From 9dd9d918bfbbb4db63c51b892bdce71bf2bd94ab Mon Sep 17 00:00:00 2001
From: FuryFire <furyfire@users.noreply.github.com>
Date: Tue, 6 Mar 2012 14:21:54 +0100
Subject: [PATCH] Solved a few more problems 003: php 005: php, ruby 006: php,
 ruby, c

---
 ProjectEuler/003/desc.yml  | 15 +++++++++++++++
 ProjectEuler/003/solve.php | 33 +++++++++++++++++++++++++++++++++
 ProjectEuler/005/desc.yml  | 17 +++++++++++++++++
 ProjectEuler/005/solve.php | 12 ++++++++++++
 ProjectEuler/005/solve.rb  | 10 ++++++++++
 ProjectEuler/006/desc.yml  | 24 ++++++++++++++++++++++++
 ProjectEuler/006/solve.c   | 19 +++++++++++++++++++
 ProjectEuler/006/solve.php |  9 +++++++++
 ProjectEuler/006/solve.rb  |  7 +++++++
 9 files changed, 146 insertions(+)
 create mode 100644 ProjectEuler/003/desc.yml
 create mode 100644 ProjectEuler/003/solve.php
 create mode 100644 ProjectEuler/005/desc.yml
 create mode 100644 ProjectEuler/005/solve.php
 create mode 100644 ProjectEuler/005/solve.rb
 create mode 100644 ProjectEuler/006/desc.yml
 create mode 100644 ProjectEuler/006/solve.c
 create mode 100644 ProjectEuler/006/solve.php
 create mode 100644 ProjectEuler/006/solve.rb

diff --git a/ProjectEuler/003/desc.yml b/ProjectEuler/003/desc.yml
new file mode 100644
index 0000000..5f9d3e0
--- /dev/null
+++ b/ProjectEuler/003/desc.yml
@@ -0,0 +1,15 @@
+title: Find the largest prime factor of a composite number.
+url: http://projecteuler.net/problem=3
+
+desc: |
+  The prime factors of 13195 are 5, 7, 13 and 29.
+  What is the largest prime factor of the number 600851475143 ?
+  
+solution: |
+  Use factorization to find the largest prime factor
+
+solutions:
+  solve.php:
+    desc: Basic solution
+    language: php
+
diff --git a/ProjectEuler/003/solve.php b/ProjectEuler/003/solve.php
new file mode 100644
index 0000000..aca79fa
--- /dev/null
+++ b/ProjectEuler/003/solve.php
@@ -0,0 +1,33 @@
+<?php
+$number = 600851475143;
+
+echo max(factorize($number));
+
+/**
+ * Returns a sorted array of the prime factorization of $num
+ * @staticvar array $aFactors
+ * @param type int Number to factorize
+ * @return type array Prime factors
+ */
+function factorize($num) {
+	// Returns a sorted array of the prime factorization of $num 
+	// Caches prior results.  Returns empty array for |$num|<2 
+	// eg. factorize(360) => [5, 3, 3, 2, 2, 2] 
+	static $aFactors = array();
+	if (2 > $num = abs($num))
+		return array();  // negatives, 1, 0 
+
+	if ($aFactors[$key = "x$num"]) {	 // handles doubles 
+		// Been there, done that 
+		if (($factor = $aFactors[$key]) == $num)
+			return array($num);
+		return array_merge(factorize($num / $factor), array($factor));
+	}
+
+	// Find a smallest factor 
+	for ($sqrt = sqrt($num), $factor = 2; $factor <= $sqrt; ++$factor)
+		if (floor($num / $factor) == $num / $factor)
+			return array_merge(factorize($num / $factor), array($aFactors[$key] = $factor));
+
+	return (array($aFactors[$key] = $num));
+}
diff --git a/ProjectEuler/005/desc.yml b/ProjectEuler/005/desc.yml
new file mode 100644
index 0000000..3fb5d6a
--- /dev/null
+++ b/ProjectEuler/005/desc.yml
@@ -0,0 +1,17 @@
+title: What is the smallest number divisible by each of the numbers 1 to 20?
