= Solution
<Computational complexity theory> studies the resources needed by an <algorithm> as a <function> of input size, after specifying the resource and computational model. For example, <time complexity> may count comparisons, and <space complexity> may count stored words. Worst-case <time complexity> $T(n)$ is the greatest cost among inputs of size $n$; best-case and average costs are different measures.
An <upper bound> guarantees that a cost is no greater than the stated bound. A <lower bound> guarantees that it is no smaller. For a problem, an <algorithm> can establish an <upper bound> on what is achievable, while a problem <lower bound> must apply to every eligible <algorithm> in the chosen model. Bounds need not be tight. Concisely,
$$
\boxed{L(n)\leq T(n)\leq U(n),\quad\text{with the resource and case specified}.}
$$
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