**π‘ Problem Formulation:** When working with data in Pandas, it’s common to need to sort the index of a DataFrame or Series. Besides sorting the data itself, sometimes we need to obtain the indices that would sort the index. Consider a Pandas Series with the index out of order. Our objective is to sort this Series by its index and additionally get the index positions that would sort the Series.

## Method 1: Using `sort_index()`

and `argsort()`

This approach uses the `sort_index()`

method to sort the DataFrame or Series by index and the `argsort()`

function from NumPy to return the indices that would sort the index. `sort_index()`

returns a new object with the index sorted, while `np.argsort()`

gives the indices that would sort an array.

Here’s an example:

import pandas as pd import numpy as np # Creating a Series with an unordered index s = pd.Series(data=[2, 1, 4, 3], index=[3, 1, 2, 0]) # Sorting the Series by index sorted_series = s.sort_index() # Getting the indices that would sort the index sort_indices = np.argsort(s.index)

Output:

sorted_series: 0 3 1 1 2 4 3 2 dtype: int64 sort_indices: array([3, 1, 2, 0])

This example demonstrates creating a Series with a scrambled index and then sorting it using `sort_index()`

. Afterward, the indices that would sort the original index are obtained using NumPy’s `argsort()`

function applied to the index.

## Method 2: Using `reset_index()`

and `sort_values()`

To sort index values while preserving the original index as a column, you can use `reset_index()`

followed by `sort_values()`

. This technique first resets the index, moving it into a column, and then sorts by that column. It returns a DataFrame with sorted values and original indices.

Here’s an example:

# Resetting index and sorting by the former index reset_sorted = s.reset_index().sort_values(by='index') # Retrieving the new order of indices new_indices = reset_sorted['index'].to_numpy()

Output:

reset_sorted: index 0 3 0 3 1 1 1 2 2 4 0 3 2 new_indices: array([0, 1, 2, 3])

After calling `reset_index()`

, the original index becomes a column in the DataFrame, which allows us to sort by this column using `sort_values()`

. The sort order is conserved in a separate array, `new_indices`

, which gives the positions of the original indices.

## Method 3: Using `sorted()`

with a Custom Lambda

Python’s built-in `sorted()`

function can sort indexes with a custom lambda function that extracts the indexes. This is a more manual approach but allows for additional flexibility if needed, such as custom sorting logic.

Here’s an example:

# Sorting the index with a lambda function and sorted() sorted_indices = sorted(range(len(s.index)), key=lambda k: s.index[k]) # Creating the sorted Series sorted_series_by_lambda = s.iloc[sorted_indices]

Output:

sorted_indices: [3, 1, 2, 0] sorted_series_by_lambda: 0 3 1 1 2 4 3 2 dtype: int64

By using the `sorted()`

function with a lambda, we can specify a custom sorting functionβhere, one that sorts the indices. Then, we use these sorted indices to rearrange the original Series.

## Method 4: Combining `Series.index`

and `Series.take()`

Another option is to use the `take()`

method, which allows you to sort by indices and preserve the original index’s order. The method `take()`

is used to return the elements in the given indices along an axis.

Here’s an example:

# Getting indices that would sort the index indices = s.index.argsort() # Using take() to sort by index sorted_series = s.take(indices)

Output:

sorted_series: 0 3 1 1 2 4 3 2 dtype: int64

By obtaining the sorted indices with `argsort()`

, we can then apply these to the Series using the `take()`

method. This results in a sorted Series while also giving us access to the sort order through `indices`

.

## Bonus One-Liner Method 5: Using `pandas.Index.get_indexer()`

The `pandas.Index.get_indexer()`

method provides an alternative one-liner to retrieve the order of indices needed to sort the index. It returns an array of index positions that shows where the target index should be inserted to maintain order.

Here’s an example:

# Using get_indexer() for a one-liner solution sorted_order = s.index.get_indexer(s.index.sort_values())

Output:

sorted_order: array([3, 1, 2, 0])

This one-liner retrieves the positions where the sorted index values need to be placed. `Index.get_indexer()`

is used on the Series index, comparing it to the sorted index, thus providing the sorted order.

## Summary/Discussion

**Method 1:**Using`sort_index()`

and`argsort()`

. Strengths: Direct and utilizes well-known Pandas and NumPy methods. Weaknesses: It involves an additional import and understanding of NumPy.**Method 2:**Using`reset_index()`

and`sort_values()`

. Strengths: Leverages Pandas’ own methods without extra imports. Weaknesses: Can be less intuitive for those unfamiliar with resetting and sorting indices.**Method 3:**Using`sorted()`

with custom lambda. Strengths: High customization potential and does not rely on Pandas-specific functionality. Weaknesses: Can be unnecessarily complex for simple sorting tasks.**Method 4:**Combining`Series.index`

and`Series.take()`

. Strengths: Pure Pandas solution with clear intent. Weaknesses: Not as widely known or used as other methods.**Method 5:**Using`pandas.Index.get_indexer()`

as a one-liner. Strengths: Efficient and compact. Weaknesses: Might not be as readable to someone learning Pandas.