Solved ProjectEuler/015: php, ruby

ProjectEuler/015/desc.yml

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+title: Find the longest sequence using a starting number under one million.	
+url: http://projecteuler.net/problem=15
+
+desc: |
+  Starting in the top left corner of a 22 grid, there are 6 routes (without backtracking) to the bottom right corner.
+  How many routes are there through a 2020 grid?
+  
+solution: |
+  (2n)!/n!^2 - Where n is the size of the grid -
+  
+todo: Find a more "programmable way" instead of this cheating mathsolution
+
+solutions:
+  solve.php:
+    desc: Using BCMath to cope with large numbers
+    language: php
+  solve.rb:
+    desc: Basic solution
+    language: ruby

ProjectEuler/015/solve.php

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+<?php
+define('GRID_SIZE',20);
+function factorial($num) {
+	if($num == 0) 
+		return 1;
+	else 
+		return bcmul($num,factorial(bcsub($num,1)));
+}
+
+echo bcdiv(factorial(2* GRID_SIZE),bcpow(factorial( GRID_SIZE),2));
+

ProjectEuler/015/solve.rb

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+GRID_SIZE = 20
+
+def factorial(num) 
+	if(num == 0) 
+		return 1
+	else 
+		return num * factorial(num - 1)
+	end
+end
+
+puts factorial(2 * GRID_SIZE) / factorial(GRID_SIZE) ** 2