text: """
  Algorithms that Involve Multiple DataFrames
  ===========================================
  
  The pandas operations ``concat``, ``join``, and ``merge`` combine multiple
  DataFrames.  This module contains analogous algorithms in the parallel case.
  
  There are two important cases:
  
  1.  We combine along a partitioned index
  2.  We combine along an unpartitioned index or other column
  
  In the first case we know which partitions of each dataframe interact with
  which others.  This lets us be significantly more clever and efficient.
  
  In the second case each partition from one dataset interacts with all
  partitions from the other.  We handle this through a shuffle operation.
  
  Partitioned Joins
  -----------------
  
  In the first case where we join along a partitioned index we proceed in the
  following stages.
  
  1.  Align the partitions of all inputs to be the same.  This involves a call
      to ``dd.repartition`` which will split up and concat existing partitions as
      necessary.  After this step all inputs have partitions that align with
      each other.  This step is relatively cheap.
      See the function ``align_partitions``.
  2.  Remove unnecessary partitions based on the type of join we perform (left,
      right, inner, outer).  We can do this at the partition level before any
      computation happens.  We'll do it again on each partition when we call the
      in-memory function.  See the function ``require``.
  3.  Embarrassingly parallel calls to ``pd.concat``, ``pd.join``, or
      ``pd.merge``.  Now that the data is aligned and unnecessary blocks have
      been removed we can rely on the fast in-memory Pandas join machinery to
      execute joins per-partition.  We know that all intersecting records exist
      within the same partition
  
  
  Hash Joins via Shuffle
  ----------------------
  
  When we join along an unpartitioned index or along an arbitrary column any
  partition from one input might interact with any partition in another.  In
  this case we perform a hash-join by shuffling data in each input by that
  column.  This results in new inputs with the same partition structure cleanly
  separated along that column.
  
  We proceed with hash joins in the following stages:
  
  1.  Shuffle each input on the specified column.  See the function
      ``dask.dataframe.shuffle.shuffle``.
  2.  Perform embarrassingly parallel join across shuffled inputs.
  """
  import math
  import pickle
  import warnings
  from functools import partial, wraps
  
  import numpy as np
  import pandas as pd
  from pandas.api.types import is_categorical_dtype, is_dtype_equal
  from tlz import first, merge_sorted, unique
  
  from ..base import is_dask_collection, tokenize
  from ..highlevelgraph import HighLevelGraph
  from ..layers import BroadcastJoinLayer
  from ..utils import M, apply
  from . import methods
  from .core import (
      DataFrame,
      Index,
      Series,
      _concat,
      _Frame,
      _maybe_from_pandas,
      is_broadcastable,
      map_partitions,
      new_dd_object,
      prefix_reduction,
      suffix_reduction,
  )
  from .dispatch import group_split_dispatch, hash_object_dispatch
  from .io import from_pandas
  from .shuffle import partitioning_index, rearrange_by_divisions, shuffle, shuffle_group
  from .utils import (
      asciitable,
      is_dataframe_like,
      is_series_like,
      make_meta,
      strip_unknown_categories,
  )
  
  
  def align_partitions(*dfs):
      """Mutually partition and align DataFrame blocks
  
      This serves as precursor to multi-dataframe operations like join, concat,
      or merge.
  
      Parameters
      ----------
      dfs: sequence of dd.DataFrame, dd.Series and dd.base.Scalar
          Sequence of dataframes to be aligned on their index
  
      Returns
      -------
      dfs: sequence of dd.DataFrame, dd.Series and dd.base.Scalar
          These must have consistent divisions with each other
      divisions: tuple
          Full divisions sequence of the entire result
      result: list
          A list of lists of keys that show which data exist on which
          divisions
      """
      _is_broadcastable = partial(is_broadcastable, dfs)
      dfs1 = [df for df in dfs if isinstance(df, _Frame) and not _is_broadcastable(df)]
      if len(dfs) == 0:
          raise ValueError("dfs contains no DataFrame and Series")
      if not all(df.known_divisions for df in dfs1):
          raise ValueError(
              "Not all divisions are known, can't align "
              "partitions. Please use `set_index` "
              "to set the index."
          )
  
      divisions = list(unique(merge_sorted(*[df.divisions for df in dfs1])))
      if len(divisions) == 1:  # single value for index
          divisions = (divisions[0], divisions[0])
      dfs2 = [
          df.repartition(divisions, force=True) if isinstance(df, _Frame) else df
          for df in dfs
      ]
  
      result = list()
      inds = [0 for df in dfs]
      for d in divisions[:-1]:
          L = list()
          for i, df in enumerate(dfs2):
              if isinstance(df, _Frame):
                  j = inds[i]
                  divs = df.divisions
                  if j < len(divs) - 1 and divs[j] == d:
                      L.append((df._name, inds[i]))
                      inds[i] += 1
                  else:
                      L.append(None)
              else:  # Scalar has no divisions
                  L.append(None)
          result.append(L)
      return dfs2, tuple(divisions), result
  
  
  def _maybe_align_partitions(args):
      """Align DataFrame blocks if divisions are different.
  
      Note that if all divisions are unknown, but have equal npartitions, then
      they will be passed through unchanged. This is different than
      `align_partitions`, which will fail if divisions aren't all known"""
      _is_broadcastable = partial(is_broadcastable, args)
      dfs = [df for df in args if isinstance(df, _Frame) and not _is_broadcastable(df)]
      if not dfs:
          return args
  
      divisions = dfs[0].divisions
      if not all(df.divisions == divisions for df in dfs):
          dfs2 = iter(align_partitions(*dfs)[0])
          return [a if not isinstance(a, _Frame) else next(dfs2) for a in args]
      return args
  
  
  def require(divisions, parts, required=None):
      """Clear out divisions where required components are not present
  
      In left, right, or inner joins we exclude portions of the dataset if one
      side or the other is not present.  We can achieve this at the partition
      level as well
  
      >>> divisions = [1, 3, 5, 7, 9]
      >>> parts = [(('a', 0), None),
      ...          (('a', 1), ('b', 0)),
      ...          (('a', 2), ('b', 1)),
      ...          (None, ('b', 2))]
  
