Introduction to Arrays

• This is chapter 11, you should read it.
• Arrays are a way to store multiple pieces of data in a single structure.
  • A struct holds data related by grouping
    • It can be heterogeneous.
    • Access is by field name.
  • An array is a collection of homogeneous data.
    • Access is by index.
•  Up until now, all of your tasks can be performed by a single pass through the data.
  • Finding max, min sum of a group of numbers.
• But what if you wanted to find the standard deviation $ \sigma $.
  • $ \bar x = \frac{\Sigma x}{n} $
  • $ \sigma = \sqrt{\frac{\Sigma (x - \bar x)^2}{n-1}} $
  • In this case you would need to loop through the data twice.
    • Once to compute $\bar x$.
    • Then a second time to compute $\sigma$
  • Reading from files is very expensive, so you might want to store all of the data.
• How could I store a bunch of numbers.
  • Let's assume that you have 10 different values.
  • You could declare 10 variables

  • int x1, x2, x3, ....  

  • But processing those up would be a real pain

  • cin >> x1 >> x2 >> ...
    
    sum = x1 + x2 + ...
    sum2 = pow((x1 -xbar),2) + pow((x2 - xbar),2) + ... 

  • What if there were 20 numbers, 100, 1000, 10,000 ...
• An array will solve these problems.
  • Arrays are declared by giving the number of elements it should hold

    int data[10]; 

  • Then the access to elements is done through a numerical index

    size_t i;
    int sum;
    
    for(i =0; i < 10; i++) {
       cin >> data[i];
    }
    
    for(i = 0; i < 10; i++) {
        sum += data[i];
    } 

• A few things
  • We need to know the array size at compile time
    • That is when we write the code.
    • Later on we will learn how to deal with array size at run time.
  • The maximum size of the array (10 in this case) should be declared as a constant.
  • It is crucial that the array index (i) be between 0 and the size -1.
    • There are 10 boxes labeled 0 though 9.
• Take a look at stdev.cpp