array

The sieve of Eratosthenes is named after Eratosthenes of Cyrene who was a Greek mathematician who devised a mechanism to find a sequence of prime numbers using a simple algorithm.

Normally, looping through a list of numbers and finding the primes can be an expensive process. The seive of Eratosthenes is one of the most efficient way of working out all of the smaller prime numbers below (below 10 million or so).

The sieve works by looping through a list of consecutive numbers, starting at 2. For each number in the sequence the multiples of that number are marked to be removed from the list of numbers. When finished the numbers that are not marked are prime numbers.

This algorithm is pretty straightforward, but from that it is possible to create a simple PHP function that will generate all the prime numbers up to a given number.

A simple way to convert a string into a set of variables is through the use of the explode() and list() functions. list() is a language construct (not really a function) that will convert an array into a list of variables. For example, to convert a simple array into a set of variables do the following:

list($variable1, $variable2) = array(1, 2);

In this example $variable1 now contains the value 1 and $variable2 contains the value 2. This can be adapted to use the explode() function to take a string and convert it into a set of variables. An example of this in use might be when dealing with addresses, simply explode the string using the comma and you have a set of variables.

$address = '123 Fake Street, Town, City, PO3T C0D3';
list($street, $town, $city, $postcode) = explode(',', $address);

You can now print out parts of the address like this:

Use the following array to print out a list of Canadian states, also know as provinces.

$canadian_states = array( 
    "BC" => "British Columbia", 
    "ON" => "Ontario", 
    "NL" => "Newfoundland and Labrador", 
    "NS" => "Nova Scotia", 
    "PE" => "Prince Edward Island", 
    "NB" => "New Brunswick", 
    "QC" => "Quebec", 
    "MB" => "Manitoba", 
    "SK" => "Saskatchewan", 
    "AB" => "Alberta", 
    "NT" => "Northwest Territories", 
    "NU" => "Nunavut",
    "YT" => "Yukon Territory"
);

Here is the same array, but with the French versions of the states.

The array_flip() function in PHP is used to swap the values of an array with the keys. Take the following array.

$array = array('key1'=>'value1', 'key2'=>'value2');

To exchange all the values with the keys we pass it through the array_flip() function.

$array = array_flip($array);
echo '<pre>'.print_r($array, true).'</pre>';

This prints out the following:

Array
(
 [value1] => key1
 [value2] => key2
)

If any of the values are the same then the highest key is overwritten. The following array:

$array = array('a', 'a', 'a', 'b');

Will produce the following array when passed through array_flip().

To randomise an array in PHP use the shuffle() function like this.

$array = range(1, 5);
shuffle($array); // randomise array

There are two limitations to this function. The first is that it completely removes any key association that you may have set up. So the following array.

$array = array('one'=>1,'two'=>2);

Would be turned into the following after using shuffle().

Array
(
  [0] => 2
  [1] => 1
)

A way around this is to use the following function, this uses the PHP function array_rand() to extract the all of the keys in the array in a random order before ensuring that the key associations are in place.