import itertools
import pickle
from functools import partial

import pytest

import dask
from dask.base import tokenize
from dask.core import get_dependencies
from dask.local import get_sync
from dask.optimization import (
    SubgraphCallable,
    cull,
    functions_of,
    fuse,
    fuse_linear,
    inline,
    inline_functions,
)
from dask.utils import apply, partial_by_order
from dask.utils_test import add, inc


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


@pytest.fixture
def compare_subgraph_callables(monkeypatch):
    """Ignore name when comparing instances of :class:`SubgraphCallable`.

    They have UUID-generated names which prevents instances generated by the
    test from comparing equal to reference values. Instead, compare the
    embedded graph using ``tokenize``.
    """
    monkeypatch.setattr(SubgraphCallable, "__eq__", _subgraph_callables_eq)


def double(x):
    return x * 2


def test_cull():
    # 'out' depends on 'x' and 'y', but not 'z'
    d = {"x": 1, "y": (inc, "x"), "z": (inc, "x"), "out": (add, "y", 10)}
    culled, dependencies = cull(d, "out")
    assert culled == {"x": 1, "y": (inc, "x"), "out": (add, "y", 10)}
    assert dependencies == {"x": [], "y": ["x"], "out": ["y"]}

    assert cull(d, "out") == cull(d, ["out"])
    assert cull(d, ["out", "z"])[0] == d
    assert cull(d, [["out"], ["z"]]) == cull(d, ["out", "z"])
    pytest.raises(KeyError, lambda: cull(d, "badkey"))


def fuse2(*args, **kwargs):
    """Run both ``fuse`` and ``fuse_linear`` and compare results"""
    rv1 = fuse_linear(*args, **kwargs)
    if kwargs.get("rename_keys") is not False:
        return rv1
    rv2 = fuse(*args, **kwargs)
    assert rv1 == rv2
    return rv1


def with_deps(dsk):
    return dsk, {k: get_dependencies(dsk, k) for k in dsk}


def test_fuse():
    fuse = fuse2  # tests both `fuse` and `fuse_linear`
    d = {
        "w": (inc, "x"),
        "x": (inc, "y"),
        "y": (inc, "z"),
        "z": (add, "a", "b"),
        "a": 1,
        "b": 2,
    }
    assert fuse(d, rename_keys=False) == with_deps(
        {"w": (inc, (inc, (inc, (add, "a", "b")))), "a": 1, "b": 2}
    )
    assert fuse(d, rename_keys=True) == with_deps(
        {
            "z-y-x-w": (inc, (inc, (inc, (add, "a", "b")))),
            "a": 1,
            "b": 2,
            "w": "z-y-x-w",
        }
    )

    d = {
        "NEW": (inc, "y"),
        "w": (inc, "x"),
        "x": (inc, "y"),
        "y": (inc, "z"),
        "z": (add, "a", "b"),
        "a": 1,
        "b": 2,
    }
    assert fuse(d, rename_keys=False) == with_deps(
        {
            "NEW": (inc, "y"),
            "w": (inc, (inc, "y")),
            "y": (inc, (add, "a", "b")),
            "a": 1,
            "b": 2,
        }
    )
    assert fuse(d, rename_keys=True) == with_deps(
        {
            "NEW": (inc, "z-y"),
            "x-w": (inc, (inc, "z-y")),
            "z-y": (inc, (add, "a", "b")),
            "a": 1,
            "b": 2,
            "w": "x-w",
            "y": "z-y",
        }
    )

    d = {
        "v": (inc, "y"),
        "u": (inc, "w"),
        "w": (inc, "x"),
        "x": (inc, "y"),
        "y": (inc, "z"),
        "z": (add, "a", "b"),
        "a": (inc, "c"),
        "b": (inc, "d"),
        "c": 1,
        "d": 2,
    }
    assert fuse(d, rename_keys=False) == with_deps(
        {
            "u": (inc, (inc, (inc, "y"))),
            "v": (inc, "y"),
            "y": (inc, (add, "a", "b")),
            "a": (inc, 1),
            "b": (inc, 2),
        }
    )
    assert fuse(d, rename_keys=True) == with_deps(
        {
            "x-w-u": (inc, (inc, (inc, "z-y"))),
            "v": (inc, "z-y"),
            "z-y": (inc, (add, "c-a", "d-b")),
            "c-a": (inc, 1),
            "d-b": (inc, 2),
            "a": "c-a",
            "b": "d-b",
            "u": "x-w-u",
            "y": "z-y",
        }
    )

    d = {
        "a": (inc, "x"),
        "b": (inc, "x"),
        "c": (inc, "x"),
        "d": (inc, "c"),
        "x": (inc, "y"),
        "y": 0,
    }
    assert fuse(d, rename_keys=False) == with_deps(
        {"a": (inc, "x"), "b": (inc, "x"), "d": (inc, (inc, "x")), "x": (inc, 0)}
    )
    assert fuse(d, rename_keys=True) == with_deps(
        {
            "a": (inc, "y-x"),
            "b": (inc, "y-x"),
            "c-d": (inc, (inc, "y-x")),
            "y-x": (inc, 0),
            "d": "c-d",
            "x": "y-x",
        }
    )

    d = {"a": 1, "b": (inc, "a"), "c": (add, "b", "b")}
    assert fuse(d, rename_keys=False) == with_deps(
        {"b": (inc, 1), "c": (add, "b", "b")}
    )
    assert fuse(d, rename_keys=True) == with_deps(
        {"a-b": (inc, 1), "c": (add, "a-b", "a-b"), "b": "a-b"}
    )


def test_fuse_keys():
    fuse = fuse2  # tests both `fuse` and `fuse_linear`
    d = {"a": 1, "b": (inc, "a"), "c": (inc, "b")}
    keys = ["b"]
    assert fuse(d, keys, rename_keys=False) == with_deps(
        {"b": (inc, 1), "c": (inc, "b")}
    )
    assert fuse(d, keys, rename_keys=True) == with_deps(
        {"a-b": (inc, 1), "c": (inc, "a-b"), "b": "a-b"}
    )

    d = {
        "w": (inc, "x"),
        "x": (inc, "y"),
        "y": (inc, "z"),
        "z": (add, "a", "b"),
        "a": 1,
        "b": 2,
    }
    keys = ["x", "z"]
    assert fuse(d, keys, rename_keys=False) == with_deps(
        {"w": (inc, "x"), "x": (inc, (inc, "z")), "z": (add, "a", "b"), "a": 1, "b": 2}
    )
    assert fuse(d, keys, rename_keys=True) == with_deps(
        {
            "w": (inc, "y-x"),
            "y-x": (inc, (inc, "z")),
            "z": (add, "a", "b"),
            "a": 1,
            "b": 2,
            "x": "y-x",
        }
    )


