Problem Description

In this problem, we're working with a DataFrame named employees that has four columns with specific data types:

• employee_id which is of type int,
• name which is of type object, indicating it could be a string or a mix of different types,
• department which is also an object,
• and salary which is an int.

The task is to create a solution that will display the first 3 rows of this DataFrame. This means we need to write a function that takes this DataFrame as an input and returns a new DataFrame composed only of the first three entries from the original.

Intuition

When dealing with DataFrames in Python, the Pandas library is the go-to tool as it provides extensive functionalities for data manipulation and analysis. One of the basic methods available in Pandas for DataFrame objects is the .head() method.

The .head() method is used to retrieve the top n rows from a DataFrame, where n defaults to 5 when no argument is provided. Since in this case, we are interested in getting just the first three rows, we can simply call employees.head(3). This line of code will return a new DataFrame with only the first three rows of the employees DataFrame.

Hence, the solution approach is straightforward:

• Import the Pandas library to be able to work with DataFrames.
• Define a function selectFirstRows() that accepts the employees DataFrame as a parameter.
• Inside the function, use the .head() method on the employees DataFrame with 3 as an argument to extract the first three rows.
• Return this subset of the DataFrame.

No complex operations or additional logic are required since this is a straight use-case of the method provided by Pandas for such tasks.

Solution Approach

The implementation of the solution for this particular problem is very straightforward because it leverages the built-in functionality provided by the Pandas library, rather than requiring a complex algorithm or data structure. Here's a step-by-step explanation:

• First, we import the Pandas library, which is a powerful tool for data manipulation in Python. It's standard to import Pandas and give it the alias pd, which is what we see in the solution import pandas as pd.

• Next, we define a function selectFirstRows(), which is our solution function. It expects one argument, employees, which is a DataFrame that we want to process.

• Inside the function, we use the Pandas DataFrame .head() method. The method .head(n) returns the first n rows of a DataFrame. By calling employees.head(3), we are asking for the first three rows of the employees DataFrame.

This is the complete function:

def selectFirstRows(employees: pd.DataFrame) -> pd.DataFrame:
    return employees.head(3)

The algorithm and pattern used here is direct and makes use of the high-level abstractions provided by Pandas for common data operations. Since the task does not require any conditional logic or iteration that would need to be explicitly programmed, we do not need to delve into more complex data structures or algorithms.

The function will output a new DataFrame object that contains only the first three rows of the employees DataFrame, maintaining the same column structure: employee_id, name, department, and salary.

In terms of computational complexity, this operation is usually O(1), constant time, as it simply returns a view of the first few rows and does not involve any re-computation of data.

Example Walkthrough

Let's consider a scenario where we have a DataFrame called employees that looks like this:

Our goal is to create a function that, when given this DataFrame, will return a new DataFrame consisting only of the first three rows. We'll use Python along with the Pandas library to achieve this.

Here is a step-by-step explanation using the given employees DataFrame:

1. First, we import the Pandas library using import pandas as pd.

2. Then, we define our function selectFirstRows() which will accept one argument, the employees DataFrame. The function signature will look like this: def selectFirstRows(employees: pd.DataFrame) -> pd.DataFrame.

3. Inside this function, we will call the .head() method on the employees DataFrame. Since we need the first three rows, we pass the integer 3 as an argument to .head(), which will be employees.head(3).

4. Finally, the function will return the result of employees.head(3), which is the new DataFrame containing the first three rows of employees.

Applying the function selectFirstRows() to our employees DataFrame will look like this:

import pandas as pd

# The DataFrame 'employees' is defined as shown in the example above
employees = pd.DataFrame({
    'employee_id': [1, 2, 3, 4, 5],
    'name': ['Alice', 'Bob', 'Charlie', 'Dana', 'Eve'],
    'department': ['Engineering', 'Marketing', 'Sales', 'HR', 'Engineering'],
    'salary': [70000, 60000, 50000, 80000, 90000]
})

# Definition of our function
def selectFirstRows(employees: pd.DataFrame) -> pd.DataFrame:
    return employees.head(3)

# Calling the function with our DataFrame
first_three_employees = selectFirstRows(employees)

# The 'first_three_employees' DataFrame now holds:
# | employee_id | name     | department  | salary |
# |-------------|----------|-------------|--------|
# | 1           | Alice    | Engineering | 70000  |
# | 2           | Bob      | Marketing   | 60000  |
# | 3           | Charlie  | Sales       | 50000  |

In this case, the output we get from first_three_employees is exactly as we expect: the top three entries from our original employees DataFrame, maintaining the integrity of the data's structure.

Solution Implementation

Time and Space Complexity

The time complexity of the selectFirstRows function is O(1) because retrieving the first few rows of a dataframe is a constant time operation. It does not depend on the size of the dataframe, as the number of rows to retrieve is always fixed at 3.

The space complexity of the function is also O(1) since it creates a new dataframe containing only a constant number of rows, regardless of the input dataframe’s size.