What data structure, exactly, are deques in C++?

Question

Is there a specific data structure that a deque in the C++ STL is supposed to implement, or is a deque just this vague notion of an array growable from both the front and th

Answer 1

This is an answer to user gravity's challenge to comment on the 2-array-solution.

• Some details are discussed here
• A suggestion for improvement is given

Discussion of details: The user "gravity" has already given a very neat summary. "gravity" also challenged us to comment on the suggestion of balancing the number of elements between two arrays in order to achieve O(1) worst case (instead of average case) runtime. Well, the solution works efficiently if both arrays are ringbuffers, and it appears to me that it is sufficient to split the deque into two segments, balanced as suggested. I also think that for practical purposes the standard STL implementation is at least good enough, but under realtime requirements and with a properly tuned memory management one might consider using this balancing technique. There is also a different implementation given by Eric Demaine in an older Dr.Dobbs article, with similar worst case runtime.

Balancing the load of both buffers requires to move between 0 or 3 elements, depending on the situation. For instance, a pushFront(x) must, if we keep the front segment in the primary array, move the last 3 elements from the primary ring to the auxiliary ring in order to keep the required balance. A pushBack(x) at the rear must get hold of the load difference and then decide when it is time to move one element from the primary to the auxiliary array.

Suggestion for improvement: There is less work and bookkeeping to do if front and rear are both stored in the auxiliary ring. This can be achieved by cutting the deque into three segments q1,q2,q3, arranged in the following manner: The front part q1 is in the auxiliary ring (the doubled-sized one) and may start at any offset from which the elements are arranged clockwise in subsequent order. The number of elements in q1 are exactly half of all elements stored in the auxiliary ring. The rear part q3 is also in the auxilary ring, located exactly opposite to part q1 in the auxilary ring, also clockwise in subsequent order. This invariant has to be kept between all deque operations. Only the middle part q2 is located (clockwise in subsequent order) in the primary ring.

Now, each operation will either move exactly one element, or allocate a new empty ringbuffer when either one gets empty. For instance, a pushFront(x) stores x before q1 in the auxilary ring. In order to keep the invariant, we move the last element from q2 to the front of the rear q3. So both, q1 and q3 get an additional element at their fronts and thus stay opposite to each other. PopFront() works the other way round, and the rear operations work the same way. The primary ring (same as the middle part q2) goes empty exactly when q1 and q3 touch each other and form a full circle of subsequent Elements within the auxiliary ring. Also, when the deque shrinks, q1,q3 will go empty exactly when q2 forms a proper circle in the primary ring.