BUG: Wrong column order after inner merge operation on empty dataframes.

[anmyachev]

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• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import pandas as pd

on = [f"col_{x}" for x in range(5)]
columns1 = ["col_0", "col_1", "col_2", "col_3", "col_4", "col_5"]
columns2 = ["col_0", "col_1", "col_2", "col_3", "col_4", "col_6", "col_7"]

last_wide_df = pd.DataFrame([[0] * 6], columns=columns1)
last_pivot_df = pd.DataFrame([[0] * 7], columns=columns2)

print(pd.merge(last_wide_df, last_pivot_df, on=on).columns)  # 1st case
print(pd.merge(last_wide_df[:0], last_pivot_df[:0], on=on).columns)  # 2nd case

Issue Description

The column order is different in these two cases:

Index(['col_0', 'col_1', 'col_2', 'col_3', 'col_4', 'col_5', 'col_6', 'col_7'], dtype='object')
Index(['col_5', 'col_0', 'col_1', 'col_2', 'col_3', 'col_4', 'col_6', 'col_7'], dtype='object')

Expected Behavior

I believe that the order of the columns should be the same in these two cases.

Installed Versions

INSTALLED VERSIONS
------------------
commit           : 2e218d10984e9919f0296931d92ea851c6a6faf5
python           : 3.9.15.final.0
python-bits      : 64
OS               : Windows
OS-release       : 10
Version          : 10.0.22000
machine          : AMD64
processor        : Intel64 Family 6 Model 140 Stepping 1, GenuineIntel
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : English_United States.1252

pandas           : 1.5.3
numpy            : 1.23.4
pytz             : 2022.6
dateutil         : 2.8.2
setuptools       : 65.5.1
pip              : 22.3.1
Cython           : None
pytest           : 7.2.0
hypothesis       : None
sphinx           : 5.3.0
blosc            : None
feather          : 0.4.1
xlsxwriter       : None
lxml.etree       : 4.9.1
html5lib         : None
pymysql          : None
psycopg2         : 2.9.3
jinja2           : 3.1.2
IPython          : 8.6.0
pandas_datareader: None
bs4              : 4.11.1
bottleneck       : None
brotli           :
fastparquet      : 2022.11.0
fsspec           : 2022.11.0
gcsfs            : None
matplotlib       : 3.6.2
numba            : None
numexpr          : 2.7.3
odfpy            : None
openpyxl         : 3.0.10
pandas_gbq       : 0.17.9
pyarrow          : 9.0.0
pyreadstat       : None
pyxlsb           : None
s3fs             : 2022.11.0
scipy            : 1.9.3
snappy           : None
sqlalchemy       : 1.4.46
tables           : 3.7.0
tabulate         : None
xarray           : 2022.11.0
xlrd             : 2.0.1
xlwt             : None
zstandard        : None
tzdata           : None

[anmyachev]

@jbrockmendel could you take a look?

[jbrockmendel]

will do

[jbrockmendel]

Looks like in MergeOperation._get_merge_keys the two cases are getting very different left_drop/right_drop. there is a check in there for if len(left) > 0: that looks sketchy. Disabling that check causes the two results in the OP to match. need to track down what that check is for and what breaks when it is disabled