Cartesian product subset returning set of mostly 0

Question

I'm trying to calculate

If we calculated every possible combination of numbers from 0 to (c-1)
with a length of x
what set would occur at point i

For example:

c = 4
x = 4
i = 3

Would yield:

[0000]
[0001]
[0002]
[0003] <- i
[0010]
....
[3333]

This is very nearly the same problem as in the related question Logic to select a specific set from Cartesian set. However, because x and i are large enough to require the use of BigInteger objects, the code has to be changed to return a List, and take an int, instead of a string array:

    int PossibleNumbers;

    public List<int> Get(BigInteger Address)
    {
        List<int> values = new List<int>();
        BigInteger sizes = new BigInteger(1);

        for (int j = 0; j < PixelArrayLength; j++)
        {
            BigInteger index = BigInteger.Divide(Address, sizes);
            index = (index % PossibleNumbers);

            values.Add((int)index);

            sizes *= PossibleNumbers;
        }

        return values;
    }

This seems to behave as I'd expect, however, when I start using values like this:

c = 66000
x = 950000
i = (66000^950000)/2

So here, I'm looking for the ith value in the cartesian set of 0 to (c-1) of length 950000, or put another way, the halfway point.

At this point, I just get a list of zeroes returned. How can I solve this problem?

Notes: It's quite a specific problem, and I apologise for the wall-of-text, I do hope it's not too much, I was just hoping to properly explain what I meant. Thanks to you all!

Edit: Here are some more examples: http://pastebin.com/zmSDQEGC

Answer 1

The first expression of the problem boils down to "write 3 as a 4-digit base-4 number". So, if the problem is "write i as an x-digit base-c number", or, in this case, "write (66000^950000)/2 as a 950000-digit base 66000 number", then does that make it easier?

If you're specifically looking for the halfway point of the cartesian product, it's not so hard. If you assume that c is even, then the most significant digit is c / 2, and the rest of the digits are zero. If your return value is all zeros, then you may have an off-by-one error, or the like, since actually only one digit is incorrect.

Answer 2

Here is a generic base converter... it takes a decimal for the base10 value to convert into your newBase and returns an array of int's. If you need a BigInteger this method works perfectly well with just changing the base10Value to BigInteger.

EDIT: Converted method to BigInteger since that's what you need.

EDIT 2: Thanks phoog for pointing out BigInteger is base2 so changing the method signature.

public static int[] ConvertToBase(BigInteger value, int newBase, int length)
{
    var result = new Stack<int>();

    while (value > 0)
    {
        result.Push((int)(value % newBase));
        if (value < newBase)
            value = 0;
        else
            value = value / newBase;
    }

    for (var i = result.Count; i < length; i++)
        result.Push(0);

    return result.ToArray();
}

usage...

int[] a = ConvertToBase(13, 4, 4) = [0,0,3,1]
int[] b = ConvertToBase(0, 4, 4) = [0,0,3,1]
int[] c = ConvertToBase(1234, 12, 4) = [0,8,6,10]

However the probelm you specifically state is a bit large to test it on. :)

Just calculating 66000 ^ 950000 / 2 is a good bit of work as Phoog mentioned. Unless of course you meant ^ to be the XOR operator. In which case it's quite fast.

EDIT: From the comments... The largest base10 number that can be represented given a particular newBase and length is...

var largestBase10 = BigInteger.Pow(newBase, length)-1;