Which statement describes Big-O worst-case growth?

Which statement describes Big-O worst-case growth?

• A. Best-case growth
• B. Average-case growth
• C. Describes worst-case growth
• D. Describes memory usage

Answer: (C)

Big-O describes how an algorithm’s resource use grows as input size increases, and it specifically captures the worst-case scenario. It provides an upper bound on time or space that holds for all inputs of size n beyond some threshold. This worst-case guarantee is what makes Big-O useful: you know the maximum amount of work the algorithm might do as the problem gets larger, regardless of peculiar inputs. For example, if a piece of code has a loop that runs n times in every case, its running time grows proportionally to n, so we say it’s O(n). If there are two nested loops each depending on n, the worst-case running time grows on the order of n^2, hence O(n^2). Even when some particular inputs cause early exits and the actual running time is smaller, Big-O still describes the upper limit the algorithm won’t exceed as n grows. Describing memory usage is a related idea (space complexity), but the phrase in question points to the general notion of how growth behaves in the worst case, which is exactly what Big-O worst-case growth conveys.

Big-O describes how an algorithm’s resource use grows as input size increases, and it specifically captures the worst-case scenario. It provides an upper bound on time or space that holds for all inputs of size n beyond some threshold. This worst-case guarantee is what makes Big-O useful: you know the maximum amount of work the algorithm might do as the problem gets larger, regardless of peculiar inputs.

For example, if a piece of code has a loop that runs n times in every case, its running time grows proportionally to n, so we say it’s O(n). If there are two nested loops each depending on n, the worst-case running time grows on the order of n^2, hence O(n^2). Even when some particular inputs cause early exits and the actual running time is smaller, Big-O still describes the upper limit the algorithm won’t exceed as n grows.

Describing memory usage is a related idea (space complexity), but the phrase in question points to the general notion of how growth behaves in the worst case, which is exactly what Big-O worst-case growth conveys.