Design an Indexable Deque with O(1) Access
Design a data structure that behaves like a deque (supporting push front, push back, pop front, pop back) but also allows for O(1) access to elements by their logical index. The structure should maintain stable logical indexing even as elements are removed from the front. Assume operations are in-memory and that logical indices refer to insertion positions. The chosen language can provide deque iterators or array-like blocks.
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Core dilemma
Balancing the efficient O(1) amortized time complexity of deque operations (push/pop front/back) with the requirement of O(1) random access by a stable logical index, which typically implies array-like structures with O(1) indexing but potentially slower insertions/deletions at arbitrary positions.
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Design an Indexable Deque with O(1) Access
Design a data structure that behaves like a deque (supporting push front, push back, pop front, pop back) but also allows for O(1) access to elements by their logical index. The structure should maintain stable logical indexing even as elements are removed from the front. Assume operations are in-memory and that logical indices refer to insertion positions. The chosen language can provide deque iterators or array-like blocks.