      >>> divisions2, parts2 = require(divisions, parts, required=[0])
      >>> divisions2
      (1, 3, 5, 7)
      >>> parts2  # doctest: +NORMALIZE_WHITESPACE
      ((('a', 0), None),
       (('a', 1), ('b', 0)),
       (('a', 2), ('b', 1)))
  
      >>> divisions2, parts2 = require(divisions, parts, required=[1])
      >>> divisions2
      (3, 5, 7, 9)
      >>> parts2  # doctest: +NORMALIZE_WHITESPACE
      ((('a', 1), ('b', 0)),
       (('a', 2), ('b', 1)),
       (None, ('b', 2)))
  
      >>> divisions2, parts2 = require(divisions, parts, required=[0, 1])
      >>> divisions2
      (3, 5, 7)
      >>> parts2  # doctest: +NORMALIZE_WHITESPACE
      ((('a', 1), ('b', 0)),
       (('a', 2), ('b', 1)))
      """
      if not required:
          return divisions, parts
      for i in required:
          present = [j for j, p in enumerate(parts) if p[i] is not None]
          divisions = tuple(divisions[min(present) : max(present) + 2])
          parts = tuple(parts[min(present) : max(present) + 1])
      return divisions, parts
  
  
  ###############################################################
  # Join / Merge
  ###############################################################
  
  
  required = {
      "left": [0],
      "leftsemi": [0],
      "leftanti": [0],
      "right": [1],
      "inner": [0, 1],
      "outer": [],
  }
  allowed_left = ("inner", "left", "leftsemi", "leftanti")
  allowed_right = ("inner", "right")
  
  
  def merge_chunk(lhs, *args, **kwargs):
      empty_index_dtype = kwargs.pop("empty_index_dtype", None)
      categorical_columns = kwargs.pop("categorical_columns", None)
  
      rhs, *args = args
      left_index = kwargs.get("left_index", False)
      right_index = kwargs.get("right_index", False)
  
      if categorical_columns is not None:
          for col in categorical_columns:
              left = None
              right = None
  
              if col in lhs:
                  left = lhs[col]
              elif col == kwargs.get("right_on", None) and left_index:
                  if is_categorical_dtype(lhs.index):
                      left = lhs.index
  
              if col in rhs:
                  right = rhs[col]
              elif col == kwargs.get("left_on", None) and right_index:
                  if is_categorical_dtype(rhs.index):
                      right = rhs.index
  
              dtype = "category"
              if left is not None and right is not None:
                  dtype = methods.union_categoricals(
                      [left.astype("category"), right.astype("category")]
                  ).dtype
  
              if left is not None:
                  if isinstance(left, pd.Index):
                      lhs.index = left.astype(dtype)
                  else:
                      lhs = lhs.assign(**{col: left.astype(dtype)})
              if right is not None:
                  if isinstance(right, pd.Index):
                      rhs.index = right.astype(dtype)
                  else:
                      rhs = rhs.assign(**{col: right.astype(dtype)})
  
      out = lhs.merge(rhs, *args, **kwargs)
  
      # Workaround pandas bug where if the output result of a merge operation is
      # an empty dataframe, the output index is `int64` in all cases, regardless
      # of input dtypes.
      if len(out) == 0 and empty_index_dtype is not None:
          out.index = out.index.astype(empty_index_dtype)
      return out
  
  
  def merge_indexed_dataframes(lhs, rhs, left_index=True, right_index=True, **kwargs):
      """Join two partitioned dataframes along their index"""
      how = kwargs.get("how", "left")
      kwargs["left_index"] = left_index
      kwargs["right_index"] = right_index
  
      (lhs, rhs), divisions, parts = align_partitions(lhs, rhs)
      divisions, parts = require(divisions, parts, required[how])
  
      name = "join-indexed-" + tokenize(lhs, rhs, **kwargs)
  
      meta = lhs._meta_nonempty.merge(rhs._meta_nonempty, **kwargs)
      kwargs["empty_index_dtype"] = meta.index.dtype
      kwargs["categorical_columns"] = meta.select_dtypes(include="category").columns
  
      dsk = dict()
      for i, (a, b) in enumerate(parts):
          dsk[(name, i)] = (apply, merge_chunk, [a, b], kwargs)
  
      graph = HighLevelGraph.from_collections(name, dsk, dependencies=[lhs, rhs])
      return new_dd_object(graph, name, meta, divisions)
  
  
  shuffle_func = shuffle  # name sometimes conflicts with keyword argument
  
  
  def hash_join(
      lhs,
      left_on,
      rhs,
      right_on,
      how="inner",
      npartitions=None,
      suffixes=("_x", "_y"),
      shuffle=None,
      indicator=False,
      max_branch=None,
  ):
      """Join two DataFrames on particular columns with hash join
  
      This shuffles both datasets on the joined column and then performs an
      embarrassingly parallel join partition-by-partition
  
      >>> hash_join(lhs, 'id', rhs, 'id', how='left', npartitions=10)  # doctest: +SKIP
      """
      if npartitions is None:
          npartitions = max(lhs.npartitions, rhs.npartitions)
  
      lhs2 = shuffle_func(
          lhs, left_on, npartitions=npartitions, shuffle=shuffle, max_branch=max_branch
      )
      rhs2 = shuffle_func(
          rhs, right_on, npartitions=npartitions, shuffle=shuffle, max_branch=max_branch
      )
  
      if isinstance(left_on, Index):
          left_on = None
          left_index = True
      else:
          left_index = False
  
      if isinstance(right_on, Index):
          right_on = None
          right_index = True
      else:
          right_index = False
  
      kwargs = dict(
          how=how,
          left_on=left_on,
          right_on=right_on,
          left_index=left_index,
          right_index=right_index,
          suffixes=suffixes,
          indicator=indicator,
      )
  
