Update 1: using BigInteger Multiply method instead of unsupported custom * Operator.
Update 2: Porting code examples to Phalanger 3 - syntax changes on namespace use.
Here below a little program in Phalanger that implements 2 classes (in fact, they are 3). There is the main class, called Fiborial (Fibo(nnacci)+(Facto)rial) that implements the Fibonacci and the Factorial algorithms in two ways, one Recursive (using recursion) and the other Imperative (using loops and states). The second class is just an instance class that does the same thing, but its there just to show the difference between static and instance classes, and finally the third one (which will not appear in other languages) is the Program class which has the static execution method "Main".
You can also find 3 more little examples at the bottom. One prints out the Factorial's Series and Fibonacci's Series, the second one just shows a class that mixes both: static and instance members, and finally the third one that uses different return types (including System.Numerics.BigInteger) for the Factorial method to compare the timing and result.
As with the previous posts, you can copy and paste the code below in your favorite IDE/Editor and start playing and learning with it. This little "working" program will teach you some more basics of the Programming Language.
There are some "comments" on the code added just to tell you what are or how are some features called. In case you want to review the theory, you can read my previous post, where I give a definition of each of the concepts mentioned on the code. You can find it here: http://carlosqt.blogspot.com/2011/01/new-series-factorial-and-fibonacci.html
The Fiborial Program
<?php
# Factorial and Fibonacci in Phalanger
namespace FiborialPhp;
use System;
use System\Collections\Generic as G;
use System\Diagnostics as D;
use System\Numerics as N;
# Instance Class
# static is not a class modifier in PHP
[\Export]
class StaticFiborial
{
# Static Field
private static $className;
# no available static __constructor support
# Static Initializer Method instead, but need to be explicitly invoked
public static function StaticFiborialConstructor()
{
$className = "Static Constructor";
echo $className . "\n";
}
# Static Method - Factorial Recursive
public static function FactorialR(int $n)
{
if($n == 1)
return N\BigInteger::$One;
else
return N\BigInteger::Multiply(new N\BigInteger($n), self::FactorialR($n-1));
}
# Static Method - Factorial Imperative
public static function FactorialI(int $n)
{
$res = N\BigInteger::$One;
for ($i = $n; $i >= 1; $i--)
$res = N\BigInteger::Multiply($res, new N\BigInteger($i));
return $res;
}
# Static Method - Fibonacci Recursive
public static function FibonacciR(int $n)
{
if ($n < 2)
return 1;
else
return self::FibonacciR($n - 1) + self::FibonacciR($n - 2);
}
# Static Method - Fibonacci Imperative
public static function FibonacciI(int $n)
{
$pre = 0; $cur = 0; $tmp = 0;
$pre = 1; $cur = 1;
for ($i = 2; $i <= $n; $i++)
{
$tmp = $cur + $pre;
$pre = $cur;
$cur = $tmp;
}
return $cur;
}
# Static Method - Benchmarking Algorithms
public static function BenchmarkAlgorithm(int $algorithm, G\List<:int:> $values)
{
$timer = new D\Stopwatch();
$i = 0;
$testValue = 0;
$facTimeResult = N\BigInteger::$Zero;
$fibTimeResult = 0;
# "Switch" Flow Constrol Statement
switch ($algorithm)
{
case 1:
echo "\nFactorial Imperative:\n";
# "For" Loop Statement
for ($i = 0; $i < $values->Count; $i++)
{
$testValue = $values->get_Item($i);
# Taking Time
$timer->Start();
$facTimeResult = self::FactorialI($testValue);
$timer->Stop();
# Getting Time
echo " ($testValue) = {$timer->Elapsed->ToString()}\n";
}
break;
case 2:
echo "\nFactorial Recursive:\n";
# "While" Loop Statement
while ($i < $values->Count)
{
$testValue = $values->get_Item($i);
# Taking Time
$timer->Start();
