Use deque if you need efficient insertion/removal at the beginning and end of the sequence and random access; use list if you need efficient insertion anywhere, at the sacrifice of random access. Iterators and references to list elements are very stable under almost any mutation of the container, while deque has very peculiar iterator and reference invalidation rules (so check them out carefully).
Deque and vector provide random access, list provides only linear accesses. So if you need to be able to do containeri, that rules out list. On the other hand, you can insert and remove items anywhere in a list efficiently, and operations in the middle of vector and deque are slow.
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