[-1]
            return result
    except Exception:
        return 'Other'


class SubgraphCallable(object):
    """Create a callable object from a dask graph.

    Parameters
    ----------
    dsk : dict
        A dask graph
    outkey : hashable
        The output key from the graph
    inkeys : list
        A list of keys to be used as arguments to the callable.
    name : str, optional
        The name to use for the function.
    """
    __slots__ = ('dsk', 'outkey', 'inkeys', 'name')

    def __init__(self, dsk, outkey, inkeys, name='subgraph_callable'):
        self.dsk = dsk
        self.outkey = outkey
        self.inkeys = inkeys
        self.name = name

    def __repr__(self):
        return self.name

    def __eq__(self, other):
        return (type(self) is type(other) and
                self.dsk == other.dsk and
                self.outkey == other.outkey and
                set(self.inkeys) == set(other.inkeys) and
                self.name == other.name)

    def __ne__(self, other):
        return not (self == other)

    def __call__(self, *args):
        if not len(args) == len(self.inkeys):
            raise ValueError("Expected %d args, got %d"
                             % (len(self.inkeys), len(args)))
        return _get_recursive(self.dsk, self.outkey,
                              dict(zip(self.inkeys, args)))

    def __reduce__(self):
        return (SubgraphCallable,
                (self.dsk, self.outkey, self.inkeys, self.name))
