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Arrays
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5.1 INTRODUCTION
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An array is a sequence of objects all of which have the same type. The objects are called the elements of the array and are numbered consecutively 0, 1, 2, 3, . . . . These numbers are called index vahes or subscripts of the array. The term subscript is used because as a mathematical sequence, an array would be written with subscripts: ao, al, a2, . . . . These numbers locate the element s position within the array, thereby giving direct access into the array. If the name of the array is a, then a [ o ] is the name of the element that is in position 0, a [ 11 is the name of the element that is in position 1, etc. In general, the ith element is in position i-l.Soifthearrayhasnelements,theirnamesare a[O], a[l], a[2], . . . . a[n-I].
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Here is how you should imagine an array:
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11.11 33.33 i
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a with 5 elements: a [ 0 ] contains 11.11, a [ l] contains 33.33, a [ 2 ] contains 55.55, a [ 3 ] contains 77.77, and a [ 4 ] contains 99.99. The diagram actually represents a region of the computer s memory because an array is always stored this way with its elements in a contiguous sequence.
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This shows an array named
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The method of numbering the ith element with index i-l is called zero-based indexing. Its use has the effect that the index of an array element is always the same as the number of steps from the initial element a [ o ] to that element. For example, element a [ 3 ] is 3 steps from element a [ o ] . The advantage of this method will become more apparent in 6 when we see the relationship between arrays and pointers.
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5.2 PROCESSING ARRAYS
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Virtually all useful programs use arrays. One reason that arrays are so useful is that they allow a single name with a variable index to be used in place of many different names. This makes it easy to do many things that would be far more difficult without arrays.
ARRAYS
[CHAP. 5
EXAMPLE 5.1 Printing a Sequence in Order
This program reads 4 numbers and then prints them in reverse order:
main0 1 double a[4]; tout cc "Enter 4 real numbers:\n'; for (int i = 1; i C= 4; i++) { tout CC i CC ": '; tin >> a[i-11; > tout cc "Here they are in reverse order:\n"; for (i = 3; i >= 0; i--) tout CC "\ta[" CC i CC "1 = ' CC a[i] -KC endl;
The declaration double a [ 4 ] declares a to be an array of 4 elements of type double. The first for loop then allows the user to enter real numbers into these 4 components. Then the second for loop prints these stored numbers in reverse order.
The array looks like this:
a 1.618 2.718
The next example works the same way. But it uses a symbolic constant for the size of the array. This makes the code easier to modify.
CHAP. 51
ARRAYS
EXAMPLE 5.2 Using a Symbolic Constant to Declare and Process an Array
main0 1 const int size = 4; double a[size]; tout << "Enter ' C-C size XC ' real numbers:\n"; for (int i = 1; i <= size; i++) { co& cc i -c-c 1': It; tin >> a[i-11; 1 tout << "Here they are in reverse order:\n"; for (i = size-l; i >= 0; i--) tout << "\ta[U << i << "1 = I' << a[i] -C-C endl; 1
The constant integer s i ze is initialized with the value 4. It is then used to declare the array a, to prompt the user, and to control both for loops. The program works the same as the previous version.
The format for an array declaration is where the array s element type and array-size is the number of elements. The declaration in Example 5.2 declares Standard C++ requires arraysize to be a positive integer constant. As we did in Example 5.2, it is customary to define the array-size as a separate constant:
const int size = 4; double a[size]; a to be an array of 4 elements, each of type double. type type is array-name[array-size];
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