Final answer:
The statement is false; average case complexity is important but should not be the only factor in deciding which algorithm to use. A comprehensive understanding of best, average, and worst-case complexities is crucial for algorithm selection.
Step-by-step explanation:
The statement that you should not rely on average case complexity when deciding which algorithm to use is false. Average case complexity refers to how an algorithm performs on average, considering a distribution of different inputs. While it's important to consider the worst-case complexity to ensure that an algorithm won't perform unacceptably slow in any situation, the average case gives a more realistic expectation of performance in everyday use.
However, relying solely on average case complexity is not recommended. It is essential to consider the specific context in which the algorithm will run, including the distribution of inputs that the algorithm will encounter, and any performance constraints. Understanding the best, average, and worst-case complexities offers a comprehensive understanding of an algorithm's performance.
For many practical decisions, the average case is relevant as algorithms will often run on a predictable set of inputs. But always keep in mind that unexpected inputs or data distributions can adversely affect performance.