The problem reduces to a classic selection‑and‑aggregation task: from an input array we must identify every element that satisfies a simple predicate (value ≥ K) and accumulate their sum. In algorithmic terms this is a linear‑time filter‑reduce operation, which can be expressed as a single pass over the data. The naïve mindset might suggest building auxiliary structures—such as sorting the array or using a priority queue—to “prepare” the data, but those approaches inflate the time complexity to O(N log N) or worse, which is unnecessary when the predicate is monotonic and does not depend on relative ordering.

Backtracking, as a paradigm, shines when the solution space branches exponentially and we need to prune infeasible paths. Here, however, the decision at each index is binary (include or skip) but the inclusion rule is deterministic: include if the element meets the threshold. Consequently, the backtracking tree collapses into a single deterministic path, making a full recursive exploration wasteful. The optimal paradigm is therefore a greedy linear scan that evaluates the predicate on‑the‑fly and updates a running total, guaranteeing O(N) time and O(1) auxiliary space.

Why the optimal solution matters in practice is twofold: first, large‑scale telemetry streams (e.g., payload metrics from distributed services) can contain millions of entries, and any super‑linear overhead quickly becomes a bottleneck. Second, the simplicity of the linear scan reduces the risk of bugs and makes the code cache‑friendly, which is crucial for high‑throughput systems where latency budgets are tight.