C hack for storing a bit that takes 1 bit space?

Question

I have a long list of numbers between 0 and 67600. Now I want to store them using an array that is 67600 elements long. An element is set to 1 if a number was in the set and it is set to 0 if the number is not in the set. ie. each time I need only 1bit information for storing the presence of a number. Is there any hack in C/C++ that helps me achieve this?

Answer 1

In C++ you can use std::vector<bool> if the size is dynamic (it's a special case of std::vector, see this) otherwise there is std::bitset (prefer std::bitset if possible.) There is also boost::dynamic_bitset if you need to set/change the size at runtime. You can find info on it here, it is pretty cool!

In C (and C++) you can manually implement this with bitwise operators. A good summary of common operations is here. One thing I want to mention is its a good idea to use unsigned integers when you are doing bit operations. << and >> are undefined when shifting negative integers. You will need to allocate arrays of some integral type like uint32_t. If you want to store N bits, it will take N/32 of these uint32_ts. Bit i is stored in the i % 32'th bit of the i / 32'th uint32_t. You may want to use a differently sized integral type depending on your architecture and other constraints. Note: prefer using an existing implementation (e.g. as described in the first paragraph for C++, search Google for C solutions) over rolling your own (unless you specifically want to, in which case I suggest learning more about binary/bit manipulation from elsewhere before tackling this.) This kind of thing has been done to death and there are "good" solutions.

There are a number of tricks that will maybe only consume one bit: e.g. arrays of bitfields (applicable in C as well), but whether less space gets used is up to compiler. See this link.

Please note that whatever you do, you will almost surely never be able to use exactly N bits to store N bits of information - your computer very likely can't allocate less than 8 bits: if you want 7 bits you'll have to waste 1 bit, and if you want 9 you will have to take 16 bits and waste 7 of them. Even if your computer (CPU + RAM etc.) could "operate" on single bits, if you're running in an OS with malloc/new it would not be sane for your allocator to track data to such a small precision due to overhead. That last qualification was pretty silly - you won't find an architecture in use that allows you to operate on less than 8 bits at a time I imagine :)