On-Demand values of Lookup-Tables.

lookuptables

/**
 * This function generates elements of lookup tables. It is assumed that we
 * have two dimensional lookup tables with x and y axis each ranging from 0
 * to n (exclusive). For n, this means there are n^n^n possible
 * permutations. <br />
 * Example table (n = 3, perm = 1)
 * 
 * <pre>
 *        y
 *      0 1 2
 *     ------
 *   0| 0 0 0
 * x 1| 0 0 0
 *   2| 0 0 1
 * </pre>
 * 
 * If this was the first permutation, all values would be zeros. The idea of
 * the algorithm is to look at these tables as a sequence of numbers. The
 * above example would therefore translate to the following sequence:
 * '0000001'. If we now look at all possible permutations of zeros, ones and
 * twos of this sequence, it should be obvious that these are nothing else
 * but the ternary representation of all numbers ranging from 0 to n^n^n.
 * 
 * @param x
 *            index of x axis
 * @param y
 *            index of y axis
 * @param perm
 *            permutation number
 * @param n
 *            number of elements in each table. must be less than 11.
 * @return the element at the specified x and y position of the perm-th
 *         permutation.
 */
static int lookup(int x, int y, int perm, int n) {
	// convert to n-number system
	String repr = Integer.toString(perm, n);
	// LSB is on the right side
	int pos = repr.length() - 1 - (x * n + y);
	// the repr string is only as long as necessary. everything else are
	// zeros
	if (pos < 0) {
		return 0;
	}
	return repr.charAt(pos) - 48;
}