def test_inline():
    d = {"a": 1, "b": (inc, "a"), "c": (inc, "b"), "d": (add, "a", "c")}
    assert inline(d) == {"a": 1, "b": (inc, 1), "c": (inc, "b"), "d": (add, 1, "c")}
    assert inline(d, ["a", "b", "c"]) == {
        "a": 1,
        "b": (inc, 1),
        "c": (inc, (inc, 1)),
        "d": (add, 1, (inc, (inc, 1))),
    }
    d = {"x": 1, "y": (inc, "x"), "z": (add, "x", "y")}
    assert inline(d) == {"x": 1, "y": (inc, 1), "z": (add, 1, "y")}
    assert inline(d, keys="y") == {"x": 1, "y": (inc, 1), "z": (add, 1, (inc, 1))}
    assert inline(d, keys="y", inline_constants=False) == {
        "x": 1,
        "y": (inc, "x"),
        "z": (add, "x", (inc, "x")),
    }

    d = {"a": 1, "b": "a", "c": "b", "d": ["a", "b", "c"], "e": (add, (len, "d"), "a")}
    assert inline(d, "d") == {
        "a": 1,
        "b": 1,
        "c": 1,
        "d": [1, 1, 1],
        "e": (add, (len, [1, 1, 1]), 1),
    }
    assert inline(d, "a", inline_constants=False) == {
        "a": 1,
        "b": 1,
        "c": "b",
        "d": [1, "b", "c"],
        "e": (add, (len, "d"), 1),
    }


def test_inline_functions():
    x, y, i, d = "xyid"
    dsk = {"out": (add, i, d), i: (inc, x), d: (double, y), x: 1, y: 1}

    result = inline_functions(dsk, [], fast_functions={inc})
    expected = {"out": (add, (inc, x), d), d: (double, y), x: 1, y: 1}
    assert result == expected


def test_inline_ignores_curries_and_partials():
    dsk = {"x": 1, "y": 2, "a": (partial(add, 1), "x"), "b": (inc, "a")}

    result = inline_functions(dsk, [], fast_functions={add})
    assert result["b"] == (inc, dsk["a"])
    assert "a" not in result


def test_inline_functions_non_hashable():
    class NonHashableCallable:
        def __call__(self, a):
            return a + 1

        def __hash__(self):
            raise TypeError("Not hashable")

    nohash = NonHashableCallable()

    dsk = {"a": 1, "b": (inc, "a"), "c": (nohash, "b"), "d": (inc, "c")}

    result = inline_functions(dsk, [], fast_functions={inc})
    assert result["c"] == (nohash, dsk["b"])
    assert "b" not in result


def test_inline_doesnt_shrink_fast_functions_at_top():
    dsk = {"x": (inc, "y"), "y": 1}
    result = inline_functions(dsk, [], fast_functions={inc})
    assert result == dsk


def test_inline_traverses_lists():
    x, y, i, d = "xyid"
    dsk = {"out": (sum, [i, d]), i: (inc, x), d: (double, y), x: 1, y: 1}
    expected = {"out": (sum, [(inc, x), d]), d: (double, y), x: 1, y: 1}
    result = inline_functions(dsk, [], fast_functions={inc})
    assert result == expected


def test_inline_functions_protects_output_keys():
    dsk = {"x": (inc, 1), "y": (double, "x")}
    assert inline_functions(dsk, [], [inc]) == {"y": (double, (inc, 1))}
    assert inline_functions(dsk, ["x"], [inc]) == {"y": (double, "x"), "x": (inc, 1)}


def test_functions_of():
    a = lambda x: x
    b = lambda x: x
    assert functions_of((a, 1)) == {a}
    assert functions_of((a, (b, 1))) == {a, b}
    assert functions_of((a, [(b, 1)])) == {a, b}
    assert functions_of((a, [[[(b, 1)]]])) == {a, b}
    assert functions_of(1) == set()
    assert functions_of(a) == set()
    assert functions_of((a,)) == {a}


def test_inline_cull_dependencies():
    d = {"a": 1, "b": "a", "c": "b", "d": ["a", "b", "c"], "e": (add, (len, "d"), "a")}

    d2, dependencies = cull(d, ["d", "e"])
    inline(d2, {"b"}, dependencies=dependencies)


def test_fuse_reductions_single_input():
    def f(*args):
        return args

    d = {"a": 1, "b1": (f, "a"), "b2": (f, "a", "a"), "c": (f, "b1", "b2")}
    assert fuse(d, ave_width=1.9, rename_keys=False) == with_deps(d)
    assert fuse(d, ave_width=1.9, rename_keys=True) == with_deps(d)
    assert fuse(d, ave_width=2, rename_keys=False) == with_deps(
        {"a": 1, "c": (f, (f, "a"), (f, "a", "a"))}
    )
    assert fuse(d, ave_width=2, rename_keys=True) == with_deps(
        {"a": 1, "b1-b2-c": (f, (f, "a"), (f, "a", "a")), "c": "b1-b2-c"}
    )

    d = {
        "a": 1,
        "b1": (f, "a"),
        "b2": (f, "a", "a"),
        "b3": (f, "a", "a", "a"),
        "c": (f, "b1", "b2", "b3"),
    }
    assert fuse(d, ave_width=2.9, rename_keys=False) == with_deps(d)
    assert fuse(d, ave_width=2.9, rename_keys=True) == with_deps(d)
    assert fuse(d, ave_width=3, rename_keys=False) == with_deps(
        {"a": 1, "c": (f, (f, "a"), (f, "a", "a"), (f, "a", "a", "a"))}
    )
    assert fuse(d, ave_width=3, rename_keys=True) == with_deps(
        {
            "a": 1,
            "b1-b2-b3-c": (f, (f, "a"), (f, "a", "a"), (f, "a", "a", "a")),
            "c": "b1-b2-b3-c",
        }
    )

    d = {"a": 1, "b1": (f, "a"), "b2": (f, "a"), "c": (f, "a", "b1", "b2")}
    assert fuse(d, ave_width=1.9, rename_keys=False) == with_deps(d)
    assert fuse(d, ave_width=1.9, rename_keys=True) == with_deps(d)
    assert fuse(d, ave_width=2, rename_keys=False) == with_deps(
        {"a": 1, "c": (f, "a", (f, "a"), (f, "a"))}
    )
    assert fuse(d, ave_width=2, rename_keys=True) == with_deps(
        {"a": 1, "b1-b2-c": (f, "a", (f, "a"), (f, "a")), "c": "b1-b2-c"}
    )

