Problem Description

In this problem, we have a DataFrame weather with three columns: city, month, and temperature. The city column contains the name of a city as a string (or 'object' type), the month column includes names of the months as strings, and the temperature column includes the recorded temperatures as integers for the given city and month. The task is to rearrange the data so that each row represents a specific month, and each column corresponds to a different city, where the cell values should be the temperatures recorded for each city-month combination.

To achieve this, the DataFrame needs to be "pivoted". Pivoting is a transformation operation that is used to reshape data in data analysis. It's similar to the "pivot table" feature in spreadsheet software like Microsoft Excel, where you rearrange data to get a more convenient or useful representation, especially for analysis purposes. The result of this pivot operation should have the months as the rows, cities as the column headers, and temperatures as the cell values in the corresponding city-month position.

Intuition

To solve this problem, we use the pivot method from the Pandas library, which is designed for exactly this kind of operation. The pivot method takes three main arguments:

1. index: the column to set as the index of the pivoted DataFrame (the rows of our desired table). In our case, it's the 'month'.
2. columns: the column with values that will become the new column headers after pivoting. In our case, that's the 'city'.
3. values: the column containing values that will populate the new pivoted table. In this instance, it's the 'temperature'.

By setting these parameters, the pivot function will take every unique value in the 'month' column and create a corresponding row for each. Similarly, it will create a column for each unique value in the 'city' column. Finally, it populates these rows and columns with the corresponding 'temperature' values, based on the original rows in the DataFrame. In the end, we get a table where each row represents a month, each column represents a city, and the intersection of each row and column contains the temperature for that city in that month.

The pivotTable function we define simply calls the pivot method on the passed weather DataFrame with the appropriate parameters and returns the new pivoted DataFrame.

Solution Approach

The solution to this problem is straightforward, thanks to the capabilities provided by the Pandas library, which is extensively used for data manipulation and analysis in Python.

Here's the approach broken down step by step:

• We identify the shape we want to achieve by looking at the input data structure. We want to pivot the DataFrame so that month values become the index (rows), city values become the columns, and temperature values fill the cells of the DataFrame.

• To implement this, we utilize the pivot function from Pandas, which is explicitly designed for reshaping or pivoting data.

• The pivotTable function is created, which accepts a DataFrame named weather as its argument. Inside this function, we call the pivot method on the weather DataFrame.

• The pivot method is called with three parameters:

  • index='month': This sets the month column as the index of the new DataFrame. Each unique month now represents a different row.
  • columns='city': This turns unique city names into column headers. Every unique city value from the city column now becomes a separate column in the new DataFrame.
  • values='temperature': This specifies that the data to fill the DataFrame should be taken from the temperature column. This sets up our cell values according to the temperature of a city for a specific month.

• The pivot method returns the restructured DataFrame, which is then returned by the pivotTable function.

• No explicit loops, conditionals, or helper data structures are needed, since the pivot method takes care of the low-level data manipulation.

The beauty of using Pandas in this case is that it abstracts away much of the complexity that would come from doing such an operation manually. It internally does the heavy lifting, likely using efficient data structures like hashtables to quickly map the index and column labels to the corresponding values.

Here is the simple, yet powerful implementation of the pivotTable function using the pivot method:

import pandas as pd

def pivotTable(weather: pd.DataFrame) -> pd.DataFrame:
    return weather.pivot(index='month', columns='city', values='temperature')

This single line of code effectively replaces what might otherwise be a complex series of operations involving sorting, grouping, and restructuring of the data.

Example Walkthrough

Let's say we have the following weather DataFrame representing temperature readings across different cities and months:

  city      month  temperature
0  New York  January   3
1  Chicago   January  -3
2  Los Angeles  January  15
3  New York  February  2
4  Chicago   February  -4
5  Los Angeles  February 14

We want to pivot this DataFrame so that we can see the temperature of each city as columns, with each row representing a different month. Here's how we can accomplish this using the solution approach:

1. We first define the pivotTable function by importing Pandas and creating a function that takes a DataFrame as its argument.

2. Inside the function, we call the pivot method of the Pandas library on our weather DataFrame. We set the index argument to 'month', columns to 'city', and values to 'temperature'.

3. When we run our function with the example DataFrame, the pivot method rearranges the data. Each unique month becomes an index (row) of the resulting DataFrame, and each unique city becomes a column.

After we apply the pivotTable function to the example weather DataFrame, our new pivoted DataFrame will look like this:

         New York  Chicago  Los Angeles
month                                  
January            3       -3           15
February           2       -4           14

Now, each month is a row with temperature readings in columns for New York, Chicago, and Los Angeles. The cell values are the temperatures recorded for each city-month combination.

By using the pivot method provided by Pandas, we avoid complex and manual data rearrangements and achieve our desired data structure in a simple and efficient manner.

Solution Implementation

Time and Space Complexity

The time complexity of the pivot operation in pandas depends on the size of the input DataFrame weather. Assuming that the input DataFrame has n rows, then the complexity of the pivot operation primarily involves sorting the index and columns, which can be considered as O(n log n) in the average case for most sorting algorithms, including those used in Pandas operations.

Since each value from the temperature column is placed into a new cell in the resulting pivot table, the space needed for the output DataFrame is proportional to the number of unique month and city pairs. If there are m unique months and c unique cities, the resultant DataFrame could have up to m * c cells for the temperature values (excluding the memory required to store the DataFrame's index and column structures).

Thus, the space complexity can be expressed as O(m * c).

In summary:

• Time Complexity: O(n log n)
• Space Complexity: O(m * c)