diff --git a/pandas/core/reshape/concat.py b/pandas/core/reshape/concat.py
index 3e8d19096a36e..c2322ae626cfd 100644
--- a/pandas/core/reshape/concat.py
+++ b/pandas/core/reshape/concat.py
@@ -2,6 +2,7 @@
 concat routines
 """
 
+from typing import List
 import warnings
 
 import numpy as np
@@ -437,13 +438,13 @@ def get_result(self):
                 mgr = self.objs[0]._data.concat(
                     [x._data for x in self.objs], self.new_axes
                 )
-                cons = _get_series_result_type(mgr, self.objs)
+                cons = self.objs[0]._constructor
                 return cons(mgr, name=name).__finalize__(self, method="concat")
 
             # combine as columns in a frame
             else:
                 data = dict(zip(range(len(self.objs)), self.objs))
-                cons = _get_series_result_type(data)
+                cons = DataFrame
 
                 index, columns = self.new_axes
                 df = cons(data, index=index)
@@ -473,7 +474,7 @@ def get_result(self):
             if not self.copy:
                 new_data._consolidate_inplace()
 
-            cons = _get_frame_result_type(new_data, self.objs)
+            cons = self.objs[0]._constructor
             return cons._from_axes(new_data, self.new_axes).__finalize__(
                 self, method="concat"
             )
@@ -520,13 +521,13 @@ def _get_new_axes(self):
         new_axes[self.axis] = self._get_concat_axis()
         return new_axes
 
-    def _get_comb_axis(self, i):
+    def _get_comb_axis(self, i: int) -> Index:
         data_axis = self.objs[0]._get_block_manager_axis(i)
         return get_objs_combined_axis(
             self.objs, axis=data_axis, intersect=self.intersect, sort=self.sort
         )
 
-    def _get_concat_axis(self):
+    def _get_concat_axis(self) -> Index:
         """
         Return index to be used along concatenation axis.
         """
@@ -537,7 +538,7 @@ def _get_concat_axis(self):
                 idx = ibase.default_index(len(self.objs))
                 return idx
             elif self.keys is None:
-                names = [None] * len(self.objs)
+                names: List = [None] * len(self.objs)
                 num = 0
                 has_names = False
                 for i, x in enumerate(self.objs):
@@ -702,27 +703,3 @@ def _make_concat_multiindex(indexes, keys, levels=None, names=None) -> MultiInde
     return MultiIndex(
         levels=new_levels, codes=new_codes, names=new_names, verify_integrity=False
     )
-
-
-def _get_series_result_type(result, objs=None):
-    """
-    return appropriate class of Series concat
-    input is either dict or array-like
-    """
-    # TODO: See if we can just inline with _constructor_expanddim
-    # now that sparse is removed.
-
-    # concat Series with axis 1
-    if isinstance(result, dict):
-        return DataFrame
-
-    # otherwise it is a SingleBlockManager (axis = 0)
-    return objs[0]._constructor
-
-
-def _get_frame_result_type(result, objs):
-    """
-    return appropriate class of DataFrame-like concat
-    """
-    # TODO: just inline this as _constructor.
-    return objs[0]
diff --git a/pandas/core/reshape/melt.py b/pandas/core/reshape/melt.py
index 16c04454898db..4cba52c5cd651 100644
--- a/pandas/core/reshape/melt.py
+++ b/pandas/core/reshape/melt.py
@@ -1,4 +1,5 @@
 import re
+from typing import List
 
 import numpy as np
 
@@ -10,7 +11,7 @@
 from pandas.core.dtypes.missing import notna
 
 from pandas.core.arrays import Categorical
-from pandas.core.frame import _shared_docs
+from pandas.core.frame import DataFrame, _shared_docs
 from pandas.core.indexes.base import Index
 from pandas.core.reshape.concat import concat
 from pandas.core.tools.numeric import to_numeric
@@ -21,13 +22,13 @@
     % dict(caller="pd.melt(df, ", versionadded="", other="DataFrame.melt")
 )
 def melt(
-    frame,
+    frame: DataFrame,
     id_vars=None,
     value_vars=None,
     var_name=None,
     value_name="value",
     col_level=None,
-):
+) -> DataFrame:
     # TODO: what about the existing index?
     # If multiindex, gather names of columns on all level for checking presence
     # of `id_vars` and `value_vars`
@@ -35,6 +36,7 @@ def melt(
         cols = [x for c in frame.columns for x in c]
     else:
         cols = list(frame.columns)
+
     if id_vars is not None:
         if not is_list_like(id_vars):
             id_vars = [id_vars]
@@ -119,7 +121,7 @@ def melt(
     return frame._constructor(mdata, columns=mcolumns)
 