    d = {
        "a": 1,
        "b1": (f, "a"),
        "b2": (f, "a"),
        "c": (f, "b1", "b2"),
        "d1": (f, "c"),
        "d2": (f, "c"),
        "e": (f, "d1", "d2"),
    }
    assert fuse(d, ave_width=1.9, rename_keys=False) == with_deps(d)
    assert fuse(d, ave_width=1.9, rename_keys=True) == with_deps(d)
    assert fuse(d, ave_width=2, rename_keys=False) == with_deps(
        {"a": 1, "c": (f, (f, "a"), (f, "a")), "e": (f, (f, "c"), (f, "c"))}
    )
    assert fuse(d, ave_width=2, rename_keys=True) == with_deps(
        {
            "a": 1,
            "b1-b2-c": (f, (f, "a"), (f, "a")),
            "d1-d2-e": (f, (f, "c"), (f, "c")),
            "c": "b1-b2-c",
            "e": "d1-d2-e",
        }
    )

    d = {
        "a": 1,
        "b1": (f, "a"),
        "b2": (f, "a"),
        "b3": (f, "a"),
        "b4": (f, "a"),
        "c1": (f, "b1", "b2"),
        "c2": (f, "b3", "b4"),
        "d": (f, "c1", "c2"),
    }
    assert fuse(d, ave_width=1.9, rename_keys=False) == with_deps(d)
    assert fuse(d, ave_width=1.9, rename_keys=True) == with_deps(d)
    expected = with_deps(
        {
            "a": 1,
            "c1": (f, (f, "a"), (f, "a")),
            "c2": (f, (f, "a"), (f, "a")),
            "d": (f, "c1", "c2"),
        }
    )
    assert fuse(d, ave_width=2, rename_keys=False) == expected
    assert fuse(d, ave_width=2.9, rename_keys=False) == expected
    expected = with_deps(
        {
            "a": 1,
            "b1-b2-c1": (f, (f, "a"), (f, "a")),
            "b3-b4-c2": (f, (f, "a"), (f, "a")),
            "d": (f, "c1", "c2"),
            "c1": "b1-b2-c1",
            "c2": "b3-b4-c2",
        }
    )
    assert fuse(d, ave_width=2, rename_keys=True) == expected
    assert fuse(d, ave_width=2.9, rename_keys=True) == expected
    assert fuse(d, ave_width=3, rename_keys=False) == with_deps(
        {"a": 1, "d": (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a")))}
    )
    assert fuse(d, ave_width=3, rename_keys=True) == with_deps(
        {
            "a": 1,
            "b1-b2-b3-b4-c1-c2-d": (
                f,
                (f, (f, "a"), (f, "a")),
                (f, (f, "a"), (f, "a")),
            ),
            "d": "b1-b2-b3-b4-c1-c2-d",
        }
    )

    d = {
        "a": 1,
        "b1": (f, "a"),
        "b2": (f, "a"),
        "b3": (f, "a"),
        "b4": (f, "a"),
        "b5": (f, "a"),
        "b6": (f, "a"),
        "b7": (f, "a"),
        "b8": (f, "a"),
        "c1": (f, "b1", "b2"),
        "c2": (f, "b3", "b4"),
        "c3": (f, "b5", "b6"),
        "c4": (f, "b7", "b8"),
        "d1": (f, "c1", "c2"),
        "d2": (f, "c3", "c4"),
        "e": (f, "d1", "d2"),
    }
    assert fuse(d, ave_width=1.9, rename_keys=False) == with_deps(d)
    assert fuse(d, ave_width=1.9, rename_keys=True) == with_deps(d)
    expected = with_deps(
        {
            "a": 1,
            "c1": (f, (f, "a"), (f, "a")),
            "c2": (f, (f, "a"), (f, "a")),
            "c3": (f, (f, "a"), (f, "a")),
            "c4": (f, (f, "a"), (f, "a")),
            "d1": (f, "c1", "c2"),
            "d2": (f, "c3", "c4"),
            "e": (f, "d1", "d2"),
        }
    )
    assert fuse(d, ave_width=2, rename_keys=False) == expected
    assert fuse(d, ave_width=2.9, rename_keys=False) == expected
    expected = with_deps(
        {
            "a": 1,
            "b1-b2-c1": (f, (f, "a"), (f, "a")),
            "b3-b4-c2": (f, (f, "a"), (f, "a")),
            "b5-b6-c3": (f, (f, "a"), (f, "a")),
            "b7-b8-c4": (f, (f, "a"), (f, "a")),
            "d1": (f, "c1", "c2"),
            "d2": (f, "c3", "c4"),
            "e": (f, "d1", "d2"),
            "c1": "b1-b2-c1",
            "c2": "b3-b4-c2",
            "c3": "b5-b6-c3",
            "c4": "b7-b8-c4",
        }
    )
    assert fuse(d, ave_width=2, rename_keys=True) == expected
    assert fuse(d, ave_width=2.9, rename_keys=True) == expected
    expected = with_deps(
        {
            "a": 1,
            "d1": (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
            "d2": (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
            "e": (f, "d1", "d2"),
        }
    )
    assert fuse(d, ave_width=3, rename_keys=False) == expected
    assert fuse(d, ave_width=4.6, rename_keys=False) == expected
    expected = with_deps(
        {
            "a": 1,
            "b1-b2-b3-b4-c1-c2-d1": (
                f,
                (f, (f, "a"), (f, "a")),
                (f, (f, "a"), (f, "a")),
            ),
            "b5-b6-b7-b8-c3-c4-d2": (
                f,
                (f, (f, "a"), (f, "a")),
                (f, (f, "a"), (f, "a")),
            ),
            "e": (f, "d1", "d2"),
            "d1": "b1-b2-b3-b4-c1-c2-d1",
            "d2": "b5-b6-b7-b8-c3-c4-d2",
        }
    )
    assert fuse(d, ave_width=3, rename_keys=True) == expected
    assert fuse(d, ave_width=4.6, rename_keys=True) == expected
    assert fuse(d, ave_width=4.7, rename_keys=False) == with_deps(
        {
            "a": 1,
            "e": (
                f,
                (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
                (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
            ),
        }
    )
    assert fuse(d, ave_width=4.7, rename_keys=True) == with_deps(
        {
            "a": 1,
            "b1-b2-b3-b4-b5-b6-b7-b8-c1-c2-c3-c4-d1-d2-e": (
                f,
                (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
                (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
            ),
            "e": "b1-b2-b3-b4-b5-b6-b7-b8-c1-c2-c3-c4-d1-d2-e",
        }
    )