      # dummy result
      # Avoid using dummy data for a collection it is empty
      _lhs_meta = lhs._meta_nonempty if len(lhs.columns) else lhs._meta
      _rhs_meta = rhs._meta_nonempty if len(rhs.columns) else rhs._meta
      meta = _lhs_meta.merge(_rhs_meta, **kwargs)
  
      if isinstance(left_on, list):
          left_on = (list, tuple(left_on))
      if isinstance(right_on, list):
          right_on = (list, tuple(right_on))
  
      token = tokenize(lhs2, rhs2, npartitions, shuffle, **kwargs)
      name = "hash-join-" + token
  
      kwargs["empty_index_dtype"] = meta.index.dtype
      kwargs["categorical_columns"] = meta.select_dtypes(include="category").columns
  
      dsk = {
          (name, i): (apply, merge_chunk, [(lhs2._name, i), (rhs2._name, i)], kwargs)
          for i in range(npartitions)
      }
  
      divisions = [None] * (npartitions + 1)
      graph = HighLevelGraph.from_collections(name, dsk, dependencies=[lhs2, rhs2])
      return new_dd_object(graph, name, meta, divisions)
  
  
  def single_partition_join(left, right, **kwargs):
      # if the merge is performed on_index, divisions can be kept, otherwise the
      # new index will not necessarily correspond with the current divisions
  
      meta = left._meta_nonempty.merge(right._meta_nonempty, **kwargs)
      kwargs["empty_index_dtype"] = meta.index.dtype
      kwargs["categorical_columns"] = meta.select_dtypes(include="category").columns
  
      name = "merge-" + tokenize(left, right, **kwargs)
      if left.npartitions == 1 and kwargs["how"] in allowed_right:
          left_key = first(left.__dask_keys__())
          dsk = {
              (name, i): (apply, merge_chunk, [left_key, right_key], kwargs)
              for i, right_key in enumerate(right.__dask_keys__())
          }
  
          if kwargs.get("right_index") or right._contains_index_name(
              kwargs.get("right_on")
          ):
              divisions = right.divisions
          else:
              divisions = [None for _ in right.divisions]
  
      elif right.npartitions == 1 and kwargs["how"] in allowed_left:
          right_key = first(right.__dask_keys__())
          dsk = {
              (name, i): (apply, merge_chunk, [left_key, right_key], kwargs)
              for i, left_key in enumerate(left.__dask_keys__())
          }
  
          if kwargs.get("left_index") or left._contains_index_name(kwargs.get("left_on")):
              divisions = left.divisions
          else:
              divisions = [None for _ in left.divisions]
      else:
          raise NotImplementedError(
              "single_partition_join has no fallback for invalid calls"
          )
  
      graph = HighLevelGraph.from_collections(name, dsk, dependencies=[left, right])
      return new_dd_object(graph, name, meta, divisions)
  
  
  def warn_dtype_mismatch(left, right, left_on, right_on):
      """Checks for merge column dtype mismatches and throws a warning (#4574)"""
  
      if not isinstance(left_on, list):
          left_on = [left_on]
      if not isinstance(right_on, list):
          right_on = [right_on]
  
      if all(col in left.columns for col in left_on) and all(
          col in right.columns for col in right_on
      ):
          dtype_mism = [
              ((lo, ro), left.dtypes[lo], right.dtypes[ro])
              for lo, ro in zip(left_on, right_on)
              if not is_dtype_equal(left.dtypes[lo], right.dtypes[ro])
          ]
  
          if dtype_mism:
              col_tb = asciitable(
                  ("Merge columns", "left dtype", "right dtype"), dtype_mism
              )
  
              warnings.warn(
                  (
                      "Merging dataframes with merge column data "
                      "type mismatches: \n{}\nCast dtypes explicitly to "
                      "avoid unexpected results."
                  ).format(col_tb)
              )
  
  
  @wraps(pd.merge)
  def merge(
      left,
      right,
      how="inner",
      on=None,
      left_on=None,
      right_on=None,
      left_index=False,
      right_index=False,
      suffixes=("_x", "_y"),
      indicator=False,
      npartitions=None,
      shuffle=None,
      max_branch=None,
      broadcast=None,
  ):
      for o in [on, left_on, right_on]:
          if isinstance(o, _Frame):
              raise NotImplementedError(
                  "Dask collections not currently allowed in merge columns"
              )
      if not on and not left_on and not right_on and not left_index and not right_index:
          on = [c for c in left.columns if c in right.columns]
          if not on:
              left_index = right_index = True
  
      if on and not left_on and not right_on:
          left_on = right_on = on
          on = None
  
      if isinstance(left, (pd.Series, pd.DataFrame)) and isinstance(
          right, (pd.Series, pd.DataFrame)
      ):
          return pd.merge(
              left,
              right,
              how=how,
              on=on,
              left_on=left_on,
              right_on=right_on,
              left_index=left_index,
              right_index=right_index,
              suffixes=suffixes,
              indicator=indicator,
          )
  
      # Transform pandas objects into dask.dataframe objects
      if not is_dask_collection(left):
          if right_index and left_on:  # change to join on index
              left = left.set_index(left[left_on])
              left_on = False
              left_index = True
          left = from_pandas(left, npartitions=1)  # turn into DataFrame
  
      if not is_dask_collection(right):
          if left_index and right_on:  # change to join on index
              right = right.set_index(right[right_on])
              right_on = False
              right_index = True
          right = from_pandas(right, npartitions=1)  # turn into DataFrame
  
      # Both sides are now dd.DataFrame or dd.Series objects
      merge_indexed_left = (
          left_index or left._contains_index_name(left_on)
      ) and left.known_divisions
  
      merge_indexed_right = (
          right_index or right._contains_index_name(right_on)
      ) and right.known_divisions
  
      # Both sides indexed
      if merge_indexed_left and merge_indexed_right:  # Do indexed join
          return merge_indexed_dataframes(
              left,
              right,
              how=how,
              suffixes=suffixes,
              indicator=indicator,
              left_on=left_on,
              right_on=right_on,
              left_index=left_index,
              right_index=right_index,
          )
  
      # Single partition on one side
      # Note that cudf supports "leftsemi" and "leftanti" joins
      elif (
          left.npartitions == 1
          and how in allowed_right
          or right.npartitions == 1
          and how in allowed_left
      ):
          return single_partition_join(
              left,
              right,
              how=how,
              right_on=right_on,
              left_on=left_on,
              left_index=left_index,
              right_index=right_index,
              suffixes=suffixes,
              indicator=indicator,
          )
  