$facTimeResult = self::FactorialR($testValue);
$timer->Stop();
# Getting Time
echo " ($testValue) = {$timer->Elapsed->ToString()}\n";
$i++;
}
break;
case 3:
echo "\nFibonacci Imperative:\n";
# "Do-While" Loop Statement
do
{
$testValue = $values->get_Item($i);
# Taking Time
$timer->Start();
$fibTimeResult = self::FibonacciI($testValue);
$timer->Stop();
# Getting Time
echo " ($testValue) = {$timer->Elapsed->ToString()}\n";
$i++;
} while ($i < $values->Count);
break;
case 4:
echo "\nFibonacci Recursive:\n";
# "ForEach" Loop Statement
foreach ($values as $item)
{
$testValue = (int)$item;
# Taking Time
$timer->Start();
$fibTimeResult = self::FibonacciR($testValue);
$timer->Stop();
# Getting Time
echo " ($testValue) = {$timer->Elapsed->ToString()}\n";
}
break;
default:
echo "DONG!\n";
break;
}
}
}
[\Export]
# Instance Class
class InstanceFiborial
{
# Instance Field
private $className;
# Instance Constructor
function __construct()
{
$this->className = "Instance Constructor";
echo $this->className . "\n";
}
# Instance Method - Factorial Recursive
public function FactorialR(int $n)
{
# Calling Static Method
return StaticFiborial::FactorialR($n);
}
# Instance Method - Factorial Imperative
public function FactorialI(int $n)
{
# Calling Static Method
return StaticFiborial::FactorialI($n);
}
# Instance Method - Fibonacci Recursive
public function FibonacciR(int $n)
{
# Calling Static Method
return StaticFiborial::FibonacciR($n);
}
# Instance Method - Fibonacci Imperative
public function FibonacciI(int $n)
{
# Calling Static Method
return StaticFiborial::FibonacciI($n);
}
}
# Console Program
class Program
{
public static function Main()
{
# Static Initializer/Constructor for StaticFiborial Class
# explicitly called somewhere in your code ^_^
StaticFiborial::StaticFiborialConstructor();
echo "\nStatic Class\n";
# Calling Static Class and Methods
# No instantiation needed. Calling method directly from the class
echo "FacImp(5) = " . StaticFiborial::FactorialI(5)->ToString() . "\n";
echo "FacRec(5) = " . StaticFiborial::FactorialR(5)->ToString() . "\n";
echo "FibImp(11)= " . StaticFiborial::FibonacciI(11)->ToString() . "\n";
echo "FibRec(11)= " . StaticFiborial::FibonacciR(11)->ToString() . "\n";
echo "\nInstance Class\n";
# Calling Instance Class and Methods
# Need to instantiate before using. Calling method from instantiated object
$ff = new InstanceFiborial();
echo "FacImp(5) = {$ff->FactorialI(5)->ToString()}\n";
echo "FacRec(5) = {$ff->FactorialR(5)->ToString()}\n";
echo "FibImp(11)= {$ff->FibonacciI(11)->ToString()}\n";
echo "FibRec(11)= {$ff->FibonacciR(11)->ToString()}\n";
# From 5 to 50 by 5
$values = new G\List<:int:>;
for($i = 5; $i <= 50; $i += 5)
$values->Add($i);
# Benchmarking Fibonacci
# 1 = Factorial Imperative
StaticFiborial::BenchmarkAlgorithm(1, $values);
# 2 = Factorial Recursive
StaticFiborial::BenchmarkAlgorithm(2, $values);
# Benchmarking Factorial
# 3 = Fibonacci Imperative
StaticFiborial::BenchmarkAlgorithm(3, $values);
# 4 = Fibonacci Recursive
StaticFiborial::BenchmarkAlgorithm(4, $values);
# Stop and exit
echo "Press any key to exit...";
fgets(STDIN);
return 0;
}
}
?>
And the Output is:
Printing the Factorial and Fibonacci Series
<?php
namespace FiborialSeries;
use System;
use System\Text as T;
use System\Numerics as N;
[\Export]
class Fiborial
{
# Using a StringBuilder as a list of string elements
static function GetFactorialSeries(int $n)
{
# Create the String that will hold the list
$series = new T\StringBuilder();
# We begin by concatenating the number you want to calculate
# in the following format: "!# ="
$series->Append("!");
$series->Append($n);
$series->Append(" = ");
# We iterate backwards through the elements of the series
for ($i = $n; $i <= $n && $i > 0; $i--)
{
# and append it to the list
$series->Append($i);
if ($i > 1)
$series->Append(" * ");
else
$series->Append(" = ");