    d = {
        "a": 1,
        "b1": (f, "a"),
        "b2": (f, "a"),
        "b3": (f, "a"),
        "b4": (f, "a"),
        "b5": (f, "a"),
        "b6": (f, "a"),
        "b7": (f, "a"),
        "b8": (f, "a"),
        "b9": (f, "a"),
        "b10": (f, "a"),
        "b11": (f, "a"),
        "b12": (f, "a"),
        "b13": (f, "a"),
        "b14": (f, "a"),
        "b15": (f, "a"),
        "b16": (f, "a"),
        "c1": (f, "b1", "b2"),
        "c2": (f, "b3", "b4"),
        "c3": (f, "b5", "b6"),
        "c4": (f, "b7", "b8"),
        "c5": (f, "b9", "b10"),
        "c6": (f, "b11", "b12"),
        "c7": (f, "b13", "b14"),
        "c8": (f, "b15", "b16"),
        "d1": (f, "c1", "c2"),
        "d2": (f, "c3", "c4"),
        "d3": (f, "c5", "c6"),
        "d4": (f, "c7", "c8"),
        "e1": (f, "d1", "d2"),
        "e2": (f, "d3", "d4"),
        "f": (f, "e1", "e2"),
    }
    assert fuse(d, ave_width=1.9, rename_keys=False) == with_deps(d)
    assert fuse(d, ave_width=1.9, rename_keys=True) == with_deps(d)
    expected = with_deps(
        {
            "a": 1,
            "c1": (f, (f, "a"), (f, "a")),
            "c2": (f, (f, "a"), (f, "a")),
            "c3": (f, (f, "a"), (f, "a")),
            "c4": (f, (f, "a"), (f, "a")),
            "c5": (f, (f, "a"), (f, "a")),
            "c6": (f, (f, "a"), (f, "a")),
            "c7": (f, (f, "a"), (f, "a")),
            "c8": (f, (f, "a"), (f, "a")),
            "d1": (f, "c1", "c2"),
            "d2": (f, "c3", "c4"),
            "d3": (f, "c5", "c6"),
            "d4": (f, "c7", "c8"),
            "e1": (f, "d1", "d2"),
            "e2": (f, "d3", "d4"),
            "f": (f, "e1", "e2"),
        }
    )
    assert fuse(d, ave_width=2, rename_keys=False) == expected
    assert fuse(d, ave_width=2.9, rename_keys=False) == expected
    expected = with_deps(
        {
            "a": 1,
            "b1-b2-c1": (f, (f, "a"), (f, "a")),
            "b3-b4-c2": (f, (f, "a"), (f, "a")),
            "b5-b6-c3": (f, (f, "a"), (f, "a")),
            "b7-b8-c4": (f, (f, "a"), (f, "a")),
            "b10-b9-c5": (f, (f, "a"), (f, "a")),
            "b11-b12-c6": (f, (f, "a"), (f, "a")),
            "b13-b14-c7": (f, (f, "a"), (f, "a")),
            "b15-b16-c8": (f, (f, "a"), (f, "a")),
            "d1": (f, "c1", "c2"),
            "d2": (f, "c3", "c4"),
            "d3": (f, "c5", "c6"),
            "d4": (f, "c7", "c8"),
            "e1": (f, "d1", "d2"),
            "e2": (f, "d3", "d4"),
            "f": (f, "e1", "e2"),
            "c1": "b1-b2-c1",
            "c2": "b3-b4-c2",
            "c3": "b5-b6-c3",
            "c4": "b7-b8-c4",
            "c5": "b10-b9-c5",
            "c6": "b11-b12-c6",
            "c7": "b13-b14-c7",
            "c8": "b15-b16-c8",
        }
    )
    assert fuse(d, ave_width=2, rename_keys=True) == expected
    assert fuse(d, ave_width=2.9, rename_keys=True) == expected
    expected = with_deps(
        {
            "a": 1,
            "d1": (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
            "d2": (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
            "d3": (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
            "d4": (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
            "e1": (f, "d1", "d2"),
            "e2": (f, "d3", "d4"),
            "f": (f, "e1", "e2"),
        }
    )
    assert fuse(d, ave_width=3, rename_keys=False) == expected
    assert fuse(d, ave_width=4.6, rename_keys=False) == expected
    expected = with_deps(
        {
            "a": 1,
            "b1-b2-b3-b4-c1-c2-d1": (
                f,
                (f, (f, "a"), (f, "a")),
                (f, (f, "a"), (f, "a")),
            ),
            "b5-b6-b7-b8-c3-c4-d2": (
                f,
                (f, (f, "a"), (f, "a")),
                (f, (f, "a"), (f, "a")),
            ),
            "b10-b11-b12-b9-c5-c6-d3": (
                f,
                (f, (f, "a"), (f, "a")),
                (f, (f, "a"), (f, "a")),
            ),
            "b13-b14-b15-b16-c7-c8-d4": (
                f,
                (f, (f, "a"), (f, "a")),
                (f, (f, "a"), (f, "a")),
            ),
            "e1": (f, "d1", "d2"),
            "e2": (f, "d3", "d4"),
            "f": (f, "e1", "e2"),
            "d1": "b1-b2-b3-b4-c1-c2-d1",
            "d2": "b5-b6-b7-b8-c3-c4-d2",
            "d3": "b10-b11-b12-b9-c5-c6-d3",
            "d4": "b13-b14-b15-b16-c7-c8-d4",
        }
    )
    assert fuse(d, ave_width=3, rename_keys=True) == expected
    assert fuse(d, ave_width=4.6, rename_keys=True) == expected
    expected = with_deps(
        {
            "a": 1,
            "e1": (
                f,
                (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
                (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
            ),
            "e2": (
                f,
                (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
                (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
            ),
            "f": (f, "e1", "e2"),
        }
    )
    assert fuse(d, ave_width=4.7, rename_keys=False) == expected
    assert fuse(d, ave_width=7.4, rename_keys=False) == expected
    expected = with_deps(
        {
            "a": 1,
            "b1-b2-b3-b4-b5-b6-b7-b8-c1-c2-c3-c4-d1-d2-e1": (
                f,
                (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
                (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
            ),
            "b10-b11-b12-b13-b14-b15-b16-b9-c5-c6-c7-c8-d3-d4-e2": (
                f,
                (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
                (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
            ),
            "f": (f, "e1", "e2"),
            "e1": "b1-b2-b3-b4-b5-b6-b7-b8-c1-c2-c3-c4-d1-d2-e1",
            "e2": "b10-b11-b12-b13-b14-b15-b16-b9-c5-c6-c7-c8-d3-d4-e2",
        }
    )
    assert fuse(d, ave_width=4.7, rename_keys=True) == expected
    assert fuse(d, ave_width=7.4, rename_keys=True) == expected
    assert fuse(d, ave_width=7.5, rename_keys=False) == with_deps(
        {
            "a": 1,
            "f": (
                f,
                (
                    f,
                    (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
                    (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
                ),
                (
                    f,
                    (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
                    (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
                ),
            ),
        }
    )
    assert fuse(d, ave_width=7.5, rename_keys=True) == with_deps(
        {
            "a": 1,
            "b1-b10-b11-b12-b13-b14-b15-b16-b2-b3-b4-b5-b6-b7-b8-b9-c1-c2-c3-c4-c5-c6-c7-c8-d1-d2-d3-d4-e1-e2-f": (
                f,
                (
                    f,
                    (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
                    (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
                ),
                (
                    f,
                    (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
                    (f, (f, (f, "a"), (f, "a")), (f, (f, "a"), (f, "a"))),
                ),
            ),
            "f": "b1-b10-b11-b12-b13-b14-b15-b16-b2-b3-b4-b5-b6-b7-b8-b9-c1-c2-c3-c4-c5-c6-c7-c8-d1-d2-d3-d4-e1-e2-f",
        }
    )

