Problem Description

You have a DataFrame called report that contains sales data for different products across four quarters. The data is currently in a "wide" format where each quarter is a separate column.

The DataFrame has the following structure:

• product: The name of the product (object/string type)
• quarter_1: Sales for the first quarter (integer)
• quarter_2: Sales for the second quarter (integer)
• quarter_3: Sales for the third quarter (integer)
• quarter_4: Sales for the fourth quarter (integer)

Your task is to reshape this data from wide format to long format. In the reshaped data:

• Each row should represent the sales of one product in one specific quarter
• Instead of having four separate quarter columns, you should have:
  • A quarter column that contains the quarter name (e.g., "quarter_1", "quarter_2", etc.)
  • A sales column that contains the sales value for that product in that quarter

For example, if the original data has one row with a product and its sales across 4 quarters, the reshaped data would have 4 rows for that same product - one row for each quarter with its corresponding sales value.

The solution uses pd.melt() function which "unpivots" the DataFrame from wide to long format. The id_vars=['product'] parameter keeps the product column as an identifier, var_name='quarter' names the new column containing the original column names (quarter_1, quarter_2, etc.), and value_name='sales' names the new column containing the sales values.

Intuition

The key insight here is recognizing that we need to transform data from a "wide" format (where related data spreads across multiple columns) to a "long" format (where related data stacks vertically in rows). This is a common data reshaping pattern in data analysis.

Think of it like converting a wide table where you can see all quarters side-by-side for each product into a tall, narrow table where each product-quarter combination gets its own row. Instead of reading across columns to see all quarters for a product, you'd read down rows.

The natural approach in pandas for this transformation is the melt() function, which is specifically designed for "unpivoting" data. The name "melt" is quite descriptive - imagine the wide DataFrame "melting" down into a longer, narrower shape.

To arrive at this solution, we need to identify:

1. What should stay constant in each row (the product name) - this becomes our id_vars
2. What columns should be "melted" or unpivoted (all the quarter columns) - these are implicitly all columns not in id_vars
3. What to call the new column that will hold the old column names (quarter) - this is our var_name
4. What to call the new column that will hold the values from those columns (sales) - this is our value_name

The beauty of pd.melt() is that it handles this entire transformation in a single function call, converting each quarter column into rows while preserving the product association, effectively multiplying the number of rows by the number of quarter columns while reducing the total number of columns.

Solution Approach

The solution uses pandas' melt() function to reshape the DataFrame from wide to long format. Here's the step-by-step implementation:

def meltTable(report: pd.DataFrame) -> pd.DataFrame:
    return pd.melt(report, id_vars=['product'], var_name='quarter', value_name='sales')

The pd.melt() function takes several key parameters:

1. report: The input DataFrame that needs to be reshaped.

2. id_vars=['product']: This specifies which columns should be kept as identifier variables. These columns won't be "melted" and will be repeated for each unpivoted column. In our case, we want to keep the product column as is, so each product will appear multiple times in the result (once for each quarter).

3. var_name='quarter': This parameter names the new column that will contain the original column headers. Since we're melting quarter_1, quarter_2, quarter_3, and quarter_4, this new column will contain these values as strings.

4. value_name='sales': This parameter names the new column that will contain the actual values from the melted columns. All the sales numbers that were previously spread across four columns will now be stacked vertically in this single column.

The transformation process works as follows:

• For each row in the original DataFrame, melt() creates 4 new rows (one for each quarter column)
• The product value is copied to all 4 new rows
• Each new row gets the quarter column name in the quarter column
• Each new row gets the corresponding sales value in the sales column

If the original DataFrame had N products, the resulting DataFrame will have N × 4 rows, transforming from a wide format with 5 columns to a long format with 3 columns.

Example Walkthrough

Let's walk through a small example to illustrate how the melt() function transforms our data.

Starting DataFrame (Wide Format):

| product | quarter_1 | quarter_2 | quarter_3 | quarter_4 |
|---------|-----------|-----------|-----------|-----------|
| Umbrella| 417       | 224       | 379       | 611       |
| SleepingBag| 800    | 936       | 93        | 875       |

We have 2 products with their sales across 4 quarters, giving us 2 rows × 5 columns.

