ProjectEuler
My Project Euler solutions
Motivations
Although Project Euler clearly states that it would rather not have mathematicians share its answers:
Please do not deprive others of going through the same process [of solving the question] by publishing your solution outside of Project Euler.
I have decided to publish mine. These are published only in an educational light, and in a less convenient way to get the answer than some other math blogs, so I deem it alright. Please do not simply copy these answers; if you wish to view the source codes, use it solely for enlightenment on my solutions.
Anatomy of a Solution Page
The template that I am using for each solution HTML file is as follows. It includes a stylesheet and sufficient scripts. Here is an example: project euler question 65.
<!DOCTYPE html>
<html>
<body onload="links('Convergents of e', '65', 'sum')">
<script src="res/bignumber.min.js"></script>
<script src="res/XBigFraction.js"></script>
<script id="script">// javascript
var t1 = performance.now();
BigNumber.config({EXPONENTIAL_AT:500});
for(var i = Math.floor(100/3), e = new XBigFraction(0, 1); i > 0; e = new XBigFraction(1,1).divide(new XBigFraction(1,1).add(new XBigFraction(1,1).divide(new XBigFraction(2*i, 1).add(new XBigFraction(1,1).divide(new XBigFraction(1,1).add(e)).reduce())).reduce())).reduce(), i--);
for(var i = 0, sum = 0, numerator = e.add(new XBigFraction(2, 1)).numerator.toString().split(""); i < numerator.length; sum += parseInt(numerator[i]), i++);
var t2 = performance.now();
</script>
~Finds the numerator of the (simplified) 100th convergent of <code><em>e</em></code> (using the formula <code><em>e</em> = [2; 1,2,1, 1,4,1, 1,6,1 , ... , 1,2k,1, ...]</code>)~
#Uses my new library <a href="res/XBigFraction.js">XBigFraction.js</a>. It can handle large fractions (needs to include <a href="res/bignumber.min.js">bignumber.min.js</a> first, however). I also made a simpler version at <a href="res/XFraction.js">XFraction.js</a>.#
<script src="res/euler.js"></script>
</body>
</html><body onload="links('Convergents of e', '65', 'sum')">Title, ID, answer<script src="{SCRIPT_SRC}"></script>Dependencies<script id="script"> ... </script>Main script to run// javascriptLanguage of script (as of now, only JS)~Finds the numerator ... ~Description#Uses my new ... #Note (can have multiple)<script src="res/euler.js"></script>Formatting script
Where's the head? Where are the styles?
The <head>, including styles, are automatically generated by the euler.js script.
Other Notes
- I include my library,
xmath.js, on many of these questions. - When files are given by Project Euler in its questions to analyze or parse, I often used a modified form, either placed directly in the HTML file or in a separate file that is retrieved using an AJAX GET request (performed with a synchronous jQuery
$.get()function). Usually, it is formatted to be a (valid) JSON file.