Problem 14 - C# Programming: From Problem Analysis to Program Design

Question

With the following declaration: int [ , ] points = {{300, 100, 200, 400, 600}, {550, 700, 900, 800, 100}}; The statement points[1, 3] = points[1, 3] + 10; will a. replace the 300 amount with 310 and 900 with 910 b. replace the 500 amount with 510 c. replace the 900 amount with 910 d. replace the 800 amount with 810 e. none of the above

Step-by-Step Solution

Answer

d. replace the 800 amount with 810

Step 1: Understanding the Initial Declaration

The given declaration creates a 2-dimensional array of integers named `points` with 2 rows. The first row is `{300, 100, 200, 400, 600}` and the second row is `{550, 700, 900, 800, 100}`. This creates a matrix-like structure where elements can be accessed using two indices: the first for the row and the second for the column.

Step 2: Analyzing the Statement

The statement `points[1, 3] = points[1, 3] + 10;` is modifying the element at the 2nd row and 4th column (index starts from 0) of the array. This corresponds to the number `800` in the second row `{550, 700, 900, 800, 100}`.

Step 3: Executing the Modification

The code `points[1, 3] = points[1, 3] + 10;` retrieves the value at `points[1, 3]`, which is `800`. It then adds `10` to this value, resulting in `810`. The modified value `810` is then stored back at the position `points[1, 3]`.

Step 4: Conclusion

After executing the statement, the element originally `800` becomes `810`. The correct choice for the effect of the operation is option `d`, which states that it will replace the 800 amount with 810.

Key Concepts

Understanding Two-Dimensional Arrays in C#

Two-dimensional arrays in C# are like a grid or a table, and they are particularly useful when dealing with data that naturally fits into a row and column format.
With two-dimensional arrays, you can think of the data being arranged in rows and columns. Imagine a spreadsheet - each cell is an element of the array. In the exercise, the array `points` has been declared with two rows:

• First row: `{300, 100, 200, 400, 600}`
• Second row: `{550, 700, 900, 800, 100}`

This structure is known as a **matrix**. It allows for an organized and efficient way to store and retrieve data based on two indices - row and column.

Exploring Array Indexing

Array indexing is the way to access elements within an array, and it's critical in understanding how to navigate through arrays effectively.
In C#, array indices start at zero. This means the first element of any array is accessed with index `0`.
For a two-dimensional array, you need two indices: one for the row and one for the column.

• For `points[0, 2]`, you would access the value 200 from the first row and third column.
• For `points[1, 3]`, you access the value 800 from the second row and fourth column.

Understanding this system is crucial as it allows you to pinpoint exactly which element you want to work with in a given array.

How Value Modification Works

Value modification in arrays is a straightforward yet powerful feature.
Once you locate the element you want to change, updating its value is simple.
In the exercise, the code `points[1, 3] = points[1, 3] + 10;` increases the current value of the element by 10. Here’s how it works:

• Fetch the current value at `points[1, 3]`, which is 800.
• Add 10 to it, changing the value to 810.
• Assign the new value back to the same position in the array.

This way, the two-dimensional array directly reflects the new state, showing how values can be dynamically adjusted as needed.

Programming Exercise Application

Programming exercises like the one provided are an excellent means to practice and reinforce your understanding of arrays, including two-dimensional arrays.
They challenge you to apply your knowledge in a hands-on manner.
For instance, this exercise requires you to understand not only how to declare a two-dimensional array but also how to modify and retrieve specific values using array indexing.

• It tests your ability to navigate arrays with indices that start from zero.
• Ensures you grasp how to perform operations within an array, such as modifying elements.

Thus, such exercises are instrumental in deepening your programming skills and solidifying your conceptual understanding of arrays in C#.