Given an integer array of size $N$, we want to check if the array is sorted (in either ascending or descending order). An algorithm solves this problem by making a single pass through the array and comparing each element of the array only with its adjacent elements. The worst-case time complexity of this algorithm is

To determine whether an array of size $N$ is sorted, a single-pass algorithm compares each element with its adjacent element.

• In the worst case (e.g., when the array is sorted or the unsorted order is detected at the very last pair), the algorithm makes $N - 1$ comparisons.

• Thus, the worst-case running time is $T_{\text{worst}}(N) = cN + d = \Theta(N)$ for some constants $c > 0$ and $d$.

• By definition of asymptotic notations, any function that is $\Theta(N)$ is both $\text{O}(N)$ (asymptotically upper-bounded by $N$) and $\Omega(N)$ (asymptotically lower-bounded by $N$).

Therefore, the worst-case time complexity is both $\text{O}(N)$ and $\Omega(N)$, corresponding to option (A).