This supplementary reading is taken from Jonathan Shewchuk's Spring 2014 61B course.

LOOPS
=====

"while" Loops
-------------
A "while" statement is like an "if" statement, but the body of the statement is
executed repeatedly, as long as the condition remains true.  The following
example tests whether n is a prime number by attempting to divide it by every
integer in the range 2...n - 1.

    public static boolean isPrime(int n) {
      int divisor = 2;
      while (divisor < n) {         _ <- "divisor < n" is the _loop_condition_.
        if (n % divisor == 0) {      |
          return false;              | These lines inside the braces
        }                            | are called the _loop_body_.  
        divisor++;                  _|
      }
      return true;
    }

Here's how the loop executes.
- When Java reaches this "while" loop, it tests whether the loop condition
  "divisor < n" is true.
- If divisor < n, Java executes the loop body {in braces}.
- When Java finishes the loop body (i.e. after executing "divisor++"), it
  tests _again_ whether "divisor < n" is true.
- If it's still true, Java jumps back up to the beginning of the loop body and
  executes it again.
- If Java tests the loop condition and finds that "divisor < n" is false, Java
  continues execution from the next line of code _after_ the loop body.

An _iteration_ is a pass through the loop body.  In this example, if n is 2 or
less, the loop body won't iterate even once.

"for" Loops
-----------
"for" loops are a convenient shorthand that can be used to write some "while"
loops in a more compact way.  The following "for" loop is equivalent to the
following "while" loop.

    for (initialize; condition; next) {      |    initialize;   
      statements;                            |    while (condition) {
    }                                        |      statements;
                                             |      next;
                                             |    }

By convention, the "initialize" and "next" are both expressions that affect a
variable that changes every loop iteration and is central to the test.  Most
commonly, "for" statements are used to iterate while advancing an index
variable over a fixed range of values.  isPrime can be rewritten thus:

    public static boolean isPrime(int n) {
      for (int divisor = 2; divisor < n; divisor++) {    _
        if (n % divisor == 0) {                           |
          return false;                                   | Loop body.
        }                                                _|
      }
      return true;
    }

A common mistake among beginning Java and C programmers is to get the condition
wrong and do one loop iteration too few.  For example, suppose you want to
print all the prime numbers in the range 2...n.

    public static void printPrimes(int n) {
      int i;
      for (i = 2; i < n; i++) {        // ERROR!!!  Condition should be i <= n.
        if (isPrime(i)) {
          System.out.print(" " + i);
        }
      }
    }

Suppose we correct this method so the loop condition is "i <= n".  Think
carefully:  what is the value of i when the printPrimes method ends?

We'll come back to iteration, but first let's investigate something more
interesting to iterate on.