}
# Get the result from the Factorial Method
# and append it to the end of the list
# $series->Append(self::Factorial($n)->ToString());
# BUT! that throws an exception with big numbers (> fact(30))
# Overflow ex "Value was either too large or too small for a Decimal."
# because I think it is a bug i used an ugly workaround which is
# using the "." in the return.
return $series->ToString() . self::Factorial($n)->ToString();
}
# Using a StringBuilder as a list of string elements
static function GetFibonnaciSeries(int $n)
{
# Create the String that will hold the list
$series = new T\StringBuilder();
# We begin by concatenating the first 3 values which
# are always constant
$series->Append("0, 1, 1");
# Then we calculate the Fibonacci of each element
# and add append it to the list
for ($i = 2; $i <= $n; $i++)
{
if ($i < $n)
$series->Append(", ");
else
$series->Append(" = ");
$series->Append(self::Fibonacci($i));
}
# return the list as a string
return $series->ToString();
}
static function Factorial(int $n)
{
if($n == 1)
return new N\BigInteger(1);
else
return N\BigInteger::Multiply(new N\BigInteger($n), self::Factorial($n - 1));
}
static function Fibonacci(int $n)
{
if ($n < 2)
return 1;
else
return self::Fibonacci($n - 1) + self::Fibonacci($n - 2);
}
}
class Program
{
public static function Main()
{
# Printing Factorial Series
echo "\n";
echo Fiborial::GetFactorialSeries(5) . "\n";
echo Fiborial::GetFactorialSeries(7) . "\n";
echo Fiborial::GetFactorialSeries(9) . "\n";
echo Fiborial::GetFactorialSeries(11) . "\n";
echo Fiborial::GetFactorialSeries(40) . "\n";
# Printing Fibonacci Series
echo "\n";
echo Fiborial::GetFibonnaciSeries(5) . "\n";
echo Fiborial::GetFibonnaciSeries(7) . "\n";
echo Fiborial::GetFibonnaciSeries(9) . "\n";
echo Fiborial::GetFibonnaciSeries(11) . "\n";
echo Fiborial::GetFibonnaciSeries(40) . "\n";
fgets(STDIN);
return 0;
}
}
?>
And the Output is:
Mixing Instance and Static Members in the same Class
Instance classes can contain both, instance and static members such as: fields, properties, constructors, methods, etc.
<?php
namespace FiborialExtras2;
use System;
# Instance Class
[\Export]
class Fiborial
{
# Instance Field
private $instanceCount;
# Static Field
private static $staticCount;
# Instance Read-Only Property/Getter
# Within instance members, you can always use
# the "this" reference pointer to access your (instance) members.
public function getInstanceCount()
{
return $this->instanceCount;
