Exercises 3

1.    Write methods to determine the following statistics for an array of ints. Create a separate method for each statistic. minimum, maximum, average, standard deviation, mode.

2.    Write a method to reverse the contents of an array of ints.

3.    Write a method to shuffle the contents of an array of ints. Use the Math.random method. You can pick a random int with the following code:

// assume list is an array of ints
int rand = (int)( Math.random() * list.length );

4. The Sieve of Eratosthenes is another method for calculating prime numbers. 

From http://www.math.utah.edu/~alfeld/Eratosthenes.html at the University of Utah.

What is the Sieve of Eratosthenes?

A prime number is a natural number greater than 1 that can be divided without remainder only by itself and by 1. Natural numbers n that can be divided by a number less than n and greater than 1 are composite numbers. The Sieve of Eratosthenes identifies all prime numbers up to a given number n as follows:

1. Write down the numbers 1, 2, 3, ..., n. We will eliminate composites by marking them. Initially all numbers are unmarked.
2. Mark the number 1 as special (it is neither prime nor composite).
3. Set k=1. Until k exceeds or equals the square root of n do this:
   • Find the first number in the list greater than k that has not been identified as composite. (The very first number so found is 2.) Call it m. Mark the numbers

      2m, 3m, 4m, ... 
     

     as composite. (Thus in the first run we mark all even numbers greater than 2. In the second run we mark all multiples of 3 greater than 3.)
   • m is a prime number. Put it on your list.
   • Set k=m and repeat.

• Put the remaining unmarked numbers in the sequence on your list of prime numbers.

Use an array of booleans to implement the Sieve and find all prime numbers between 2 and a given value.