      # One side is indexed, the other not
      elif (
          left_index
          and left.known_divisions
          and not right_index
          or right_index
          and right.known_divisions
          and not left_index
      ):
          left_empty = left._meta_nonempty
          right_empty = right._meta_nonempty
          meta = left_empty.merge(
              right_empty,
              how=how,
              on=on,
              left_on=left_on,
              right_on=right_on,
              left_index=left_index,
              right_index=right_index,
              suffixes=suffixes,
              indicator=indicator,
          )
          categorical_columns = meta.select_dtypes(include="category").columns
  
          if merge_indexed_left and left.known_divisions:
              right = rearrange_by_divisions(
                  right, right_on, left.divisions, max_branch, shuffle=shuffle
              )
              left = left.clear_divisions()
          elif merge_indexed_right and right.known_divisions:
              left = rearrange_by_divisions(
                  left, left_on, right.divisions, max_branch, shuffle=shuffle
              )
              right = right.clear_divisions()
          return map_partitions(
              merge_chunk,
              left,
              right,
              meta=meta,
              how=how,
              on=on,
              left_on=left_on,
              right_on=right_on,
              left_index=left_index,
              right_index=right_index,
              suffixes=suffixes,
              indicator=indicator,
              empty_index_dtype=meta.index.dtype,
              categorical_columns=categorical_columns,
          )
      # Catch all hash join
      else:
          if left_on and right_on:
              warn_dtype_mismatch(left, right, left_on, right_on)
  
          # Check if we should use a broadcast_join
          # See note on `broadcast_bias` below.
          broadcast_bias = 0.5
          if isinstance(broadcast, float):
              broadcast_bias = float(broadcast)
              broadcast = None
          elif not isinstance(broadcast, bool) and broadcast is not None:
              # Let's be strict about the `broadcast` type to
              # avoid arbitrarily casting int to float or bool.
              raise ValueError(
                  f"Optional `broadcast` argument must be float or bool."
                  f"Type={type(broadcast)} is not supported."
              )
          bcast_side = "left" if left.npartitions < right.npartitions else "right"
          n_small = min(left.npartitions, right.npartitions)
          n_big = max(left.npartitions, right.npartitions)
          if (
              shuffle == "tasks"
              and how in ("inner", "left", "right")
              and how != bcast_side
              and broadcast is not False
          ):
              # Note on `broadcast_bias`:
              # We can expect the broadcast merge to be competitive with
              # the shuffle merge when the number of partitions in the
              # smaller collection is less than the logarithm of the number
              # of partitions in the larger collection.  By default, we add
              # a small preference for the shuffle-based merge by multiplying
              # the log result by a 0.5 scaling factor.  We call this factor
              # the `broadcast_bias`, because a larger number will make Dask
              # more likely to select the `broadcast_join` code path.  If
              # the user specifies a floating-point value for the `broadcast`
              # kwarg, that value will be used as the `broadcast_bias`.
              if broadcast or (n_small < math.log2(n_big) * broadcast_bias):
                  return broadcast_join(
                      left,
                      left.index if left_index else left_on,
                      right,
                      right.index if right_index else right_on,
                      how,
                      npartitions,
                      suffixes,
                      indicator=indicator,
                  )
  
          return hash_join(
              left,
              left.index if left_index else left_on,
              right,
              right.index if right_index else right_on,
              how,
              npartitions,
              suffixes,
              shuffle=shuffle,
              indicator=indicator,
              max_branch=max_branch,
          )
  
  
  ###############################################################
  # ASOF Join
  ###############################################################
  
  
  def most_recent_tail(left, right):
      if len(right.index) == 0:
          return left
      return right.tail(1)
  
  
  def most_recent_tail_summary(left, right, by=None):
      return pd.concat([left, right]).drop_duplicates(subset=by, keep="last")
  
  
  def compute_tails(ddf, by=None):
      """For each partition, returns the last row of the most recent nonempty
      partition.
      """
      empty = ddf._meta.iloc[0:0]
  
      if by is None:
          return prefix_reduction(most_recent_tail, ddf, empty)
      else:
          kwargs = {"by": by}
          return prefix_reduction(most_recent_tail_summary, ddf, empty, **kwargs)
  
  
  def most_recent_head(left, right):
      if len(left.index) == 0:
          return right
      return left.head(1)
  
  
  def most_recent_head_summary(left, right, by=None):
      return pd.concat([left, right]).drop_duplicates(subset=by, keep="first")
  
  
  def compute_heads(ddf, by=None):
      """For each partition, returns the first row of the next nonempty
      partition.
      """
      empty = ddf._meta.iloc[0:0]
  
      if by is None:
          return suffix_reduction(most_recent_head, ddf, empty)
      else:
          kwargs = {"by": by}
          return suffix_reduction(most_recent_head_summary, ddf, empty, **kwargs)
  
  
  def pair_partitions(L, R):
      """Returns which partitions to pair for the merge_asof algorithm and the
      bounds on which to split them up
      """
      result = []
  
      n, m = len(L) - 1, len(R) - 1
      i, j = 0, -1
      while j + 1 < m and R[j + 1] <= L[i]:
          j += 1
      J = []
      while i < n:
          partition = max(0, min(m - 1, j))
          lower = R[j] if j >= 0 and R[j] > L[i] else None
          upper = (
              R[j + 1]
              if j + 1 < m
              and (R[j + 1] < L[i + 1] or R[j + 1] == L[i + 1] and i == n - 1)
              else None
          )
  
          J.append((partition, lower, upper))
  
          i1 = i + 1 if j + 1 == m or (i + 1 < n and R[j + 1] >= L[i + 1]) else i
          j1 = j + 1 if i + 1 == n or (j + 1 < m and L[i + 1] >= R[j + 1]) else j
          if i1 > i:
              result.append(J)
              J = []
          elif i == n - 1 and R[j1] > L[n]:
              result.append(J)
              break
          i, j = i1, j1
  
      return result
  
  
  def merge_asof_padded(left, right, prev=None, next=None, **kwargs):
      """merge_asof but potentially adding rows to the beginning/end of right"""
      frames = []
      if prev is not None:
          frames.append(prev)
      frames.append(right)
      if next is not None:
          frames.append(next)
  
      frame = pd.concat(frames)
      result = pd.merge_asof(left, frame, **kwargs)
      # pd.merge_asof() resets index name (and dtype) if left is empty df
      if result.index.name != left.index.name:
          result.index.name = left.index.name
      return result
  
  
  def get_unsorted_columns(frames):
      """
      Determine the unsorted column order.
  