}
# Static Read-Only Property/Getter
# As with Static Methods, you cannot reference your class members
# with the "this" reference pointer since static members are not
# instantiated.
public static function getStaticCount()
{
return $staticCount;
}
# Instance Constructor
public function __construct()
{
$this->instanceCount = 0;
echo "\nInstance Constructor {$this->instanceCount}\n";
}
# Static Constructor
public static function FiborialStaticConstructor()
{
$staticCount = 0;
echo "\nStatic Constructor {$staticCount}\n";
}
# Instance Method
public function Factorial(int $n)
{
$this->instanceCount += 1;
echo "\nFactorial({$n})\n";
}
# Static Method
public static function Fibonacci(int $n)
{
$staticCount += 1;
echo "\nFibonacci({$n})\n";
}
}
class Program
{
public static function Main()
{
# Calling Static Constructor/Initializer and Methods
# No need to instantiate
Fiborial::FiborialStaticConstructor();
Fiborial::Fibonacci(5);
// Calling Instance Constructor and Methods
// Instance required
$fib = new Fiborial();
$fib->Factorial(5);
Fiborial::Fibonacci(15);
$fib->Factorial(5);
// Calling Instance Constructor and Methods
// for a second object
$fib2 = new Fiborial();
$fib2->Factorial(5);
echo "\n";
// Calling Static Property
echo "Static Count = " . Fiborial::getStaticCount() . "\n";
// Calling Instance Property of object 1 and 2
echo "Instance 1 Count = {$fib->getInstanceCount()}\n";
echo "Instance 2 Count = {$fib2->getInstanceCount()}\n";
fgets(STDIN);
return 0;
}
}
?>
And the Output is:
Factorial using System.Int64, System.Double, System.Numerics.BigInteger
The Factorial of numbers over 20 are massive!
For instance: !40 = 815915283247897734345611269596115894272000000000!
Because of this, the previous version of this program was giving the "wrong" result
!40 = -70609262346240000 when using "long" (System.Int64) type, but it was not until I did the Fiborial version in VB.NET that I realized about this faulty code, because instead of giving me a wrong value, VB.NET, JScript.NET, Boo execution thrown an Overflow Exception when using the "Long/long" (System.Int64) type.
My first idea was to use ulong and ULong, but both failed for "big" numbers. I then used Double (double floating point) type and got no more exception/wrong result. The result of the factorial was now correct !40 = 1.1962222086548E+56, but still I wanted to show the Integer value of it, so I did some research and found that there is a new System.Numerics.BigInteger class in the .NET Framework 4.0. Adding the reference to the project and using this new class as the return type of the Factorial methods, I was able to get the result I was expecting.
!40 = 815915283247897734345611269596115894272000000000
What I also found was that using different types change the time the algorithm takes to finish:
System.Int64 < System.Double < System.Numerics.BigInteger
Almost by double!
To illustrate what I just "tried" to say, lets have a look at the following code and the output we get.
<?php
use System\Numerics as N;
use System\Diagnostics as D;
function FactorialInt64(int $n)
{
if ($n == 1)
return 1;
else
return $n * FactorialInt64($n - 1);
}
function FactorialDouble(int $n)
{
if ($n == 1)
return (double)1;
else
return (double)($n * FactorialDouble($n - 1));
}
function FactorialBigInteger(int $n)
{
if($n == 1)
return N\BigInteger::$One;
else
return N\BigInteger::Multiply(new N\BigInteger($n), FactorialBigInteger($n - 1));
}
class Program
{
public static function Main()
{
$timer = new D\Stopwatch();
$facIntResult = 0;
$facDblResult = (double)0;
$facBigResult = N\BigInteger::$Zero;
echo "\nFactorial using Int64\n";
// Benchmark Factorial using Int64
for ($i = 5; $i <= 50; $i += 5)
{
$timer->Start();
$facIntResult = FactorialInt64($i);
$timer->Stop();
echo " ({$i}) = {$timer->Elapsed->ToString()} : {$facIntResult}\n";
}
echo "\nFactorial using Double\n";
// Benchmark Factorial using Double
for ($i = 5; $i <= 50; $i += 5)
{
$timer->Start();
$facDblResult = FactorialDouble($i);
$timer->Stop();
echo " ({$i}) = {$timer->Elapsed->ToString()} : {$facDblResult}\n";
}
echo "\nFactorial using N\BigInteger\n";
// Benchmark Factorial using N\BigInteger
for ($i = 5; $i <= 50; $i += 5)
{
$timer->Start();
$facBigResult = FactorialBigInteger($i);
$timer->Stop();
echo " ({$i}) = {$timer->Elapsed->ToString()} : {$facBigResult->ToString()}\n";
}
fgets(STDIN);
return 0;
}
}
?>
NOTE: you need to manually add a reference to the System.Numerics.dll assembly to your project so you can add it to your code.
And the Output is:
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