STL deque accessing by index is O(1)?

I found this deque implementation from Wikipedia:

Storing contents in multiple smaller arrays, allocating additional arrays at the beginning or end as needed. Indexing is implemented by keeping a dynamic array containing pointers to each of the smaller arrays.

I guess it answers my question.

The datas in deque are stored by chuncks of fixed size vector, which are

pointered by a map(which is also a chunk of vector, but its size may change)

The main part code of the deque iterator is as below:

/*
buff_size is the length of the chunk
*/
template <class T, size_t buff_size>
struct __deque_iterator{
    typedef __deque_iterator<T, buff_size>              iterator;
    typedef T**                                         map_pointer;

    // pointer to the chunk
    T* cur;       
    T* first;     // the begin of the chunk
    T* last;      // the end of the chunk

    //because the pointer may skip to other chunk
    //so this pointer to the map
    map_pointer node;    // pointer to the map
}

The main part code of the deque is as below:

/*
buff_size is the length of the chunk
*/
template<typename T, size_t buff_size = 0>
class deque{
    public:
        typedef T              value_type;
        typedef T&            reference;
        typedef T*            pointer;
        typedef __deque_iterator<T, buff_size> iterator;

        typedef size_t        size_type;
        typedef ptrdiff_t     difference_type;

    protected:
        typedef pointer*      map_pointer;

        // allocate memory for the chunk 
        typedef allocator<value_type> dataAllocator;

        // allocate memory for map 
        typedef allocator<pointer>    mapAllocator;

    private:
        //data members

        iterator start;
        iterator finish;

        map_pointer map;
        size_type   map_size;
}

Below i will give you the core code of deque, mainly about two parts:

1. iterator

2. How to Random access a deque realize

1. iterator(__deque_iterator)

The main problem of iterator is, when ++, -- iterator, it may skip to other chunk(if it pointer to edge of chunk). For example, there are three data chunks: chunk 1,chunk 2,chunk 3.

The pointer1 pointers to the begin of chunk 2, when operator --pointer it will pointer to the end of chunk 1, so as to the pointer2.

Below I will give the main function of __deque_iterator:

Firstly, skip to any chunk:

void set_node(map_pointer new_node){
    node = new_node;
    first = *new_node;
    last = first + chunk_size();
}

Note that, the chunk_size() function which compute the chunk size, you can think of it returns 8 for simplify here.

operator* get the data in the chunk

reference operator*()const{
    return *cur;
}

operator++, --

// prefix forms of increment

self& operator++(){
    ++cur;
    if (cur == last){      //if it reach the end of the chunk
        set_node(node + 1);//skip to the next chunk
        cur = first;
    }
    return *this;
}

// postfix forms of increment
self operator++(int){
    self tmp = *this;
    ++*this;//invoke prefix ++
    return tmp;
}
self& operator--(){
    if(cur == first){      // if it pointer to the begin of the chunk
        set_node(node - 1);//skip to the prev chunk
        cur = last;
    }
    --cur;
    return *this;
}

self operator--(int){
    self tmp = *this;
    --*this;
    return tmp;
}

iterator skip n steps / random access

self& operator+=(difference_type n){ // n can be postive or negative
    difference_type offset = n + (cur - first);
    if(offset >=0 && offset < difference_type(buffer_size())){
        // in the same chunk
        cur += n;
    }else{//not in the same chunk
        difference_type node_offset;
        if (offset > 0){
            node_offset = offset / difference_type(chunk_size());
        }else{
            node_offset = -((-offset - 1) / difference_type(chunk_size())) - 1 ;
        }
        // skip to the new chunk
        set_node(node + node_offset);
        // set new cur
        cur = first + (offset - node_offset * chunk_size());
    }

    return *this;
}

// skip n steps
self operator+(difference_type n)const{
    self tmp = *this;
    return tmp+= n; //reuse  operator +=
}

self& operator-=(difference_type n){
    return *this += -n; //reuse operator +=
}

self operator-(difference_type n)const{
    self tmp = *this;
    return tmp -= n; //reuse operator +=
}

// random access (iterator can skip n steps)
// invoke operator + ,operator *
reference operator[](difference_type n)const{
    return *(*this + n);
}

2. Random access deque elements

common function of deque

iterator begin(){return start;}
iterator end(){return finish;}

reference front(){
    //invoke __deque_iterator operator*
    // return start's member *cur
    return *start;
}

reference back(){
    // cna't use *finish
    iterator tmp = finish;
    --tmp; 
    return *tmp; //return finish's  *cur
}

reference operator[](size_type n){
    //random access, use __deque_iterator operator[]
    return start[n];
}

You also see this question which give the main code of deque

https://stackoverflow.com/a/50959796/6329006