在C ++中复制变量的复杂性是什么

Question

A friend of mine said that bitmasks are better than bitsets because it takes O(N) time to copy a bitset whereas only O(1) time to copy a bitmask, making it far faster for applications such as in Dynamic Programming. So I was wondering is it the same for all other data types?

For eg what would be the complexity of this block of code?

vector <int> vec1 = {1,2,3,4,5,6,7,8,9,10};
vector <int> vec2 = vec1;

If it is O(N), why is it so? Shouldn't it be O(1) just like doing something like

int x = 530210;
int y = x;

would be?

Answer 1

You have vec1 which is a std::vector<T> represented by this truck with a black-container attached to its trailer.

(source: bigcommerce.com)

Now, there are millions of papers in its black-container (by black-container , std::vector<T> 's memory for the elements). Now, you want to photocopy the papers into another similar vehicle, vec2 . How best can you do it? What is the photo- copy complexity? It is going to be O(Number of papers)

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Now, assuming you want to move the contents... All std::vector needs to do is to detach its black-container from the truck, and attach it into another truck's... That makes move complexity of the container to be O(1)

Answer 2

To understand the complexity of an operation, you first have to define your model of computation. In particular, you have to define what operations are O(1) and what operations you consider free.

For example, if you are looking at programs needing a lot of hard disk access, you would only consider reading a block from disk as one operation and memory access as free.

In the example of bitmasks and bitssets, you are probably counting memory block copy operations. Then copying a bit mask that fits into one memory block costs only one memory copy. However, copying bitmasks is still O(N) in this model because a large bitmask will span many memory blocks. More precisely, if b is the number of bits in one block of memory and N the number of bits in the bitmask, then you need ceil(N/b) memory block copy operations to copy the bitmask.

Answer 3

Copying a vector of length N can be measured in several ways:

• O(1) vector copy operations
• O(N) element copy operations
• O(NT) units of measure, if the element copy operation is O(T)

Incidentally, your friend is wrong about bitset , or you misunderstood. The advantage of bitset is that the data structure is optimized to take advantage of a low level form of parallel execution that can be done by a single thread — ie 64-bit integer operations can be used to work on 64 different bits simultaneously.