Problem Description

In this problem, we are given a DataFrame named animals that contains information about different animals, including their name, species, age, and weight. Our task is to write a Python function that uses Pandas to list the names of animals that have a weight strictly greater than 100 kilograms. After finding the relevant animals, we need to sort this list by the animals' weight in descending order so the heaviest animals appear first.

The DataFrame is structured with columns for each attribute of the animals, and each row corresponds to a distinct animal. We are interested in filtering the rows based on a particular column (weight) and then manipulating the DataFrame to return a specific subset of its data (the name column).

In the context of the problem, we are also asked to leverage method chaining in Pandas which allows us to execute multiple operations in a compact and readable one-liner. This is efficient and elegant, minimizing the need for creating temporary variables and making the code easier to understand at a glance.

Intuition

The intuition behind the solution involves two main steps, which we can implement in Pandas through method chaining:

1. Filtering: First, we need to filter the DataFrame to include only those rows where the animals' weight is more than 100 kilograms. In Pandas, this is achieved with a boolean indexing operation, where we compare the weight column against the value 100. The comparison generates a boolean Series that we use to filter out rows that don't meet the condition.

2. Sorting and Selecting Columns: After filtering the rows, we should sort them by the weight column in descending order to meet the requirement of listing heavier animals first. The sort_values function in Pandas can be used for this purpose by specifying the ascending=False parameter. Once sorted, we need to select the name column as this is what we want to return. By indexing the DataFrame with a list of column names (['name']), we can select the required column(s).

The final solution combines filtering, sorting, and column selection in a single expression using method chaining. Each operation returns a DataFrame or Series that is immediately used as the input for the next operation in the chain, resulting in concise and efficient code.

Solution Approach

The solution is implemented using a Python function that expects a Pandas DataFrame as an input and returns a DataFrame as an output. Here is a step-by-step breakdown of the one-liner solution within the function:

1. Filtering with Boolean Indexing:

   In animals[animals['weight'] > 100], we perform a boolean indexing operation. This creates a boolean Series by comparing each value in the weight column to the number 100. This Series is then used to filter the DataFrame, keeping only the rows where the condition (weight greater than 100) is True.

2. Sorting Values:

   The .sort_values('weight', ascending=False) method is chained after the boolean indexing. This call sorts the filtered DataFrame by the weight column in descending order (ascending=False). The resulting DataFrame maintains only the filtered rows, now sorted so that the heaviest animals are at the top.

3. Selecting Columns:

   The last part of the chain [['name']] selects only the name column of the sorted DataFrame. This indexing operation constrains the output to contain only the names of the heavy animals, as requested.

By following these steps, the function returns the names of animals that weigh more than 100 kilograms, sorted by their weight in descending order. The entire process is a demonstration of method chaining in Pandas and showcases how expressive and efficient this approach can be for data manipulation tasks.

The algorithm's complexity essentially depends on the filtering and sorting operations. The filtering runs in O(n) time, where n is the number of rows in the DataFrame, as it involves checking each weight once. Sorting can be expected to run on average in O(n log n) time. Consequently, the overall complexity of the operation would be dominated by the sorting step, resulting in an average time complexity of O(n log n).

Example Walkthrough

Let's illustrate the solution approach with a small example:

Suppose we have the following DataFrame named animals:

We want to extract the names of animals weighing more than 100 kilograms, sorted by their weight in descending order.

Step-by-Step Walkthrough

1. Filtering with Boolean Indexing:

   We apply the boolean indexing operation animals['weight'] > 100 to create the following boolean Series:

   Daisy      True
   Bubbles    False
   Boomer     False
   Zeus       True
   Fluffy     False

   Using this Series to filter the DataFrame, we get:

   name	species	age	weight
   Daisy	cow	5	200
   Zeus	elephant	10	500

2. Sorting Values:

   We then sort the filtered results by the weight column in descending order:

   name	species	age	weight
   Zeus	elephant	10	500
   Daisy	cow	5	200

3. Selecting Columns:

   Finally, we select just the name column:

   name
   Zeus
   Daisy

The Code

def heavy_animals(df):
    return df[df['weight'] > 100].sort_values('weight', ascending=False)[['name']]

# Now, let’s use our `animals` DataFrame as an input to our function
result = heavy_animals(animals)
print(result)

Expected Output:

    name
Zeus
Daisy

This output matches our criteria, listing the names of the animals that weigh more than 100 kilograms, sorted in descending order by weight. With the above approach, we are able to efficiently filter, sort, and select the necessary data using method chaining in Pandas.

Solution Implementation

Time and Space Complexity

The time complexity of the findHeavyAnimals function involves several steps. First, we filter the animals DataFrame, which requires O(n) time, where n is the number of rows in animals. Then we sort this filtered DataFrame, which takes O(m log m) time where m is the number of rows with weight greater than 100. Finally, we slice the DataFrame to include only the name column, which is an O(m) operation. Therefore, the overall time complexity is O(n + m log m).

The space complexity of the findHeavyAnimals function also involves several components. The filtering operation generates a new DataFrame which can be up to O(n) space if all animals are heavier than 100 units. The sorting operation takes place in-place in pandas by default, so it does not change the space complexity, but if a copy was made during this process, it would require additional O(m) space. Selecting a single column from the DataFrame does not require additional space as it creates a view on the existing DataFrame, not a copy. Hence, the overall space complexity is O(n) if a copy is made during sorting, otherwise it remains O(n) due to the initial filter result.