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Arrays are useful foils for illustrating scan algorithms, and they are introduced now for that reason. This discussion is brief. Arrays are covered in more detail later.
An array is a collection of numbered variables, all having the same type. Each variable is referred to by its index in the array. Notation A[i] means the variable at index i in array A. A[i] is often called "A sub i" for short.
The indices of an array always start at 0. For example, an array A of 5 items has indices 0, 1, 2, 3 and 4, so A[0], A[1], A[2], A[3] and A[4] are the variables in array A.
When carrying out hand simulations with arrays, it is common practice to draw an array as a column or row of boxes. Number the boxes, starting at 0. For example, an array called B of 4 integers is diagrammed as follows.
| B | |
| 0 | |
| 1 | |
| 2 | |
| 3 |
Notice that the variables in the array are shown empty. They are uninitialized when the array is created. Performing statements
B[0] = 2; B[1] = B[0] + 2;changes array B as follows.
| B | |
| 0 | 2 |
| 1 | 4 |
| 2 | |
| 3 |
You are required to declare an array before you use it. Declaration
int A[10];
declares array A of 10 integers.
In general, the form is
T name[size];where T is the type of each variable in the array, name is the array's name and size is the number of variables. For example,
double stuff[100];
creates an array called stuff of size 100, where each
variable in array stuff has type double.
At an elementary level, C++ arrays look a lot like Java arrays, but there are some important differences. A big difference is that a C++ program cannot ask an array how large it is. Really! To deal with that, when we pass an array to a function, we will also pass its size.
That means that we cannot say that a function returns the smallest value in array A, but instead we must say that it returns the smallest value of A[0], A[1], …, A[n − 1]. That is awkward, so we will use notation A[0, …, n − 1] in comments. That is not C++ notation, and should only occur in comments or descriptions of functions or algorithms.
To indicate in a function heading that a parameter is an array, write [] after the parameter. For example, a function that returns the smallest member of A[0, …, n − 1] might have the following heading.
int smallest(int A[], int n)
To pass an array to a function in a function call, just write the name of the array. For example,
int s = smallest(B, 5)returns the smallest value in B[0, …, 4].
Write a statement that defines a constant called maxNumKangaroos, with value 200. Write another statement that creates an array integers called kangaroo of size maxNumKangaroos. Answer
Using the array kangaroo from the preceding question, write a statement that sets the first variable in array kangaroo to 7. Answer
Using array kangaroo from question 1, does the following make sense?
kangaroo[maxNumKangaroos] = -1;Answer
Using function smallest discussed above, write a statement that creates variable r of type int and sets it equal to the smallest number in kangaroo[0, …, 10]. Answer
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