+url: http://projecteuler.net/problem=5
+
+desc: |
+  2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder.
+  What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
+  
+solution: |
+  See code
+
+solutions:
+  solve.php:
+    desc: Basic solution
+    language: php
+  solve.rb:
+    desc: Basic solution in Ruby
+    language: ruby
diff --git a/ProjectEuler/005/solve.php b/ProjectEuler/005/solve.php
new file mode 100644
index 0000000..388c715
--- /dev/null
+++ b/ProjectEuler/005/solve.php
@@ -0,0 +1,12 @@
+<?php
+for($i=20;true;$i+=20) {
+	$div = 19;
+
+	while(!($i % $div)) {
+		$div--;
+		if($div == 0) {
+			echo $i;
+			die;
+		}
+	}
+}
diff --git a/ProjectEuler/005/solve.rb b/ProjectEuler/005/solve.rb
new file mode 100644
index 0000000..17651b4
--- /dev/null
+++ b/ProjectEuler/005/solve.rb
@@ -0,0 +1,10 @@
+max = 0;
+(100..1000).each do |num1|
+	(100..1000).each do |num2|
+		sum = num1 * num2
+		if( sum > max and sum.to_s.reverse  == sum.to_s) 
+			max = sum
+		end
+	end
+end
+print max
\ No newline at end of file
diff --git a/ProjectEuler/006/desc.yml b/ProjectEuler/006/desc.yml
new file mode 100644
index 0000000..77ebe89
--- /dev/null
+++ b/ProjectEuler/006/desc.yml
@@ -0,0 +1,24 @@
+title: What is the smallest number divisible by each of the numbers 1 to 20?
+url: http://projecteuler.net/problem=6
+
+desc: |
+  The sum of the squares of the first ten natural numbers is,
+  1^2 + 2^2 + ... + 10^2 = 385
+  The square of the sum of the first ten natural numbers is,
+  (1 + 2 + ... + 10)^2 = 55^2 = 3025
+  Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025  385 = 2640.
+  Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.
+  
+solution: |
+  See code
+
+solutions:
+  solve.php:
+    desc: Basic solution
+    language: php
+  solve.rb:
+    desc: Basic Ruby solution
+    language: ruby
+  solve.rb
+    desc: ANSI C solution (Tested with TCC)
+    language: c
\ No newline at end of file
diff --git a/ProjectEuler/006/solve.c b/ProjectEuler/006/solve.c
new file mode 100644
index 0000000..3f510a4
--- /dev/null
+++ b/ProjectEuler/006/solve.c
@@ -0,0 +1,19 @@
+#include <stdio.h>
+#include <math.h>
+
+int main( )
+{
+	int num;
+	int result;
+	
+	int square = 0;
+	int sum = 0;
+	
+	for(num=1; num<=100; num++) {
+		square += pow(num,2);
+		sum += num;
+
+	}
+	result = pow(sum,2) - square;
+	printf("%d", result);
+}
\ No newline at end of file
diff --git a/ProjectEuler/006/solve.php b/ProjectEuler/006/solve.php
new file mode 100644
index 0000000..a347e14
--- /dev/null
+++ b/ProjectEuler/006/solve.php
@@ -0,0 +1,9 @@
+<?php
+$square =0;
+$sum =0;
+for($num=1;$num<101;$num++) {
+	$square += pow($num,2);
+	$sum += $num;
+
+}
+echo pow($sum,2) - $square;
\ No newline at end of file
diff --git a/ProjectEuler/006/solve.rb b/ProjectEuler/006/solve.rb
new file mode 100644
index 0000000..1d6ffaa
--- /dev/null
+++ b/ProjectEuler/006/solve.rb
@@ -0,0 +1,7 @@
+square = 0
+sum = 0
+(1..100).each do |num| 
+	square += num**2;
+	sum += num;
+end
+puts sum**2 - square;
\ No newline at end of file