(Double Array Initialization) Label the elements of a 3 -by- 5 two-dimensional array sales to indicate the order in which they're set to zero by the following program segment: for ( row = 0; row < 3; ++row ) for ( column = 0; column < 5; ++column ) sales[ row ][ column ] = 0;

Understanding nested loops is crucial for handling multi-dimensional data structures like 2D arrays in C++. Imagine nested loops as loops within loops, where we have an outer loop and one or more inner loops. In our exercise with the two-dimensional array, the outer loop iterates through each row, while the inner loop iterates through each column within a specific row. Think of it as a grid: for every single row, we move column by column, like reading a book—left to right, top to bottom.

For instance, in a 3-by-5 array, the outer loop runs three times, one for each row. Within each row iteration, the inner loop runs five times to visit each column. This structure helps us access each array element in a systematic way to perform operations like initialization. The ability to control the flow of these loops is a powerful tool for matrix operations, image processing, and more complex algorithms where action on multi-dimensional data is required.

Array indexing refers to accessing elements within an array using their positions, which in programming are usually referred to by integer indexes. In C++, indices start at 0, not 1. This means that the first element of an array is accessed with index 0. For a 2D array, we use two indices: one for the row and one for the column.

For example, in the context of our array 'sales', sales[0][2] refers to the element in the first row (index 0) and the third column (index 2). It's important to note that incorrect indexing, such as using an index that's out of the range of the array, can lead to errors or undefined behavior. In our 3-by-5 array, valid row indices are 0, 1, and 2, while valid column indices are 0 through 4. Understanding how indexing works is fundamental to manipulating array data effectively and avoiding common programming pitfalls.

Zero initialization is the process of assigning a value of zero to each element in an array. It is a common practice to initialize an array for various reasons, such as to reset the data or to ensure that all elements have a known default value before starting operations. In C++, you can manually set each element to zero using loops, or you could use value-initialization syntax (such as 'int array[3][5] = {};') when declaring the array to automatically initialize all elements to zero.

In the provided exercise, the nested loops methodically set each element to zero, ensuring that no element is left uninitialized. This process guarantees that when we start to use the array, we won't encounter garbage values, which could lead to incorrect calculations or unpredictable program behavior. Zero initialization is especially useful for algorithms that depend on a known starting state, ensuring the integrity of the program's logic from the very beginning.