    d = {"a": 1, "b": (f, "a")}
    assert fuse(d, ave_width=1, rename_keys=False) == with_deps({"b": (f, 1)})
    assert fuse(d, ave_width=1, rename_keys=True) == with_deps(
        {"a-b": (f, 1), "b": "a-b"}
    )

    d = {"a": 1, "b": (f, "a"), "c": (f, "b"), "d": (f, "c")}
    assert fuse(d, ave_width=1, rename_keys=False) == with_deps({"d": (f, (f, (f, 1)))})
    assert fuse(d, ave_width=1, rename_keys=True) == with_deps(
        {"a-b-c-d": (f, (f, (f, 1))), "d": "a-b-c-d"}
    )

    d = {"a": 1, "b": (f, "a"), "c": (f, "a", "b"), "d": (f, "a", "c")}
    assert fuse(d, ave_width=1, rename_keys=False) == with_deps(
        {"a": 1, "d": (f, "a", (f, "a", (f, "a")))}
    )
    assert fuse(d, ave_width=1, rename_keys=True) == with_deps(
        {"a": 1, "b-c-d": (f, "a", (f, "a", (f, "a"))), "d": "b-c-d"}
    )

    d = {
        "a": 1,
        "b1": (f, "a"),
        "b2": (f, "a"),
        "c1": (f, "b1"),
        "d1": (f, "c1"),
        "e1": (f, "d1"),
        "f": (f, "e1", "b2"),
    }
    expected = with_deps(
        {"a": 1, "b2": (f, "a"), "e1": (f, (f, (f, (f, "a")))), "f": (f, "e1", "b2")}
    )
    assert fuse(d, ave_width=1, rename_keys=False) == expected
    assert fuse(d, ave_width=1.9, rename_keys=False) == expected
    expected = with_deps(
        {
            "a": 1,
            "b2": (f, "a"),
            "b1-c1-d1-e1": (f, (f, (f, (f, "a")))),
            "f": (f, "e1", "b2"),
            "e1": "b1-c1-d1-e1",
        }
    )
    assert fuse(d, ave_width=1, rename_keys=True) == expected
    assert fuse(d, ave_width=1.9, rename_keys=True) == expected
    assert fuse(d, ave_width=2, rename_keys=False) == with_deps(
        {"a": 1, "f": (f, (f, (f, (f, (f, "a")))), (f, "a"))}
    )
    assert fuse(d, ave_width=2, rename_keys=True) == with_deps(
        {
            "a": 1,
            "b1-b2-c1-d1-e1-f": (f, (f, (f, (f, (f, "a")))), (f, "a")),
            "f": "b1-b2-c1-d1-e1-f",
        }
    )

    d = {
        "a": 1,
        "b1": (f, "a"),
        "b2": (f, "a"),
        "c1": (f, "a", "b1"),
        "d1": (f, "a", "c1"),
        "e1": (f, "a", "d1"),
        "f": (f, "a", "e1", "b2"),
    }
    expected = with_deps(
        {
            "a": 1,
            "b2": (f, "a"),
            "e1": (f, "a", (f, "a", (f, "a", (f, "a")))),
            "f": (f, "a", "e1", "b2"),
        }
    )
    assert fuse(d, ave_width=1, rename_keys=False) == expected
    assert fuse(d, ave_width=1.9, rename_keys=False) == expected
    expected = with_deps(
        {
            "a": 1,
            "b2": (f, "a"),
            "b1-c1-d1-e1": (f, "a", (f, "a", (f, "a", (f, "a")))),
            "f": (f, "a", "e1", "b2"),
            "e1": "b1-c1-d1-e1",
        }
    )
    assert fuse(d, ave_width=1, rename_keys=True) == expected
    assert fuse(d, ave_width=1.9, rename_keys=True) == expected
    assert fuse(d, ave_width=2, rename_keys=False) == with_deps(
        {"a": 1, "f": (f, "a", (f, "a", (f, "a", (f, "a", (f, "a")))), (f, "a"))}
    )
    assert fuse(d, ave_width=2, rename_keys=True) == with_deps(
        {
            "a": 1,
            "b1-b2-c1-d1-e1-f": (
                f,
                "a",
                (f, "a", (f, "a", (f, "a", (f, "a")))),
                (f, "a"),
            ),
            "f": "b1-b2-c1-d1-e1-f",
        }
    )