 
-def lreshape(data, groups, dropna=True, label=None):
+def lreshape(data: DataFrame, groups, dropna: bool = True, label=None) -> DataFrame:
     """
     Reshape long-format data to wide. Generalized inverse of DataFrame.pivot
 
@@ -129,6 +131,8 @@ def lreshape(data, groups, dropna=True, label=None):
     groups : dict
         {new_name : list_of_columns}
     dropna : boolean, default True
+    label : object, default None
+        Dummy kwarg, not used.
 
     Examples
     --------
@@ -188,7 +192,7 @@ def lreshape(data, groups, dropna=True, label=None):
     return data._constructor(mdata, columns=id_cols + pivot_cols)
 
 
-def wide_to_long(df, stubnames, i, j, sep: str = "", suffix: str = r"\d+"):
+def wide_to_long(df: DataFrame, stubnames, i, j, sep: str = "", suffix: str = r"\d+"):
     r"""
     Wide panel to long format. Less flexible but more user-friendly than melt.
 
@@ -412,14 +416,14 @@ def wide_to_long(df, stubnames, i, j, sep: str = "", suffix: str = r"\d+"):
                 two  2.9
     """
 
-    def get_var_names(df, stub, sep, suffix):
+    def get_var_names(df, stub: str, sep: str, suffix: str) -> List[str]:
         regex = r"^{stub}{sep}{suffix}$".format(
             stub=re.escape(stub), sep=re.escape(sep), suffix=suffix
         )
         pattern = re.compile(regex)
         return [col for col in df.columns if pattern.match(col)]
 
-    def melt_stub(df, stub, i, j, value_vars, sep: str):
+    def melt_stub(df, stub: str, i, j, value_vars, sep: str):
         newdf = melt(
             df,
             id_vars=i,
diff --git a/pandas/core/reshape/merge.py b/pandas/core/reshape/merge.py
index 76c4b328eb4db..4d838db6c95f6 100644
--- a/pandas/core/reshape/merge.py
+++ b/pandas/core/reshape/merge.py
@@ -92,7 +92,7 @@ def merge(
 
 
 def _groupby_and_merge(
-    by, on, left, right, _merge_pieces, check_duplicates: bool = True
+    by, on, left, right: "DataFrame", _merge_pieces, check_duplicates: bool = True
 ):
     """
     groupby & merge; we are always performing a left-by type operation
@@ -313,7 +313,7 @@ def merge_asof(
     suffixes=("_x", "_y"),
     tolerance=None,
     allow_exact_matches: bool = True,
-    direction="backward",
+    direction: str = "backward",
 ):
     """
     Perform an asof merge. This is similar to a left-join except that we
@@ -1299,11 +1299,13 @@ def _get_join_indexers(
         right_keys
     ), "left_key and right_keys must be the same length"
 
-    # bind `sort` arg. of _factorize_keys
-    fkeys = partial(_factorize_keys, sort=sort)
-
     # get left & right join labels and num. of levels at each location
-    llab, rlab, shape = map(list, zip(*map(fkeys, left_keys, right_keys)))
+    mapped = (
+        _factorize_keys(left_keys[n], right_keys[n], sort=sort)
+        for n in range(len(left_keys))
+    )
+    zipped = zip(*mapped)
+    llab, rlab, shape = [list(x) for x in zipped]
 
     # get flat i8 keys from label lists
     lkey, rkey = _get_join_keys(llab, rlab, shape, sort)
@@ -1311,7 +1313,7 @@ def _get_join_indexers(
     # factorize keys to a dense i8 space
     # `count` is the num. of unique keys
     # set(lkey) | set(rkey) == range(count)
-    lkey, rkey, count = fkeys(lkey, rkey)
+    lkey, rkey, count = _factorize_keys(lkey, rkey, sort=sort)
 
     # preserve left frame order if how == 'left' and sort == False
     kwargs = copy.copy(kwargs)
@@ -1487,12 +1489,12 @@ def get_result(self):
         return result
 
 
-def _asof_function(direction):
+def _asof_function(direction: str):
     name = "asof_join_{dir}".format(dir=direction)
     return getattr(libjoin, name, None)
 
