Backport PR pandas-dev#42110: DOC-Modified documentation for the issue GH42106 (pandas-dev#42161)

Co-authored-by: Abhishek R <[email protected]>

Author: meeseeksmachine

doc/source/user_guide/indexing.rst

@@ -1523,18 +1523,17 @@ Looking up values by index/column labels
 ----------------------------------------
 
 Sometimes you want to extract a set of values given a sequence of row labels
-and column labels, this can be achieved by ``DataFrame.melt`` combined by filtering the corresponding
-rows with ``DataFrame.loc``.  For instance:
+and column labels, this can be achieved by ``pandas.factorize``  and NumPy indexing.
+For instance:
 
 .. ipython:: python
 
     df = pd.DataFrame({'col': ["A", "A", "B", "B"],
                        'A': [80, 23, np.nan, 22],
                        'B': [80, 55, 76, 67]})
     df
-    melt = df.melt('col')
-    melt = melt.loc[melt['col'] == melt['variable'], 'value']
-    melt.reset_index(drop=True)
+    idx, cols = pd.factorize(df['col'])
+    df.reindex(cols, axis=1).to_numpy()[np.arange(len(df)), idx]
 
 Formerly this could be achieved with the dedicated ``DataFrame.lookup`` method
 which was deprecated in version 1.2.0.