A deque supports insertion and removal at both the front and back, often using a circular array or linked blocks.
How to reason about it
Start by identifying the state the method maintains and the operation that changes it. Then trace one small input by hand. This separates the invariant that makes the method correct from implementation details such as arrays, pointers, counters, or protocol messages.
Worked example
A sliding-window algorithm can add a new rightmost value and remove an expired leftmost value without shifting the rest.
Write down the state before and after each step. For a larger input, repeat the same transition rather than guessing from the final output. That habit makes edge cases visible and gives you a concrete basis for testing.
Trade-offs and common mistakes
A deque is not automatically a priority queue; it does not order items by their values.'
Choose this technique when its assumptions match the problem. State those assumptions explicitly, test an empty or boundary input, and compare the cost of the operation you perform most often with the memory or setup cost it introduces.
Takeaway
Deques: Efficient Operations at Both Ends becomes easier to use once its invariant, input assumptions, and failure cases are clear. A small worked example is a useful first test; measurements and proofs should follow when the system grows.