 
-def _asof_by_function(direction):
+def _asof_by_function(direction: str):
     name = "asof_join_{dir}_on_X_by_Y".format(dir=direction)
     return getattr(libjoin, name, None)
 
@@ -1536,7 +1538,7 @@ def __init__(
         how: str = "asof",
         tolerance=None,
         allow_exact_matches: bool = True,
-        direction="backward",
+        direction: str = "backward",
     ):
 
         self.by = by
@@ -1775,11 +1777,11 @@ def flip(xs):
 
 def _get_multiindex_indexer(join_keys, index: MultiIndex, sort: bool):
 
-    # bind `sort` argument
-    fkeys = partial(_factorize_keys, sort=sort)
-
     # left & right join labels and num. of levels at each location
-    mapped = (fkeys(index.levels[n], join_keys[n]) for n in range(len(index.levels)))
+    mapped = (
+        _factorize_keys(index.levels[n], join_keys[n], sort=sort)
+        for n in range(index.nlevels)
+    )
     zipped = zip(*mapped)
     rcodes, lcodes, shape = [list(x) for x in zipped]
     if sort:
@@ -1804,7 +1806,7 @@ def _get_multiindex_indexer(join_keys, index: MultiIndex, sort: bool):
     lkey, rkey = _get_join_keys(lcodes, rcodes, shape, sort)
 
     # factorize keys to a dense i8 space
-    lkey, rkey, count = fkeys(lkey, rkey)
+    lkey, rkey, count = _factorize_keys(lkey, rkey, sort=sort)
 
     return libjoin.left_outer_join(lkey, rkey, count, sort=sort)
 
diff --git a/pandas/core/reshape/pivot.py b/pandas/core/reshape/pivot.py
index 0626420d9c114..b126b6e221ccc 100644
--- a/pandas/core/reshape/pivot.py
+++ b/pandas/core/reshape/pivot.py
@@ -1,3 +1,5 @@
+from typing import TYPE_CHECKING, Callable, Dict, Tuple, Union
+
 import numpy as np
 
 from pandas.util._decorators import Appender, Substitution
@@ -14,6 +16,9 @@
 from pandas.core.reshape.util import cartesian_product
 from pandas.core.series import Series
 
+if TYPE_CHECKING:
+    from pandas import DataFrame
+
 
 # Note: We need to make sure `frame` is imported before `pivot`, otherwise
 # _shared_docs['pivot_table'] will not yet exist.  TODO: Fix this dependency
@@ -180,14 +185,14 @@ def pivot_table(
 
 
 def _add_margins(
-    table,
+    table: Union["Series", "DataFrame"],
     data,
     values,
     rows,
     cols,
     aggfunc,
     observed=None,
-    margins_name="All",
+    margins_name: str = "All",
     fill_value=None,
 ):
     if not isinstance(margins_name, str):
@@ -200,14 +205,16 @@ def _add_margins(
 
     grand_margin = _compute_grand_margin(data, values, aggfunc, margins_name)
 
-    # could be passed a Series object with no 'columns'
-    if hasattr(table, "columns"):
+    if table.ndim == 2:
+        # i.e. DataFramae
         for level in table.columns.names[1:]:
             if margins_name in table.columns.get_level_values(level):
                 raise ValueError(msg)
 
     if len(rows) > 1:
-        key = (margins_name,) + ("",) * (len(rows) - 1)
+        key = (margins_name,) + ("",) * (
+            len(rows) - 1
+        )  # type: Union[str, Tuple[str, ...]]
     else:
         key = margins_name
 
@@ -216,7 +223,7 @@ def _add_margins(
         # one column in the data. Compute grand margin and return it.
         return table.append(Series({key: grand_margin[margins_name]}))
 
-    if values:
+    elif values:
         marginal_result_set = _generate_marginal_results(
             table,
             data,
@@ -232,12 +239,15 @@ def _add_margins(
             return marginal_result_set
         result, margin_keys, row_margin = marginal_result_set
     else:
+        # no values, and table is a DataFrame
+        assert isinstance(table, ABCDataFrame)
         marginal_result_set = _generate_marginal_results_without_values(
             table, data, rows, cols, aggfunc, observed, margins_name
         )
         if not isinstance(marginal_result_set, tuple):
             return marginal_result_set
         result, margin_keys, row_margin = marginal_result_set
+
     row_margin = row_margin.reindex(result.columns, fill_value=fill_value)
     # populate grand margin
     for k in margin_keys:
@@ -266,7 +276,7 @@ def _add_margins(
     return result
 
