NuggetSaverLinear.cs

void Main()
{
	var n = new NuggetSaver(7,11);
	(n.BestOrder(20) == (3, 0)).Dump();
	(n.BestOrder(100) == (8, 4)).Dump();
	(n.BestOrder(-20) == (0, 0)).Dump();
	(n.BestOrder(1000000) == (142854, 2)).Dump();
}

class NuggetSaver
{
	public int Size1 { get; private set; }
	public int Size2 { get; private set; }
	
	public NuggetSaver(int size1, int size2)
	{
		Size1 = size1;
		Size2 = size2;
	}

	public (int o1, int o2) BestOrder(int count)
	{
		var check = ReducedWaste(count);
		var total = check.o1 * Size1 + check.o2 * Size2;

		if (total == count || check == (0, 0))
			return check;

		var altTotal1 = (check.o1 - 1) * Size1 + (check.o2 + 1) * Size2;
		var altTotal2 = (check.o1 + 1) * Size1 + (check.o2 - 1) * Size2;

		if (altTotal1 <= altTotal2)
			return (check.o1 - 1, check.o2 + 1);
		else
			return (check.o1 + 1, check.o2 - 1);

	}

	(int o1, int o2) ReducedWaste(int count)
	{
		int o1 = 0;
		int o2 = 0;
		int remaining = count;
		while (remaining > 0)
		{
			var order = LeastWaste(remaining);
			if (order.choice1 == 1)
			{
				o1++;
				remaining -= Size1;
			}
			else
			{
				o2++;
				remaining -= Size2;
			}
		}
		return (o1, o2);
	}

	(int choice1, int choice2) LeastWaste(int count)
	{
		if ((count % Size1) <= (count % Size2))
			return (1, 0);
		return (0, 1);
	}

}