Getting Your Ducks in a Row

Let us now return to a programming task we discussed in class, namely finding the sum and average of a set of numbers. In class, we looked at the particular case of three numbers. What happens if we want to do this for, say, 100 numbers. We could begin by declaring 100 variables with names like: num1, num2, num3, ..., num100 and read them in with 100 scanf() statements. Then we could add them up in a really huge expression like:

sum = num1 + num2 + num3 + num4 + num5
    + num6 + num7 + num8 + num9 + num10
    ...
    + num96 + num97 + num98 + num99 + num100 ;

Once we've done that, the task of finding the average is still as simple as it was for three numbers. This already seems needlessly complex.

Now in a real situation, the user of our program would likely not always have 100 numbers to average, but would sometimes have fewer. That means our program needs to determine how many of the scanf() statements to execute and how many of the numbers to add up. While it's possible to do all this with a bunch of if statement, things are really getting ridiculous.

What we'd really like to do is to be able to refer to the 1st number, then the 2nd then the 3rd and so on using one of those loops we saw in the last part. This is why nearly every programming language, including the first widely used language (FORTRAN), includes some way to have a list of items. In most languages (including C), this list mechanism is called the array. Using an array, we can solve this programming task with a program like:

#include <stdio.h>

main()
{
   int nums[100] ;
   int num_nums, i, sum ;

   printf( "How many numbers do you want to average? " ) ;
   scanf( "%d", &num_nums ) ;
   for( i = 0; i < num_nums; ++i ) {
      printf( "What is number %d? ", i ) ;
      scanf( "%d", &nums[i] ) ;
   }
   sum = 0 ;
   for( i = 0; i < num_nums; ++i )
      sum += nums[i] ;
   printf( "The sum is %d, and the average is %d.\n",
      sum, sum / num_nums ) ;
}

Study this program carefully; it's one of the more complex programs we've seen. Some of the more important features of this program include:

The square brackets ([]) are used with arrays in C. When we use them in a declaration as in the line:
```
int nums[100] ;
```
the value in the brackets indicates how big we want the array made. This value must be a constant number (or expression). Often we will use a symbolic constant created with a #define for array sizes.
When we use the brackets after an array name in an expression, we are determining which element of the array we want to use. So in the statement
```
sum += nums[i] ;
```
we're adding the ith number to sum.
If we have an array of integers (as nums is here), then we can use an array reference such as nums[i] anywhere we could use an integer variable. Notice how we've taken advantage of this in the scanf() statement.
In C arrays are numbered starting at 0, not 1. That means that if we have an array of 100 elements, the elements are numbered 0 to 99.
Also study how we use the for statement to scan through an array. This is a common action.

Write the declaration for an array of 1000 floating point numbers to be called samples.