Question

Suppose that scores is an array of 10 components of type double, and: \\[ \text { scores }=\\{2.5,3.9,4.8,6.2,6.2,7.4,7.9,8.5,8.5,9.9\\} \\] The following is supposed to ensure that the elements of scores are in nondecreasing order. However, there are errors in the code. Find and correct the errors. for (int i = 1; i <= 10; i++) if (scores[i] >= scores[i + 1]) cout << i << " and " << (i + 1) << " elements of scores are out of order." << endl;

Short answer

Change the loop to iterate from 0 to 8 (i.e., `for (int i = 0; i < 9; i++)`).

Step-by-step solution

Understand the Loop Condition

The loop condition `for (int i = 1; i <= 10; i++)` is incorrect for accessing array elements since arrays in programming are generally zero-indexed. This means the first element is at index 0, and the loop should check indices within the bounds of the array.

Correct the Loop Boundaries

We need to iterate from the first element up to the second-to-last element to avoid accessing an index out of bounds. Thus we change the loop to `for (int i = 0; i < 9; i++)` to correctly access each pair of elements.

Understand the Condition Inside the Loop

The condition `if (scores[i] >= scores[i + 1])` is incorrect. We are checking if the current score is greater than or equal to the next score to flag them as out of order. However, scores should be in non-decreasing order, which does not require any change here. But clarification about inclusivity may be needed; however, given this being a logical check, the condition doesn't change.

Modify Output Statements Accordingly

If any scores are found to be out of order, the indices need to be printed. As mentioned, ensure indices reflect zero-based indexing. Use `cout << i << " and " << (i + 1) << " elements of scores are out of order." << endl;` in a zero-indexed context.

Final Revised Code

Revised code: ```cpp for (int i = 0; i < 9; i++) { if (scores[i] >= scores[i + 1]) cout << i << " and " << (i + 1) << " elements of scores are out of order." << endl; } ``` This ensures we correctly check each pair of elements in the zero-indexed `scores` array to verify order.

Key concepts

Array Indexing

When working with arrays in C++, understanding how to index them is crucial. Arrays in C++ are zero-indexed, meaning the first element is accessed with index 0, and the last element of an array with size \( n \) is accessed with index \( n-1 \).
This means if you have an array of 10 elements, the indices will range from 0 to 9.

• Example: `scores[0]` refers to the first element \( 2.5 \), and `scores[9]` refers to the last element \( 9.9 \).

Since arrays use zero-based indexing, any operations or loops that interact with them must correctly reflect this. Failure to properly use indexing can lead to errors and unexpected results, such as accessing the wrong elements or encountering an array out-of-bounds error.

For Loop

A `for` loop in C++ is a control flow statement that allows code to be executed repeatedly based on a condition.
It is ideal for iterating over arrays. The typical structure of a for loop looks like this: `for (initialization; condition; increment)`.

• Initialization: Sets the starting point of the loop, often with a counter variable.
• Condition: Keeps the loop running as long as the condition is true.
• Increment: Changes the counter variable, usually by adding 1, moving the loop to the next iteration.

In the context of iterating over an array, the loop should start at 0 and run while the index is less than the array size, to avoid accessing out-of-bounds indices.

Out of Bounds

An out-of-bounds error occurs when you try to access an array index that is outside the valid range. In C++, accessing an out-of-bounds element can lead to undefined behavior, which might crash the program or result in incorrect data being used.
In the example code, the previous mistake was trying to access `scores[10]` in a 10-element array, so always ensure your loop properly fits within bounds.

• Accessing beyond `scores[9]` would cause this error in our initial setup.

To prevent these errors, remember to ensure any indices you use are valid and within the defined size of the array. Adjust loop conditions accordingly to avoid stepping out of the array's boundary.

Condition Checking

Condition checking in programming is essential for controlling what your code does in different scenarios. It's especially useful in loops when you need specific conditions to trigger actions. In this context, you want to ensure the elements in the scores array are in non-decreasing order.

• Use `if (scores[i] >= scores[i + 1])` to check if the current element `scores[i]` is greater than or equal to the next element `scores[i + 1]`.

Each time this condition is true, the indices are printed as being 'out of order.'
Logical checks like these help in maintaining control over data processing and ensuring certain rules or conditions within a program's logic are met. Understanding how conditions work will help you implement effective checks without errors.