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== Cost models ==

== 成本模型 Cost models ==

Time efficiency estimates depend on what we define to be a step. For the analysis to correspond usefully to the actual execution time, the time required to perform a step must be guaranteed to be bounded above by a constant. One must be careful here; for instance, some analyses count an addition of two numbers as one step. This assumption may not be warranted in certain contexts. For example, if the numbers involved in a computation may be arbitrarily large, the time required by a single addition can no longer be assumed to be constant.

Time efficiency estimates depend on what we define to be a step. For the analysis to correspond usefully to the actual execution time, the time required to perform a step must be guaranteed to be bounded above by a constant. One must be careful here; for instance, some analyses count an addition of two numbers as one step. This assumption may not be warranted in certain contexts. For example, if the numbers involved in a computation may be arbitrarily large, the time required by a single addition can no longer be assumed to be constant.

一个经常被忽略的关键点是，公布的问题的下界通常是给定一个计算模型，这个模型比你在实践中可以使用的操作集更加有限，因此有一些算法比天真地认为可能的要快。

一个经常被忽略的关键点是，公布的问题的下界通常是给定一个计算模型，这个模型比你在实践中可以使用的操作集更加有限，因此有一些算法比天真地认为可能的要快。

==Run-time analysis==

==Run-time analysis==