Running Accumulator: When to Use It

Start with the idea

A problem is a good match for Running Accumulator when it asks for totals, checksums, balances, stream summaries. Here the concrete task is: Return the alternating sum a0 - a1 + a2 - a3 and so on. The visible input [7, 2, 5, 1] is an example, not a definition of the whole problem. Ask what operations the solution must support and what the input guarantees. Ask whether one pass is enough, whether order matters, and whether a later query will need information you already discarded. The right choice follows from those guarantees, not from a familiar noun in the prompt.

The decisive invariant is: Fold a stream into one state such as a sum, product, checksum, or balance. Try to say why it applies to the task without quoting the implementation. Which fact becomes known after one update, and which possible answers remain? A scan turns a sequence into a small piece of state. Say what the state means after the first i elements, before you describe a loop body. If that claim cannot be maintained on a legal input, the pattern is wrong or one of its preconditions is missing. A counterexample is more useful than a vague warning: change one property of the sample, trace the first two steps, and identify the exact claim that fails.

Compare costs before committing. The advertised bound is O(n) time · O(1) extra space; identify the operation responsible for it and the extra memory it needs.