    d = {
        "a": 1,
        "b1": (f, "a"),
        "b2": (f, "a"),
        "b3": (f, "a"),
        "c1": (f, "b1"),
        "c2": (f, "b2"),
        "c3": (f, "b3"),
        "d1": (f, "c1"),
        "d2": (f, "c2"),
        "d3": (f, "c3"),
        "e": (f, "d1", "d2", "d3"),
        "f": (f, "e"),
        "g": (f, "f"),
    }
    assert fuse(d, ave_width=1, rename_keys=False) == with_deps(
        {
            "a": 1,
            "d1": (f, (f, (f, "a"))),
            "d2": (f, (f, (f, "a"))),
            "d3": (f, (f, (f, "a"))),
            "g": (f, (f, (f, "d1", "d2", "d3"))),
        }
    )
    assert fuse(d, ave_width=1, rename_keys=True) == with_deps(
        {
            "a": 1,
            "b1-c1-d1": (f, (f, (f, "a"))),
            "b2-c2-d2": (f, (f, (f, "a"))),
            "b3-c3-d3": (f, (f, (f, "a"))),
            "e-f-g": (f, (f, (f, "d1", "d2", "d3"))),
            "d1": "b1-c1-d1",
            "d2": "b2-c2-d2",
            "d3": "b3-c3-d3",
            "g": "e-f-g",
        }
    )

    d = {
        "a": 1,
        "b": (f, "a"),
        "c": (f, "b"),
        "d": (f, "b", "c"),
        "e": (f, "d"),
        "f": (f, "e"),
        "g": (f, "d", "f"),
    }
    assert fuse(d, ave_width=1, rename_keys=False) == with_deps(
        {"b": (f, 1), "d": (f, "b", (f, "b")), "g": (f, "d", (f, (f, "d")))}
    )
    assert fuse(d, ave_width=1, rename_keys=True) == with_deps(
        {
            "a-b": (f, 1),
            "c-d": (f, "b", (f, "b")),
            "e-f-g": (f, "d", (f, (f, "d"))),
            "b": "a-b",
            "d": "c-d",
            "g": "e-f-g",
        }
    )


def test_fuse_stressed():
    def f(*args):
        return args

    d = {
        "array-original-27b9f9d257a80fa6adae06a98faf71eb": 1,
        ("cholesky-upper-26a6b670a8aabb7e2f8936db7ccb6a88", 0, 0): (
            f,
            ("cholesky-26a6b670a8aabb7e2f8936db7ccb6a88", 0, 0),
        ),
        ("cholesky-26a6b670a8aabb7e2f8936db7ccb6a88", 1, 0): (
            f,
            ("cholesky-upper-26a6b670a8aabb7e2f8936db7ccb6a88", 0, 1),
        ),
        ("array-27b9f9d257a80fa6adae06a98faf71eb", 0, 0): (
            f,
            "array-original-27b9f9d257a80fa6adae06a98faf71eb",
            (slice(0, 10, None), slice(0, 10, None)),
        ),
        ("cholesky-upper-26a6b670a8aabb7e2f8936db7ccb6a88", 1, 0): (
            "cholesky-26a6b670a8aabb7e2f8936db7ccb6a88",
            0,
            1,
        ),
        ("cholesky-26a6b670a8aabb7e2f8936db7ccb6a88", 1, 1): (
            f,
            (
                f,
                ("array-27b9f9d257a80fa6adae06a98faf71eb", 1, 1),
                (f, [("cholesky-lt-dot-26a6b670a8aabb7e2f8936db7ccb6a88", 1, 0, 1, 0)]),
            ),
        ),
        ("cholesky-lt-dot-26a6b670a8aabb7e2f8936db7ccb6a88", 1, 0, 1, 0): (
            f,
            ("cholesky-26a6b670a8aabb7e2f8936db7ccb6a88", 1, 0),
            ("cholesky-upper-26a6b670a8aabb7e2f8936db7ccb6a88", 0, 1),
        ),
        ("array-27b9f9d257a80fa6adae06a98faf71eb", 0, 1): (
            f,
            "array-original-27b9f9d257a80fa6adae06a98faf71eb",
            (slice(0, 10, None), slice(10, 20, None)),
        ),
        ("cholesky-upper-26a6b670a8aabb7e2f8936db7ccb6a88", 1, 1): (
            f,
            ("cholesky-26a6b670a8aabb7e2f8936db7ccb6a88", 1, 1),
        ),
        ("cholesky-26a6b670a8aabb7e2f8936db7ccb6a88", 0, 1): (f, (10, 10)),
        ("array-27b9f9d257a80fa6adae06a98faf71eb", 1, 1): (
            f,
            "array-original-27b9f9d257a80fa6adae06a98faf71eb",
            (slice(10, 20, None), slice(10, 20, None)),
        ),
        ("cholesky-upper-26a6b670a8aabb7e2f8936db7ccb6a88", 0, 1): (
            f,
            ("cholesky-26a6b670a8aabb7e2f8936db7ccb6a88", 0, 0),
            ("array-27b9f9d257a80fa6adae06a98faf71eb", 0, 1),
        ),
        ("cholesky-26a6b670a8aabb7e2f8936db7ccb6a88", 0, 0): (
            f,
            ("array-27b9f9d257a80fa6adae06a98faf71eb", 0, 0),
        ),
    }
    keys = {
        ("cholesky-upper-26a6b670a8aabb7e2f8936db7ccb6a88", 0, 0),
        ("cholesky-upper-26a6b670a8aabb7e2f8936db7ccb6a88", 0, 1),
        ("cholesky-upper-26a6b670a8aabb7e2f8936db7ccb6a88", 1, 0),
        ("cholesky-upper-26a6b670a8aabb7e2f8936db7ccb6a88", 1, 1),
    }
    rv = fuse(d, keys=keys, ave_width=2, rename_keys=True)
    assert rv == with_deps(rv[0])


def test_fuse_reductions_multiple_input():
    def f(*args):
        return args

    d = {"a1": 1, "a2": 2, "b": (f, "a1", "a2"), "c": (f, "b")}
    assert fuse(d, ave_width=2, rename_keys=False) == with_deps({"c": (f, (f, 1, 2))})
    assert fuse(d, ave_width=2, rename_keys=True) == with_deps(
        {"a1-a2-b-c": (f, (f, 1, 2)), "c": "a1-a2-b-c"}
    )
    assert fuse(d, ave_width=1, rename_keys=False) == with_deps(
        {"a1": 1, "a2": 2, "c": (f, (f, "a1", "a2"))}
    )
    assert fuse(d, ave_width=1, rename_keys=True) == with_deps(
        {"a1": 1, "a2": 2, "b-c": (f, (f, "a1", "a2")), "c": "b-c"}
    )

