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What data-structure should I use to create my own “BigInteger” class?
Out of pure interest, I am trying to design a type that can hold an arbitrarily large integer. I want to support four basic operations [+, -, *, /] and optimise for speed of those operations.
I was thinking about some sort of a doubly-linked list and a bit flag to indicate positive or negative value. But I am not really sure how to add, for example, to large numbers of different sizes. Shall I walk to the last element of both numbers and then return back (using the second reverse pointer to the previous element).
123456789 //one large number + 123 //another large number with different size
Providing I can have an arbitrarily large memory, what is the best data structure for this task?
I would appreciate a small hint and any comments on worst-case complexity of the arithmetic operations. Thanks!
Usually one would go for an array/vector in this case, perhaps little-endian (lowest-significant word first). If you implement in-place operations, use a constant factor when growing the array, then amortized complexity for the reallocation remains O(1).
All operations should be doable in O(n) run time where n is the size of the input. EDIT: No, of course, multiplication and division will need more, this answer says it’s at least O(N log N).
Just out of curiosity: Why are you reimplementing the wheel? Find here an implementation in Java. C# has one with .NET 4.0, too. While it might be a good exercise to implement this yourself (I remember myself doing it once), if you just need the functionality then it’s there in many computing environments already.