Question

Consider the following declarations: const int CAR_TYPES = 5; const int COLOR_TYPES = 6; double sales [CAR TYPES] [COLOR_TYPES]; a. How many components does the array sales have? b. What is the number of rows in the array sales? c. What is the number of columns in the array sales? d. To sum the sales by CAR_TYPES, what kind of processing is required? e. To sum the sales by COLOR_TYPES, what kind of processing is required?

Short answer

a. 30 components; b. 5 rows; c. 6 columns; d. Column-wise sum for each row; e. Row-wise sum for each column.

Step-by-step solution

Determine Total Components in the Array

The array, `sales`, is declared with dimensions defined by `CAR_TYPES` and `COLOR_TYPES`. The number of components is the product of these two dimensions.\[CAR\_TYPES \times COLOR\_TYPES = 5 \times 6 = 30\]So, the array has 30 components.

Determine Number of Rows in the Array

In the declaration `double sales [CAR_TYPES] [COLOR_TYPES]`, the first dimension is `CAR_TYPES`, which represents the number of rows. Thus, the number of rows is 5.

Determine Number of Columns in the Array

The second dimension `COLOR_TYPES` in `double sales [CAR_TYPES] [COLOR_TYPES]` represents the number of columns. Thus, the number of columns is 6.

Summing Sales by Car Types

To sum the sales by `CAR_TYPES`, you need to add the sales for each color (column-wise sum) within each row. This requires iterating over the columns for each row and summing the elements.

Summing Sales by Color Types

To sum the sales by `COLOR_TYPES`, you add the sales for each car type (row-wise sum) across each column. This requires iterating over the rows for each column and summing the elements.

Key concepts

Array Elements Calculation

In a multidimensional array, calculating the total number of elements involves multiplying the dimensions defined during declaration. Each dimension represents a level of structure in the array. For example, if we have a two-dimensional array like `sales` declared with dimensions `CAR_TYPES` and `COLOR_TYPES`, the total number of elements can be found using the formula: \[ \text{Total Elements} = \text{CAR\_TYPES} \times \text{COLOR\_TYPES} \] Given `CAR_TYPES = 5` and `COLOR_TYPES = 6`, the total elements will be: \[ 5 \times 6 = 30 \] So, the array `sales` contains 30 components. This calculation is crucial as it helps in understanding the full structure and capacity of the array, allowing for effective data storage and retrieval purposes.

Rows and Columns in Arrays

Understanding rows and columns in a multidimensional array is key to correctly accessing and processing data. For a two-dimensional array, the first dimension often represents the rows, while the second represents the columns. In `double sales [CAR_TYPES][COLOR_TYPES]`, `CAR_TYPES = 5` indicates that there are 5 rows, and `COLOR_TYPES = 6` suggests that there are 6 columns. To visualize this, think of each row as representing a specific set of data related to car types, and each column as representing the colors. This structured approach allows for a systematic way to input, organize, and retrieve data based on specific indices related to each dimension. Understanding the orientation of rows and columns helps prevent mix-ups in data manipulation processes, ensuring that operations are performed on the correct subset of data.

Processing Arrays by Dimensions

When processing a multidimensional array like `sales`, operations may need to be performed along specific dimensions. Knowing how to process arrays by rows or by columns can be incredibly beneficial. Summing by Car Types: To sum the sales data by car types, iterate through each row and compute a column-wise sum. This involves summing every element in a row, where each row corresponds to a particular car type:

• Access each row independently.
• Iterate through each column within the row.
• Add up every color's sales for a particular row.

Summing by Color Types: Conversely, to sum sales by color types, perform a row-wise sum across columns. This approach requires iterating over each column and summing the sales figures from every row within that column:

• Access each column independently.
• Iterate through each row in the column.
• Add up every car type's sales for a particular column.

By distinguishing which dimension to process, whether row-wise or column-wise, one can efficiently obtain insights and patterns relevant to the dataset.