问题
Does anybody know of a way I can calculate very large integers in c#
I am trying to calculate the factorial of numbers e.g.
5! = 5*4*3*2*1 = 120
with small numbers this is not a problem but trying to calculate the factorial of the bigest value of a unsigned int which is 4,294,967,295 it doesn't seem possible.
I have looked into the BigInteger class but it doesn't seem to do what I need
any help would be greatly appreciated
回答1:
4294967295! = 10^(10^10.597) ~ 10^(40000000000) This value requires about 40 Gb of RAM to store, even if you will find any BigInteger implementation for C#!
P.S. Well, with optimized storing, let's say 9 digits in 4 bytes, it will take ~18 Gb of RAM.
回答2:
To calculate the factorial of uint.MaxValue you'd need a lot of storage.
For example, the Wikipedia article as 8.2639316883... × 10^5,565,708. You're going to gain information like crazy.
I strongly suspect you're not going find any way of calculating it on a sane computer in a sane amount of time. Why do you need this value? Would Stirling's approximation be close enough?
回答3:
Firstly, it's worth pointing out that the factorial of uint.MaxValue is astronomically large. I'm not able to find a good estimate of the order of magnitude of its factorial, but its bit representation will probably occupy a high percentage of a standard RAM, if not well exceed.
A BigInteger class seems to be what you want, providing you only want to go up to around 1,000,000 or so (very roughly). After that, time and memory become very prohibitive. In current (stable) versions of .NET, up to 3.5, you have to go with a custom implementation. This one on the CodeProject seems to be highly rated. If you happen to be developing for .NET 4.0, the Microsoft team have finally gotten around to including a BigInteger class in the System.Numerics namespace of the BCL. Unlike some BigInteger implementations, the one existing in .NET 4.0 doesn't have a built-in factorial method (I'm not sure about the CodeProject one), but it should be trivial to implement one - an extension method would be a nice way.
Since you seem to think you don't want to use a BigInteger type, it would be helpful if you could verify that it's not what you want having read my reply, and then explain precisely why it doesn't suit your purposes.
回答4:
Why do you think that you need to calculate those factorials? It's not practiacally useful for anything to do the actual calculations.
Just the result of calculating factorial of (2^32-1) would take up a lot of space, approximately 16 GB.
The calculation itself will of course take a lot of time. If you build the program so that you can transfer the calculation process to faster hardware as it is invented, you should be able to get the result within your lifetime.
If it's something like an Euler problem that you are trying to solve, consider that a lot of solutions are found by elliminating what it is that you actually don't have to calculate in order to get the answer.
回答5:
Here . The fastest one, straight from the Factorial Man - Peter Luschny.
回答6:
You can use the BigInteger class from the J# libraries for now. Here's an article on how. It makes deployment harder because you have to send out the J# redistributable. You can also consider going to VS2010 beta as Framework 4.0 will have BigInteger.
回答7:
In case you have J# redist installed, an alternative way would be using java.math.BigInteger by adding a reference to the vjslib assembly.
回答8:
Try to use an array for this task. You could use as long integers as you have free memory space. Every member of array repsesents one decimal digit. The only you need is to implement multipication.
回答9:
If you are doing calculations with factorials like combinations for example you rarely need to multiply all the way down to 1 (eg. 98 * 98 * 97 since everything else cancels out).
来源：https://stackoverflow.com/questions/930611/working-with-very-large-integers-in-c-sharp