Step 1: Apply pd.melt() When we call pd.melt(report, id_vars=['product'], var_name='quarter', value_name='sales'):

Step 2: Process First Product (Umbrella) The function takes the Umbrella row and creates 4 new rows:

• Row 1: product='Umbrella', quarter='quarter_1', sales=417
• Row 2: product='Umbrella', quarter='quarter_2', sales=224
• Row 3: product='Umbrella', quarter='quarter_3', sales=379
• Row 4: product='Umbrella', quarter='quarter_4', sales=611

Step 3: Process Second Product (SleepingBag) Similarly, for SleepingBag, it creates 4 more rows:

• Row 5: product='SleepingBag', quarter='quarter_1', sales=800
• Row 6: product='SleepingBag', quarter='quarter_2', sales=936
• Row 7: product='SleepingBag', quarter='quarter_3', sales=93
• Row 8: product='SleepingBag', quarter='quarter_4', sales=875

Final DataFrame (Long Format):

| product     | quarter   | sales |
|-------------|-----------|-------|
| Umbrella    | quarter_1 | 417   |
| Umbrella    | quarter_2 | 224   |
| Umbrella    | quarter_3 | 379   |
| Umbrella    | quarter_4 | 611   |
| SleepingBag | quarter_1 | 800   |
| SleepingBag | quarter_2 | 936   |
| SleepingBag | quarter_3 | 93    |
| SleepingBag | quarter_4 | 875   |

The transformation converted our 2 rows × 5 columns wide format into 8 rows × 3 columns long format. Each product-quarter combination now has its own row, making the data structure more suitable for certain types of analysis and visualization.

Solution Implementation

Time and Space Complexity

Time Complexity: O(n * m) where n is the number of rows in the DataFrame and m is the number of columns being melted (total columns minus id_vars columns).

The pd.melt() function needs to iterate through each row and transform each value column into a separate row in the resulting DataFrame. For each of the n rows, it processes m value columns (where m = total_columns - 1 since 'product' is the id_var), creating n * m new rows in the output DataFrame.

Space Complexity: O(n * m) where n is the number of rows in the original DataFrame and m is the number of columns being melted.

The space complexity is dominated by the output DataFrame created by pd.melt(). The resulting DataFrame will have n * m rows and 3 columns ('product', 'quarter', 'sales'). Since each original row with m value columns gets transformed into m rows in the output, the total space required is proportional to O(n * m * 3) = O(n * m).

Additionally, there may be temporary space used during the melting operation, but this doesn't change the overall space complexity class.

Common Pitfalls

1. Assuming Column Names Match Exactly

One common pitfall is assuming that the quarter columns will always be named exactly quarter_1, quarter_2, quarter_3, and quarter_4. If the DataFrame has different column names (like Q1, Q2, or q1_sales), the current solution will attempt to melt ALL columns except 'product', which might include unwanted columns.

Solution: Explicitly specify which columns to melt using the value_vars parameter:

def meltTable(report: pd.DataFrame) -> pd.DataFrame:
    quarter_cols = ['quarter_1', 'quarter_2', 'quarter_3', 'quarter_4']
    return pd.melt(report, 
                   id_vars=['product'], 
                   value_vars=quarter_cols,
                   var_name='quarter', 
                   value_name='sales')

2. Missing or NaN Values in Sales Data

The original wide-format data might contain NaN or missing values in some quarter columns. After melting, these NaN values will create rows with missing sales data, potentially affecting downstream analysis.

Solution: Add a dropna() call to remove rows with missing sales values:

def meltTable(report: pd.DataFrame) -> pd.DataFrame:
    melted_df = pd.melt(report, 
                        id_vars=['product'], 
                        var_name='quarter', 
                        value_name='sales')
    return melted_df.dropna(subset=['sales'])

3. Data Type Inconsistencies

If the quarter columns contain mixed data types (some integers, some strings, or some floats), the melted 'sales' column might end up with an unexpected dtype (like object), which can cause issues in numerical operations.

Solution: Ensure consistent data types after melting:

def meltTable(report: pd.DataFrame) -> pd.DataFrame:
    melted_df = pd.melt(report, 
                        id_vars=['product'], 
                        var_name='quarter', 
                        value_name='sales')
    melted_df['sales'] = pd.to_numeric(melted_df['sales'], errors='coerce')
    return melted_df

4. Multiple Identifier Columns

If the DataFrame has additional identifier columns beyond 'product' (like 'region', 'store_id', etc.) that should be preserved in the long format, forgetting to include them in id_vars will cause data loss.

Solution: Dynamically identify all non-quarter columns as identifiers:

def meltTable(report: pd.DataFrame) -> pd.DataFrame:
    quarter_cols = ['quarter_1', 'quarter_2', 'quarter_3', 'quarter_4']
    id_columns = [col for col in report.columns if col not in quarter_cols]
    return pd.melt(report, 
                   id_vars=id_columns,
                   value_vars=quarter_cols,
                   var_name='quarter', 
                   value_name='sales')