    d = {
        "a1": 1,
        "a2": 2,
        "b1": (f, "a1"),
        "b2": (f, "a1", "a2"),
        "b3": (f, "a2"),
        "c": (f, "b1", "b2", "b3"),
    }
    expected = with_deps(d)
    assert fuse(d, ave_width=1, rename_keys=False) == expected
    assert fuse(d, ave_width=2.9, rename_keys=False) == expected
    assert fuse(d, ave_width=1, rename_keys=True) == expected
    assert fuse(d, ave_width=2.9, rename_keys=True) == expected
    assert fuse(d, ave_width=3, rename_keys=False) == with_deps(
        {"a1": 1, "a2": 2, "c": (f, (f, "a1"), (f, "a1", "a2"), (f, "a2"))}
    )
    assert fuse(d, ave_width=3, rename_keys=True) == with_deps(
        {
            "a1": 1,
            "a2": 2,
            "b1-b2-b3-c": (f, (f, "a1"), (f, "a1", "a2"), (f, "a2")),
            "c": "b1-b2-b3-c",
        }
    )

    d = {
        "a1": 1,
        "a2": 2,
        "b1": (f, "a1"),
        "b2": (f, "a1", "a2"),
        "b3": (f, "a2"),
        "c1": (f, "b1", "b2"),
        "c2": (f, "b2", "b3"),
    }
    assert fuse(d, ave_width=1, rename_keys=False) == with_deps(d)
    assert fuse(d, ave_width=1, rename_keys=True) == with_deps(d)
    assert fuse(d, ave_width=2, rename_keys=False) == with_deps(
        {
            "a1": 1,
            "a2": 2,
            "b2": (f, "a1", "a2"),
            "c1": (f, (f, "a1"), "b2"),
            "c2": (f, "b2", (f, "a2")),
        }
    )
    assert fuse(d, ave_width=2, rename_keys=True) == with_deps(
        {
            "a1": 1,
            "a2": 2,
            "b2": (f, "a1", "a2"),
            "b1-c1": (f, (f, "a1"), "b2"),
            "b3-c2": (f, "b2", (f, "a2")),
            "c1": "b1-c1",
            "c2": "b3-c2",
        }
    )

    d = {
        "a1": 1,
        "a2": 2,
        "b1": (f, "a1"),
        "b2": (f, "a1", "a2"),
        "b3": (f, "a2"),
        "c1": (f, "b1", "b2"),
        "c2": (f, "b2", "b3"),
        "d": (f, "c1", "c2"),
    }
    assert fuse(d, ave_width=1, rename_keys=False) == with_deps(d)
    assert fuse(d, ave_width=1, rename_keys=True) == with_deps(d)

    # A more aggressive heuristic could do this at `ave_width=2`.  Perhaps
    # we can improve this.  Nevertheless, this is behaving as intended.
    assert fuse(d, ave_width=3, rename_keys=False) == with_deps(
        {
            "a1": 1,
            "a2": 2,
            "b2": (f, "a1", "a2"),
            "d": (f, (f, (f, "a1"), "b2"), (f, "b2", (f, "a2"))),
        }
    )
    assert fuse(d, ave_width=3, rename_keys=True) == with_deps(
        {
            "a1": 1,
            "a2": 2,
            "b2": (f, "a1", "a2"),
            "b1-b3-c1-c2-d": (f, (f, (f, "a1"), "b2"), (f, "b2", (f, "a2"))),
            "d": "b1-b3-c1-c2-d",
        }
    )


def func_with_kwargs(a, b, c=2):
    return a + b + c


def test_SubgraphCallable():
    non_hashable = [1, 2, 3]

    dsk = {
        "a": (apply, add, ["in1", 2]),
        "b": (
            apply,
            partial_by_order,
            ["in2"],
            {"function": func_with_kwargs, "other": [(1, 20)], "c": 4},
        ),
        "c": (
            apply,
            partial_by_order,
            ["in2", "in1"],
            {"function": func_with_kwargs, "other": [(1, 20)]},
        ),
        "d": (inc, "a"),
        "e": (add, "c", "d"),
        "f": ["a", 2, "b", (add, "b", (sum, non_hashable))],
        "h": (add, (sum, "f"), (sum, ["a", "b"])),
    }

    f = SubgraphCallable(dsk, "h", ["in1", "in2"], name="test")

    assert f.name == "test"
    assert repr(f) == "test"

    f2 = SubgraphCallable(dsk, "h", ["in1", "in2"], name="test")
    assert f == f2

    f3 = SubgraphCallable(dsk, "g", ["in1", "in2"], name="test")
    assert f != f3

    assert hash(SubgraphCallable(None, None, [None]))
    assert hash(f3) != hash(f2)
    dsk2 = dsk.copy()
    dsk2.update({"in1": 1, "in2": 2})
    assert f(1, 2) == get_sync(cull(dsk2, ["h"])[0], ["h"])[0]
    assert f(1, 2) == f(1, 2)

    f2 = pickle.loads(pickle.dumps(f))
    assert f2 == f
    assert hash(f2) == hash(f)
    assert f2(1, 2) == f(1, 2)


def test_SubgraphCallable_with_numpy():
    np = pytest.importorskip("numpy")

    # Testing support of numpy arrays in `dsk`, which uses elementwise equalities.
    dsk1 = {"a": np.arange(10)}
    f1 = SubgraphCallable(dsk1, "a", [None], name="test")
    f2 = SubgraphCallable(dsk1, "a", [None], name="test")
    assert f1 == f2

    # Notice, even though `dsk1` and `dsk2` are not equal they compare equal because
    # SubgraphCallable.__eq__() only checks name, outkeys, and inkeys.
    dsk2 = {"a": np.arange(10) + 1}
    f3 = SubgraphCallable(dsk2, "a", [None], name="test")
    assert f1 == f3

    f4 = SubgraphCallable(dsk1, "a", [None], name="test2")
    assert f1 != f4


def test_SubgraphCallable_eq():
    dsk1 = {"a": 1, "b": 2, "c": (add, "d", "e")}
    dsk2 = {"a": (inc, 0), "b": (inc, "a"), "c": (add, "d", "e")}
    f1 = SubgraphCallable(dsk1, "c", ["d", "e"])
    f2 = SubgraphCallable(dsk2, "c", ["d", "e"])
    # Different graphs must compare unequal (when no name given)
    assert f1 != f2

    # Different inputs must compare unequal
    f3 = SubgraphCallable(dsk2, "c", ["d", "f"], name=f1.name)
    assert f3 != f1

    # Different outputs must compare unequal
    f4 = SubgraphCallable(dsk2, "a", ["d", "e"], name=f1.name)
    assert f4 != f1