      This should match the output of concat([frames], sort=False)
      """
      new_columns = pd.concat([frame._meta for frame in frames]).columns
      order = []
      for frame in frames:
          order.append(new_columns.get_indexer_for(frame.columns))
  
      order = np.concatenate(order)
      order = pd.unique(order)
      order = new_columns.take(order)
      return order
  
  
  def merge_asof_indexed(left, right, **kwargs):
      dsk = dict()
      name = "asof-join-indexed-" + tokenize(left, right, **kwargs)
      meta = pd.merge_asof(left._meta_nonempty, right._meta_nonempty, **kwargs)
  
      if all(map(pd.isnull, left.divisions)):
          # results in an empty df that looks like ``meta``
          return from_pandas(meta.iloc[len(meta) :], npartitions=left.npartitions)
  
      if all(map(pd.isnull, right.divisions)):
          # results in an df that looks like ``left`` with nulls for
          # all ``right.columns``
          return map_partitions(
              pd.merge_asof,
              left,
              right=right,
              left_index=True,
              right_index=True,
              meta=meta,
          )
  
      dependencies = [left, right]
      tails = heads = None
      if kwargs["direction"] in ["backward", "nearest"]:
          tails = compute_tails(right, by=kwargs["right_by"])
          dependencies.append(tails)
      if kwargs["direction"] in ["forward", "nearest"]:
          heads = compute_heads(right, by=kwargs["right_by"])
          dependencies.append(heads)
  
      for i, J in enumerate(pair_partitions(left.divisions, right.divisions)):
          frames = []
          for j, lower, upper in J:
              slice = (methods.boundary_slice, (left._name, i), lower, upper, False)
              tail = (tails._name, j) if tails is not None else None
              head = (heads._name, j) if heads is not None else None
              frames.append(
                  (
                      apply,
                      merge_asof_padded,
                      [slice, (right._name, j), tail, head],
                      kwargs,
                  )
              )
          dsk[(name, i)] = (methods.concat, frames)
  
      graph = HighLevelGraph.from_collections(name, dsk, dependencies=dependencies)
      result = new_dd_object(graph, name, meta, left.divisions)
      return result
  
  
  @wraps(pd.merge_asof)
  def merge_asof(
      left,
      right,
      on=None,
      left_on=None,
      right_on=None,
      left_index=False,
      right_index=False,
      by=None,
      left_by=None,
      right_by=None,
      suffixes=("_x", "_y"),
      tolerance=None,
      allow_exact_matches=True,
      direction="backward",
  ):
      if direction not in ["backward", "forward", "nearest"]:
          raise ValueError(
              "Invalid merge_asof direction. Choose from 'backward'"
              " 'forward', or 'nearest'"
          )
  
      kwargs = {
          "on": on,
          "left_on": left_on,
          "right_on": right_on,
          "left_index": left_index,
          "right_index": right_index,
          "by": by,
          "left_by": left_by,
          "right_by": right_by,
          "suffixes": suffixes,
          "tolerance": tolerance,
          "allow_exact_matches": allow_exact_matches,
          "direction": direction,
      }
  
      if left is None or right is None:
          raise ValueError("Cannot merge_asof on None")
  
      # if is_dataframe_like(left) and is_dataframe_like(right):
      if isinstance(left, pd.DataFrame) and isinstance(right, pd.DataFrame):
          return pd.merge_asof(left, right, **kwargs)
  
      if on is not None:
          left_on = right_on = on
      for o in [left_on, right_on]:
          if isinstance(o, _Frame):
              raise NotImplementedError(
                  "Dask collections not currently allowed in merge columns"
              )
  
      if not is_dask_collection(left):
          left = from_pandas(left, npartitions=1)
      ixname = ixcol = divs = None
      if left_on is not None:
          if right_index:
              divs = left.divisions if left.known_divisions else None
              ixname = left.index.name
              left = left.reset_index()
              ixcol = left.columns[0]
          left = left.set_index(left_on, sorted=True)
  
      if not is_dask_collection(right):
          right = from_pandas(right, npartitions=1)
      if right_on is not None:
          right = right.set_index(right_on, sorted=True)
  
      if by is not None:
          kwargs["left_by"] = kwargs["right_by"] = by
  
      del kwargs["on"], kwargs["left_on"], kwargs["right_on"], kwargs["by"]
      kwargs["left_index"] = kwargs["right_index"] = True
  
      if not left.known_divisions or not right.known_divisions:
          raise ValueError("merge_asof input must be sorted!")
  
      result = merge_asof_indexed(left, right, **kwargs)
      if left_on or right_on:
          result = result.reset_index()
          if ixcol is not None:
              if divs is not None:
                  result = result.set_index(ixcol, sorted=True, divisions=divs)
              else:
                  result = result.map_partitions(M.set_index, ixcol)
              result = result.map_partitions(M.rename_axis, ixname)
  
      return result
  
  
  ###############################################################
  # Concat
  ###############################################################
  
  
  def concat_and_check(dfs, ignore_order=False):
      if len(set(map(len, dfs))) != 1:
          raise ValueError("Concatenated DataFrames of different lengths")
      return methods.concat(dfs, axis=1, ignore_order=ignore_order)
  
  
  def concat_unindexed_dataframes(dfs, ignore_order=False, **kwargs):
      name = "concat-" + tokenize(*dfs)
  
      dsk = {
          (name, i): (concat_and_check, [(df._name, i) for df in dfs], ignore_order)
          for i in range(dfs[0].npartitions)
      }
      kwargs.update({"ignore_order": ignore_order})
      meta = methods.concat([df._meta for df in dfs], axis=1, **kwargs)
  
      graph = HighLevelGraph.from_collections(name, dsk, dependencies=dfs)
      return new_dd_object(graph, name, meta, dfs[0].divisions)
  
  
  def concat_indexed_dataframes(dfs, axis=0, join="outer", ignore_order=False, **kwargs):
      """Concatenate indexed dataframes together along the index"""
      warn = axis != 0
      kwargs.update({"ignore_order": ignore_order})
      meta = methods.concat(
          [df._meta for df in dfs],
          axis=axis,
          join=join,
          filter_warning=warn,
          **kwargs,
      )
      empties = [strip_unknown_categories(df._meta) for df in dfs]
  
      dfs2, divisions, parts = align_partitions(*dfs)
  
      name = "concat-indexed-" + tokenize(join, *dfs)
  
      parts2 = [
          [df if df is not None else empty for df, empty in zip(part, empties)]
          for part in parts
      ]
  
      filter_warning = True
      uniform = False
  
      dsk = dict(
          (
              (name, i),
              (methods.concat, part, axis, join, uniform, filter_warning, kwargs),
          )
          for i, part in enumerate(parts2)
      )
      for df in dfs2:
          dsk.update(df.dask)
  
      return new_dd_object(dsk, name, meta, divisions)
  
  
  def stack_partitions(dfs, divisions, join="outer", ignore_order=False, **kwargs):
      """Concatenate partitions on axis=0 by doing a simple stack"""
      # Use _meta_nonempty as pandas.concat will incorrectly cast float to datetime
      # for empty data frames. See https://github.com/pandas-dev/pandas/issues/32934.
  
