public static ModulusMatrix Identity(int size)
{
ModulusMatrix result = new ModulusMatrix(size, size);
for (int i = 0; i < size; i++)
{
result[i, i] = ModulusNumber.One;
}
return(result);
}
public static ModulusMatrix operator +(ModulusMatrix left, ModulusMatrix right)
{
if ((left._columns != right._columns) || (left._rows != right._rows))
{
throw new Exception("Incompatible matrices");
}
ModulusMatrix result = new ModulusMatrix(left._rows, right._columns);
for (int i = 0; i < left._rows; i++)
{
for (int j = 0; j < left._columns; j++)
{
result._values[i, j] = left[i, j] + right[i, j];
}
}
return(result);
}
public static ModulusMatrix Power(ModulusMatrix matrix, BigInteger power)
{
ModulusMatrix result = ModulusMatrix.Identity(matrix._rows);
byte[] powerBytes = power.ToByteArray();
BitArray powerBitArray = new BitArray(powerBytes);
ModulusMatrix powerMatrix = new ModulusMatrix(matrix._rows, matrix._columns, (ModulusNumber[, ])matrix._values.Clone());
for (int i = 0; i < powerBitArray.Count; i++)
{
if (powerBitArray[i])
{
result *= powerMatrix;
}
powerMatrix *= powerMatrix;
}
return(result);
}
private static ModulusNumber Solve(BigInteger w, int h)
{
int size = h * 2;
ModulusMatrix matrix = new ModulusMatrix(size, size);
ModulusMatrix initial = new ModulusMatrix(size, 1);
ModulusMatrix temp = new ModulusMatrix(size, 1);
// matrix loop
for (int i = 0; i < size; i++)
{
for (int j = 0; j < size; j++)
{
if (j == i)
{
initial[j, 0] = ModulusNumber.One;
}
else
{
initial[j, 0] = ModulusNumber.Zero;
}
temp[j, 0] = ModulusNumber.Zero;
}
// temp loop
for (int j = 0; j < h; j++)
{
ModulusEvenOdd total = new ModulusEvenOdd();
// initial loop
for (int k = 0; k < h; k++)
{
ModulusEvenOdd value = Get(initial, k);
if (k >= j)
{
total += value;
}
else
{
if (((j - k) % 2) == 1)
{
total += value.Swap;
}
else
{
total += value;
}
}
}
Set(temp, j, total);
}
matrix.SetColumn(i, temp.GetColumn(0));
}
for (int i = 0; i < h; i++)
{
if (i % 2 == 0)
{
Set(initial, i, ModulusEvenOdd.OneEven);
}
else
{
Set(initial, i, ModulusEvenOdd.OneOdd);
}
}
ModulusMatrix powerMatrix = ModulusMatrix.Power(matrix, w - 1);
ModulusMatrix result = powerMatrix * initial;
ModulusNumber sum = ModulusNumber.Zero;
for (int i = 0; i < h; i++)
{
sum += result[i * 2 + 1, 0];
}
return(sum);
}
private static void Set(ModulusMatrix values, int index, ModulusEvenOdd value)
{
values[index * 2, 0] = value.Even;
values[index * 2 + 1, 0] = value.Odd;
}
private static ModulusEvenOdd Get(ModulusMatrix values, int index)
{
ModulusEvenOdd result = new ModulusEvenOdd(values[index * 2, 0], values[index * 2 + 1, 0]);
return(result);
}