    # Reordering the inputs must not prevent equality
    f5 = SubgraphCallable(dsk1, "c", ["e", "d"], name=f1.name)
    assert f1 == f5
    assert hash(f1) == hash(f5)

    # Explicitly named graphs with different names must be unequal
    unnamed1 = SubgraphCallable(dsk1, "c", ["d", "e"], name="first")
    unnamed2 = SubgraphCallable(dsk1, "c", ["d", "e"], name="second")
    assert unnamed1 != unnamed2


def test_fuse_subgraphs(compare_subgraph_callables):
    dsk = {
        "x-1": 1,
        "inc-1": (inc, "x-1"),
        "inc-2": (inc, "inc-1"),
        "add-1": (add, "x-1", "inc-2"),
        "inc-3": (inc, "add-1"),
        "inc-4": (inc, "inc-3"),
        "add-2": (add, "add-1", "inc-4"),
        "inc-5": (inc, "add-2"),
        "inc-6": (inc, "inc-5"),
    }

    res = fuse(dsk, "inc-6", fuse_subgraphs=True)
    sol = with_deps(
        {
            "inc-6": "add-inc-x-1",
            "add-inc-x-1": (
                SubgraphCallable(
                    {
                        "x-1": 1,
                        "add-1": (add, "x-1", (inc, (inc, "x-1"))),
                        "inc-6": (inc, (inc, (add, "add-1", (inc, (inc, "add-1"))))),
                    },
                    "inc-6",
                    (),
                ),
            ),
        }
    )
    assert res == sol

    res = fuse(dsk, "inc-6", fuse_subgraphs=True, rename_keys=False)
    sol = with_deps(
        {
            "inc-6": (
                SubgraphCallable(
                    {
                        "x-1": 1,
                        "add-1": (add, "x-1", (inc, (inc, "x-1"))),
                        "inc-6": (inc, (inc, (add, "add-1", (inc, (inc, "add-1"))))),
                    },
                    "inc-6",
                    (),
                ),
            )
        }
    )
    assert res == sol

    res = fuse(dsk, "add-2", fuse_subgraphs=True)
    sol = with_deps(
        {
            "add-inc-x-1": (
                SubgraphCallable(
                    {
                        "x-1": 1,
                        "add-1": (add, "x-1", (inc, (inc, "x-1"))),
                        "add-2": (add, "add-1", (inc, (inc, "add-1"))),
                    },
                    "add-2",
                    (),
                ),
            ),
            "add-2": "add-inc-x-1",
            "inc-6": (inc, (inc, "add-2")),
        }
    )
    assert res == sol

    res = fuse(dsk, "inc-2", fuse_subgraphs=True)
    # ordering of arguments is unstable, check all permutations
    sols = []
    for inkeys in itertools.permutations(("x-1", "inc-2")):
        sols.append(
            with_deps(
                {
                    "x-1": 1,
                    "inc-2": (inc, (inc, "x-1")),
                    "inc-6": "inc-add-1",
                    "inc-add-1": (
                        SubgraphCallable(
                            {
                                "add-1": (add, "x-1", "inc-2"),
                                "inc-6": (
                                    inc,
                                    (inc, (add, "add-1", (inc, (inc, "add-1")))),
                                ),
                            },
                            "inc-6",
                            inkeys,
                        ),
                    )
                    + inkeys,
                }
            )
        )
    assert res in sols

    res = fuse(dsk, ["inc-2", "add-2"], fuse_subgraphs=True)
    # ordering of arguments is unstable, check all permutations
    sols = []
    for inkeys in itertools.permutations(("x-1", "inc-2")):
        sols.append(
            with_deps(
                {
                    "x-1": 1,
                    "inc-2": (inc, (inc, "x-1")),
                    "inc-add-1": (
                        SubgraphCallable(
                            {
                                "add-1": (add, "x-1", "inc-2"),
                                "add-2": (add, "add-1", (inc, (inc, "add-1"))),
                            },
                            "add-2",
                            inkeys,
                        ),
                    )
                    + inkeys,
                    "add-2": "inc-add-1",
                    "inc-6": (inc, (inc, "add-2")),
                }
            )
        )
    assert res in sols


def test_fuse_subgraphs_linear_chains_of_duplicate_deps(compare_subgraph_callables):
    dsk = {
        "x-1": 1,
        "add-1": (add, "x-1", "x-1"),
        "add-2": (add, "add-1", "add-1"),
        "add-3": (add, "add-2", "add-2"),
        "add-4": (add, "add-3", "add-3"),
        "add-5": (add, "add-4", "add-4"),
    }

    res = fuse(dsk, "add-5", fuse_subgraphs=True)
    sol = with_deps(
        {
            "add-x-1": (
                SubgraphCallable(
                    {
                        "x-1": 1,
                        "add-1": (add, "x-1", "x-1"),
                        "add-2": (add, "add-1", "add-1"),
                        "add-3": (add, "add-2", "add-2"),
                        "add-4": (add, "add-3", "add-3"),
                        "add-5": (add, "add-4", "add-4"),
                    },
                    "add-5",
                    (),
                ),
            ),
            "add-5": "add-x-1",
        }
    )
    assert res == sol


def test_dont_fuse_numpy_arrays():
    """
    Some types should stay in the graph bare

    This helps with things like serialization
    """
    np = pytest.importorskip("numpy")
    dsk = {"x": np.arange(5), "y": (inc, "x")}

    assert fuse(dsk, "y")[0] == dsk


def test_fuse_config():
    with dask.config.set({"optimization.fuse.active": False}):
        d = {
            "a": 1,
            "b": (inc, "a"),
        }
        dependencies = {"b": ("a",)}
        assert fuse(d, "b", dependencies=dependencies) == (d, dependencies)


def test_fused_keys_max_length():  # generic fix for gh-5999
    d = {
        "u-looooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooong": (
            inc,
            "v-looooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooong",
        ),
        "v-looooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooong": (
            inc,
            "w-looooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooong",
        ),
        "w-looooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooong": (
            inc,
            "x-looooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooong",
        ),
        "x-looooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooong": (
            inc,
            "y-looooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooong",
        ),
        "y-looooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooong": (
            inc,
            "z-looooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooong",
        ),
        "z-looooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooong": (
            add,
            "a",
            "b",
        ),
        "a": 1,
        "b": 2,
    }

    fused, deps = fuse(d, rename_keys=True)
    for key in fused:
        assert len(key) < 150