      kwargs.update({"ignore_order": ignore_order})
  
      meta = make_meta(
          methods.concat(
              [df._meta_nonempty for df in dfs],
              join=join,
              filter_warning=False,
              **kwargs,
          )
      )
      empty = strip_unknown_categories(meta)
  
      name = "concat-{0}".format(tokenize(*dfs))
      dsk = {}
      i = 0
      for df in dfs:
          # dtypes of all dfs need to be coherent
          # refer to https://github.com/dask/dask/issues/4685
          # and https://github.com/dask/dask/issues/5968.
          if is_dataframe_like(df):
  
              shared_columns = df.columns.intersection(meta.columns)
              needs_astype = [
                  col
                  for col in shared_columns
                  if df[col].dtype != meta[col].dtype
                  and not is_categorical_dtype(df[col].dtype)
              ]
  
              if needs_astype:
                  # Copy to avoid mutating the caller inplace
                  df = df.copy()
                  df[needs_astype] = df[needs_astype].astype(meta[needs_astype].dtypes)
  
          if is_series_like(df) and is_series_like(meta):
              if not df.dtype == meta.dtype and not is_categorical_dtype(df.dtype):
                  df = df.astype(meta.dtype)
          else:
              pass  # TODO: there are other non-covered cases here
          dsk.update(df.dask)
          # An error will be raised if the schemas or categories don't match. In
          # this case we need to pass along the meta object to transform each
          # partition, so they're all equivalent.
          try:
              df._meta == meta
              match = True
          except (ValueError, TypeError):
              match = False
  
          filter_warning = True
          uniform = False
  
          for key in df.__dask_keys__():
              if match:
                  dsk[(name, i)] = key
              else:
                  dsk[(name, i)] = (
                      apply,
                      methods.concat,
                      [[empty, key], 0, join, uniform, filter_warning],
                      kwargs,
                  )
              i += 1
  
      return new_dd_object(dsk, name, meta, divisions)
  
  
  def concat(
      dfs,
      axis=0,
      join="outer",
      interleave_partitions=False,
      ignore_unknown_divisions=False,
      ignore_order=False,
      **kwargs,
  ):
      """Concatenate DataFrames along rows.
  
      - When axis=0 (default), concatenate DataFrames row-wise:
  
        - If all divisions are known and ordered, concatenate DataFrames keeping
          divisions. When divisions are not ordered, specifying
          interleave_partition=True allows concatenate divisions each by each.
  
        - If any of division is unknown, concatenate DataFrames resetting its
          division to unknown (None)
  
      - When axis=1, concatenate DataFrames column-wise:
  
        - Allowed if all divisions are known.
  
        - If any of division is unknown, it raises ValueError.
  
      Parameters
      ----------
      dfs : list
          List of dask.DataFrames to be concatenated
      axis : {0, 1, 'index', 'columns'}, default 0
          The axis to concatenate along
      join : {'inner', 'outer'}, default 'outer'
          How to handle indexes on other axis
      interleave_partitions : bool, default False
          Whether to concatenate DataFrames ignoring its order. If True, every
          divisions are concatenated each by each.
      ignore_unknown_divisions : bool, default False
          By default a warning is raised if any input has unknown divisions.
          Set to True to disable this warning.
      ignore_order : bool, default False
          Whether to ignore order when doing the union of categoricals.
  
      Notes
      -----
      This differs in from ``pd.concat`` in the when concatenating Categoricals
      with different categories. Pandas currently coerces those to objects
      before concatenating. Coercing to objects is very expensive for large
      arrays, so dask preserves the Categoricals by taking the union of
      the categories.
  
      Examples
      --------
      If all divisions are known and ordered, divisions are kept.
  
      >>> import dask.dataframe as dd
      >>> a                                               # doctest: +SKIP
      dd.DataFrame<x, divisions=(1, 3, 5)>
      >>> b                                               # doctest: +SKIP
      dd.DataFrame<y, divisions=(6, 8, 10)>
      >>> dd.concat([a, b])                               # doctest: +SKIP
      dd.DataFrame<concat-..., divisions=(1, 3, 6, 8, 10)>
  
      Unable to concatenate if divisions are not ordered.
  
      >>> a                                               # doctest: +SKIP
      dd.DataFrame<x, divisions=(1, 3, 5)>
      >>> b                                               # doctest: +SKIP
      dd.DataFrame<y, divisions=(2, 3, 6)>
      >>> dd.concat([a, b])                               # doctest: +SKIP
      ValueError: All inputs have known divisions which cannot be concatenated
      in order. Specify interleave_partitions=True to ignore order
  
      Specify interleave_partitions=True to ignore the division order.
  