 
-def _compute_grand_margin(data, values, aggfunc, margins_name="All"):
+def _compute_grand_margin(data, values, aggfunc, margins_name: str = "All"):
 
     if values:
         grand_margin = {}
@@ -289,7 +299,15 @@ def _compute_grand_margin(data, values, aggfunc, margins_name="All"):
 
 
 def _generate_marginal_results(
-    table, data, values, rows, cols, aggfunc, observed, grand_margin, margins_name="All"
+    table,
+    data,
+    values,
+    rows,
+    cols,
+    aggfunc,
+    observed,
+    grand_margin,
+    margins_name: str = "All",
 ):
     if len(cols) > 0:
         # need to "interleave" the margins
@@ -353,7 +371,7 @@ def _all_key(key):
 
 
 def _generate_marginal_results_without_values(
-    table, data, rows, cols, aggfunc, observed, margins_name="All"
+    table: "DataFrame", data, rows, cols, aggfunc, observed, margins_name: str = "All"
 ):
     if len(cols) > 0:
         # need to "interleave" the margins
@@ -406,7 +424,7 @@ def _convert_by(by):
 
 @Substitution("\ndata : DataFrame")
 @Appender(_shared_docs["pivot"], indents=1)
-def pivot(data, index=None, columns=None, values=None):
+def pivot(data: "DataFrame", index=None, columns=None, values=None):
     if values is None:
         cols = [columns] if index is None else [index, columns]
         append = index is None
@@ -436,8 +454,8 @@ def crosstab(
     colnames=None,
     aggfunc=None,
     margins=False,
-    margins_name="All",
-    dropna=True,
+    margins_name: str = "All",
+    dropna: bool = True,
     normalize=False,
 ):
     """
@@ -546,7 +564,7 @@ def crosstab(
     if pass_objs:
         common_idx = get_objs_combined_axis(pass_objs, intersect=True, sort=False)
 
-    data = {}
+    data = {}  # type: dict
     data.update(zip(rownames, index))
     data.update(zip(colnames, columns))
 
@@ -585,7 +603,7 @@ def crosstab(
     return table
 
 
-def _normalize(table, normalize, margins, margins_name="All"):
+def _normalize(table, normalize, margins: bool, margins_name="All"):
 
     if not isinstance(normalize, (bool, str)):
         axis_subs = {0: "index", 1: "columns"}
@@ -601,7 +619,7 @@ def _normalize(table, normalize, margins, margins_name="All"):
             "all": lambda x: x / x.sum(axis=1).sum(axis=0),
             "columns": lambda x: x / x.sum(),
             "index": lambda x: x.div(x.sum(axis=1), axis=0),
-        }
+        }  # type: Dict[Union[bool, str], Callable]
 
         normalizers[True] = normalizers["all"]
 
@@ -668,7 +686,7 @@ def _normalize(table, normalize, margins, margins_name="All"):
     return table
 
 
-def _get_names(arrs, names, prefix="row"):
+def _get_names(arrs, names, prefix: str = "row"):
     if names is None:
         names = []
         for i, arr in enumerate(arrs):
diff --git a/pandas/core/reshape/tile.py b/pandas/core/reshape/tile.py
index 073bb4707f890..bfaa49dd576dc 100644
--- a/pandas/core/reshape/tile.py
+++ b/pandas/core/reshape/tile.py
@@ -496,7 +496,7 @@ def _convert_bin_to_datelike_type(bins, dtype):
 
 
 def _format_labels(
-    bins, precision, right: bool = True, include_lowest: bool = False, dtype=None
+    bins, precision: int, right: bool = True, include_lowest: bool = False, dtype=None
 ):
     """ based on the dtype, return our labels """
 
@@ -565,7 +565,7 @@ def _postprocess_for_cut(fac, bins, retbins: bool, dtype, original):
     return fac, bins
 
 
-def _round_frac(x, precision):
+def _round_frac(x, precision: int):
     """
     Round the fractional part of the given number
     """
@@ -580,7 +580,7 @@ def _round_frac(x, precision):
         return np.around(x, digits)
 
 
-def _infer_precision(base_precision, bins):
+def _infer_precision(base_precision: int, bins) -> int:
     """Infer an appropriate precision for _round_frac
     """
     for precision in range(base_precision, 20):