Question

Suppose that scores is an array of 10 components of type double, and: 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

Fix the loop to `for (int i = 0; i < 9; i++)`, check with `scores[i] > scores[i + 1]`, and adjust output to reflect correct indices.

Step-by-step solution

Identify the Array Index Range

In programming languages such as C++ and Java, array indexing starts at 0. This means for an array of 10 elements, the valid indices range from 0 to 9. The loop starts with `i = 1` and goes till `i <= 10` which means it goes out of the valid range of the array. We need to modify the loop to end at `i < 9` since comparison is made with `i+1`.

Fix the Loop's Logical Condition

The loop checks `scores[i] >= scores[i + 1]`. However, since `i + 1` could be greater than 9 if `i` becomes 9 or more, this will cause an out-of-bounds error. Therefore, change the loop to `for (int i = 0; i < 9; i++)`.

Adjust Comparison Logic

In the given logic, scores are checked to ensure non-decreasing order. If `scores[i]` is greater than `scores[i + 1]`, it means the sequence is out of order for those elements. Hence the condition `if (scores[i] > scores[i + 1])` should be used since equality (`>=`) accounts for non-decreasing sequences.

Correct Output Formatting

In the original code, the message might be interpreted as elements out of order, and the way indices are printed (`i` and `i + 1`) is correct but starts from 1. With the fixed loop (`i` starting at 0), ensure indices are printed correctly by adding 1 to them in the message. Print `i + 1` and `i + 2` instead of `i` and `i + 1`.

Key concepts

Loop Conditions

When dealing with arrays in C++, understanding loop conditions is crucial for accessing elements correctly. At its core, a loop condition determines how many times the loop will execute. In our problem, the loop iterates through an array to perform comparisons and check the ordering of its elements.

To begin with, let's discuss how loops work with arrays. In C++, array indexing starts from 0. So, when you have an array containing 10 elements, the indices range from 0 to 9. In the original exercise, the loop condition was set as `i <= 10`, which exceeds the boundary of the array, leading to potential errors.

For a loop intended to compare each element with the next in the sequence, the condition should ensure that the loop does not go out of bounds. The corrected loop condition should thus be `for (int i = 0; i < 9; i++)`, providing safe and controlled access to each element.

Array Out-of-Bounds Error

An array out-of-bounds error occurs when a program attempts to access an index of an array that falls outside its defined range. These errors are common pitfalls in programming, especially for beginners learning languages like C++. Let’s explore this scenario based on our exercise.

Imagine an array with 10 elements: `scores = {2.5, 3.9, 4.8 ... 9.9}`. Attempting to access `scores[10]` leads to an out-of-bounds access because the last valid index for this array is 9. Understanding this helps us realize why certain loop conditions can lead to errors:

• Indices must remain within the bounds (0 to n-1 for an n-element array).
• Loops iterating over arrays must be carefully managed to avoid access errors.

Catching and correcting these out-of-bound accesses can prevent your program from crashing and ensure more reliable execution.

Conditional Statements

Conditional statements are essential in programming for making decisions. They evaluate a condition and execute specific actions based on whether the condition is true or false. In our exercise, the conditional statement `if (scores[i] >= scores[i + 1])` is used to assess the order of array elements.

In practical terms, this checks whether an element is greater than or equal to the next element in a sequence. However, our logic needed refinement. Because the array must be non-decreasing, the correct condition should be `if (scores[i] > scores[i + 1])`. This ensures that two adjacent elements are specifically evaluated for order breach when one surpasses the other.

Conditional statements aid in controlling the flow of your program and are vital for debugging and ensuring your code behaves as intended.

Comparison Operators

Comparison operators allow us to compare two values and are fundamental in programming for creating conditions. They include operators like `>`, `<`, `>=`, `<=`, `==`, and `!=`. These operators return a boolean value (true or false) based on the comparison.

In our code example, the operator used `>=` checks if the current element of the array is greater than or equal to the next one. However, because we wanted to flag elements out of order, we focused on the strict condition of them being greater. Hence, switching to the `>` operator was necessary to highlight any deviations from the non-decreasing sequence.

Understanding how to effectively choose and implement comparison operators will improve your ability to write correct and efficient conditions in your programs.