      >>> dd.concat([a, b], interleave_partitions=True)   # doctest: +SKIP
      dd.DataFrame<concat-..., divisions=(1, 2, 3, 5, 6)>
  
      If any of division is unknown, the result division will be unknown
  
      >>> a                                               # doctest: +SKIP
      dd.DataFrame<x, divisions=(None, None)>
      >>> b                                               # doctest: +SKIP
      dd.DataFrame<y, divisions=(1, 4, 10)>
      >>> dd.concat([a, b])                               # doctest: +SKIP
      dd.DataFrame<concat-..., divisions=(None, None, None, None)>
  
      By default concatenating with unknown divisions will raise a warning.
      Set ``ignore_unknown_divisions=True`` to disable this:
  
      >>> dd.concat([a, b], ignore_unknown_divisions=True)# doctest: +SKIP
      dd.DataFrame<concat-..., divisions=(None, None, None, None)>
  
      Different categoricals are unioned
  
      >>> dd.concat([
      ...     dd.from_pandas(pd.Series(['a', 'b'], dtype='category'), 1),
      ...     dd.from_pandas(pd.Series(['a', 'c'], dtype='category'), 1),
      ... ], interleave_partitions=True).dtype
      CategoricalDtype(categories=['a', 'b', 'c'], ordered=False)
      """
  
      if not isinstance(dfs, list):
          raise TypeError("dfs must be a list of DataFrames/Series objects")
      if len(dfs) == 0:
          raise ValueError("No objects to concatenate")
      if len(dfs) == 1:
          if axis == 1 and isinstance(dfs[0], Series):
              return dfs[0].to_frame()
          else:
              return dfs[0]
  
      if join not in ("inner", "outer"):
          raise ValueError("'join' must be 'inner' or 'outer'")
  
      axis = DataFrame._validate_axis(axis)
      dasks = [df for df in dfs if isinstance(df, _Frame)]
      dfs = _maybe_from_pandas(dfs)
  
      if axis == 1:
          if all(df.known_divisions for df in dasks):
              return concat_indexed_dataframes(
                  dfs, axis=axis, join=join, ignore_order=ignore_order, **kwargs
              )
          elif (
              len(dasks) == len(dfs)
              and all(not df.known_divisions for df in dfs)
              and len({df.npartitions for df in dasks}) == 1
          ):
              if not ignore_unknown_divisions:
                  warnings.warn(
                      "Concatenating dataframes with unknown divisions.\n"
                      "We're assuming that the indices of each dataframes"
                      " are \n aligned. This assumption is not generally "
                      "safe."
                  )
              return concat_unindexed_dataframes(dfs, ignore_order=ignore_order, **kwargs)
          else:
              raise ValueError(
                  "Unable to concatenate DataFrame with unknown "
                  "division specifying axis=1"
              )
      else:
          if all(df.known_divisions for df in dasks):
              # each DataFrame's division must be greater than previous one
              if all(
                  dfs[i].divisions[-1] < dfs[i + 1].divisions[0]
                  for i in range(len(dfs) - 1)
              ):
                  divisions = []
                  for df in dfs[:-1]:
                      # remove last to concatenate with next
                      divisions += df.divisions[:-1]
                  divisions += dfs[-1].divisions
                  return stack_partitions(
                      dfs, divisions, join=join, ignore_order=ignore_order, **kwargs
                  )
              elif interleave_partitions:
                  return concat_indexed_dataframes(
                      dfs, join=join, ignore_order=ignore_order, **kwargs
                  )
              else:
                  divisions = [None] * (sum([df.npartitions for df in dfs]) + 1)
                  return stack_partitions(
                      dfs, divisions, join=join, ignore_order=ignore_order, **kwargs
                  )
          else:
              divisions = [None] * (sum([df.npartitions for df in dfs]) + 1)
              return stack_partitions(
                  dfs, divisions, join=join, ignore_order=ignore_order, **kwargs
              )
  
  
  def _contains_index_name(df, columns_or_index):
      """
      Test whether ``columns_or_index`` contains a reference
      to the index of ``df
  
      This is the local (non-collection) version of
      ``dask.core.DataFrame._contains_index_name``.
      """
  
      def _is_index_level_reference(x, key):
          return (
              x.index.name is not None
              and (np.isscalar(key) or isinstance(key, tuple))
              and key == x.index.name
              and key not in getattr(x, "columns", ())
          )
  
      if isinstance(columns_or_index, list):
          return any(_is_index_level_reference(df, n) for n in columns_or_index)
      else:
          return _is_index_level_reference(df, columns_or_index)
  
  
  def _select_columns_or_index(df, columns_or_index):
      """
      Returns a DataFrame with columns corresponding to each
      column or index level in columns_or_index.  If included,
      the column corresponding to the index level is named _index.
  
      This is the local (non-collection) version of
      ``dask.core.DataFrame._select_columns_or_index``.
      """
  
      def _is_column_label_reference(df, key):
          return (np.isscalar(key) or isinstance(key, tuple)) and key in df.columns
  
      # Ensure columns_or_index is a list
      columns_or_index = (
          columns_or_index if isinstance(columns_or_index, list) else [columns_or_index]
      )
  
      column_names = [n for n in columns_or_index if _is_column_label_reference(df, n)]
  
      selected_df = df[column_names]
      if _contains_index_name(df, columns_or_index):
          # Index name was included
          selected_df = selected_df.assign(_index=df.index)
  
      return selected_df
  
  
  def _split_partition(df, on, nsplits):
      """
      Split-by-hash a DataFrame into `nsplits` groups.
  
      Hashing will be performed on the columns or index specified by `on`.
      """
  
      if isinstance(on, bytes):
          on = pickle.loads(on)
  
      if isinstance(on, str) or pd.api.types.is_list_like(on):
          # If `on` is a column name or list of column names, we
          # can hash/split by those columns.
          on = [on] if isinstance(on, str) else list(on)
          nset = set(on)
          if nset.intersection(set(df.columns)) == nset:
              ind = hash_object_dispatch(df[on], index=False)
              ind = ind % nsplits
              return group_split_dispatch(df, ind.values, nsplits, ignore_index=False)
  
      # We are not joining (purely) on columns.  Need to
      # add a "_partitions" column to perform the split.
      if not isinstance(on, _Frame):
          on = _select_columns_or_index(df, on)
      partitions = partitioning_index(on, nsplits)
      df2 = df.assign(_partitions=partitions)
      return shuffle_group(
          df2,
          ["_partitions"],
          0,
          nsplits,
          nsplits,
          False,
          nsplits,
      )
  
  
  def _concat_wrapper(dfs):
      """Concat and remove temporary "_partitions" column"""
      df = _concat(dfs, False)
      if "_partitions" in df.columns:
          del df["_partitions"]
      return df
  
  
  def _merge_chunk_wrapper(*args, **kwargs):
      return merge_chunk(
          *args,
          **{
              k: pickle.loads(v) if isinstance(v, bytes) else v for k, v in kwargs.items()
          },
      )
  
  
  def broadcast_join(
      lhs,
      left_on,
      rhs,
      right_on,
      how="inner",
      npartitions=None,
      suffixes=("_x", "_y"),
      shuffle=None,
      indicator=False,
      parts_out=None,
  ):
      """Join two DataFrames on particular columns by broadcasting
  
