Euler 24 solution

euler24.js

#!/usr/local/bin/node

// basic problem setup
// the answer we want for the millionth iteration is 2783915460

var iteration = 999999;
var size = 2; 

// figure out the size of the largest factorial smaller than our target iteration
var tempi = iteration;
while (tempi/size > 1) {
	size++;
	tempi = tempi/size; 
}

// the arrays we'll use
var permutation = new Array();
var answer = new Array();
var f = new Array();

for (i=0; i <= size; i++) {
	permutation[i] = i;
}

// I wrote a slightly slower factorial function, I took this one from http://stackoverflow.com/questions/3959211/fast-factorial-function-in-javascript
function factorial(n) {
	if (n<=1) { return 1; }
	else if (f[n]>0) { return f[n]; }
	else { return f[n]=factorial(n-1)*n; }
}

// pull out the next value for the iterator by taking the floor of the divisor of the remainder and the next smallest factorial
function findTumbler(rem, b) {
	var f = Math.floor(rem/factorial(b));	

	if (rem == 0) {
		// fill in the rest of the answers array, we're done!
		l = permutation.length;
		for (j=0; j <= l; j++) {
			answer[size-b+j] = permutation.splice(0,1); 
		}
	} else {
		answer[size-b] = permutation.splice(f,1);
		findTumbler(rem % factorial(b), b-1);
	}
}

findTumbler(iteration, size);
console.log ("final answer:",  answer.join(''));