      This broadcasts the partitions of the smaller DataFrame to each
      partition of the larger DataFrame, joins each partition pair,
      and then concatenates the new data for each output partition.
      """
  
      if npartitions:
          # Repartition the larger collection before the merge
          if lhs.npartitions < rhs.npartitions:
              rhs = rhs.repartition(npartitions=npartitions)
          else:
              lhs = lhs.repartition(npartitions=npartitions)
  
      if how not in ("inner", "left", "right"):
          # Broadcast algorithm cannot handle an "outer" join
          raise ValueError(
              "Only 'inner', 'left' and 'right' broadcast joins are supported."
          )
  
      if how == "left" and lhs.npartitions < rhs.npartitions:
          # Must broadcast rhs for a "left" broadcast join
          raise ValueError("'left' broadcast join requires rhs broadcast.")
  
      if how == "right" and rhs.npartitions <= lhs.npartitions:
          # Must broadcast lhs for a "right" broadcast join
          raise ValueError("'right' broadcast join requires lhs broadcast.")
  
      # TODO: It *may* be beneficial to perform the hash
      # split for "inner" join as well (even if it is not
      # technically needed for correctness).  More testing
      # is needed here.
      if how != "inner":
          # Shuffle to-be-broadcasted side by hash. This
          # means that we will need to perform a local
          # shuffle and split on each partition of the
          # "other" collection (with the same hashing
          # approach) to ensure the correct rows are
          # joined by `merge_chunk`.  The local hash and
          # split of lhs is in `_split_partition`.
          if lhs.npartitions < rhs.npartitions:
              lhs2 = shuffle_func(
                  lhs,
                  left_on,
                  shuffle="tasks",
              )
              lhs_name = lhs2._name
              lhs_dep = lhs2
              rhs_name = rhs._name
              rhs_dep = rhs
          else:
              rhs2 = shuffle_func(
                  rhs,
                  right_on,
                  shuffle="tasks",
              )
              lhs_name = lhs._name
              lhs_dep = lhs
              rhs_name = rhs2._name
              rhs_dep = rhs2
      else:
          lhs_name = lhs._name
          lhs_dep = lhs
          rhs_name = rhs._name
          rhs_dep = rhs
  
      if isinstance(left_on, Index):
          left_on = None
          left_index = True
      else:
          left_index = False
  
      if isinstance(right_on, Index):
          right_on = None
          right_index = True
      else:
          right_index = False
  
      merge_kwargs = dict(
          how=how,
          left_on=left_on,
          right_on=right_on,
          left_index=left_index,
          right_index=right_index,
          suffixes=suffixes,
          indicator=indicator,
      )
  
      # dummy result
      meta = lhs._meta_nonempty.merge(rhs._meta_nonempty, **merge_kwargs)
      merge_kwargs["empty_index_dtype"] = meta.index.dtype
      merge_kwargs["categorical_columns"] = meta.select_dtypes(include="category").columns
  
      # Assume the output partitions/divisions
      # should correspond to the collection that
      # is NOT broadcasted.
      if lhs.npartitions < rhs.npartitions:
          npartitions = rhs.npartitions
          divisions = rhs.divisions
          _index_names = set(rhs._meta_nonempty.index.names)
      else:
          npartitions = lhs.npartitions
          divisions = lhs.divisions
          _index_names = set(lhs._meta_nonempty.index.names)
  
      # Cannot preserve divisions if the index is lost
      if _index_names != set(meta.index.names):
          divisions = [None] * (npartitions + 1)
  
      token = tokenize(lhs, rhs, npartitions, **merge_kwargs)
      name = "bcast-join-" + token
      broadcast_join_layer = BroadcastJoinLayer(
          name,
          npartitions,
          lhs_name,
          lhs.npartitions,
          rhs_name,
          rhs.npartitions,
          parts_out=parts_out,
          **merge_kwargs,
      )
  
      graph = HighLevelGraph.from_collections(
          name,
          broadcast_join_layer,
          dependencies=[lhs_dep, rhs_dep],
      )
  
      return new_dd_object(graph, name, meta, divisions)
  
  
  def _recursive_pairwise_outer_join(
      dataframes_to_merge, on, lsuffix, rsuffix, npartitions, shuffle
  ):
      """
      Schedule the merging of a list of dataframes in a pairwise method. This is a recursive function that results
      in a much more efficient scheduling of merges than a simple loop
      from:
      [A] [B] [C] [D] -> [AB] [C] [D] -> [ABC] [D] -> [ABCD]
      to:
      [A] [B] [C] [D] -> [AB] [CD] -> [ABCD]
      Note that either way, n-1 merges are still required, but using a pairwise reduction it can be completed in parallel.
      :param dataframes_to_merge: A list of Dask dataframes to be merged together on their index
      :return: A single Dask Dataframe, comprised of the pairwise-merges of all provided dataframes
      """
      number_of_dataframes_to_merge = len(dataframes_to_merge)
  
      merge_options = {
          "on": on,
          "lsuffix": lsuffix,
          "rsuffix": rsuffix,
          "npartitions": npartitions,
          "shuffle": shuffle,
      }
  
      # Base case 1: just return the provided dataframe and merge with `left`
      if number_of_dataframes_to_merge == 1:
          return dataframes_to_merge[0]
  
      # Base case 2: merge the two provided dataframe to be merged with `left`
      if number_of_dataframes_to_merge == 2:
          merged_ddf = dataframes_to_merge[0].join(
              dataframes_to_merge[1], how="outer", **merge_options
          )
          return merged_ddf
  
      # Recursive case: split the list of dfs into two ~even sizes and continue down
      else:
          middle_index = number_of_dataframes_to_merge // 2
          merged_ddf = _recursive_pairwise_outer_join(
              [
                  _recursive_pairwise_outer_join(
                      dataframes_to_merge[:middle_index], **merge_options
                  ),
                  _recursive_pairwise_outer_join(
                      dataframes_to_merge[middle_index:], **merge_options
                  ),
              ],
              **merge_options,
          )
          return merged_ddf
  