This paper abstracts three practical maximum problems from the real world and gives their formal mathematical descriptions. Their algorithms and complexity are fully discussed.

本文从现实世界中抽象出三类极大问题，给出了形式化的数学描述，并详细讨论了各自的算法和复杂度。

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At the theoretical end, this focus manifests itself in complexity theory, which groups algorithms according to their time and space requirements for execution.

除理论之外，这种专注表现在本身复杂性的理论，它根据它们运行的时间和空间需求来组织算法。

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In the same way as other algorithms, the use of efficient board representations is a tradeoff between complexity, speed, and space requirements.

而在使用相同方法的其他算法中，采用有效的棋盘表现方法是一个介于复杂性，速度和空间需求之间的权衡。

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So in fact, over the next thirty or forty minutes we're going to show you a set of examples of sort of canonical algorithms, and the different classes of complexity.

在接下来的三四十分钟里面,我们将要讲一系列的,权威算法，以及不同种类的复杂度问题。

麻省理工公开课 - 计算机科学及编程导论课程节选

I want you to recognize classes of algorithms and match what you see in the performance of the algorithm to the complexity of that algorithm. All right?

让我再试一次这么说,我期望大家能通过,算法的复杂度,来看到算法的性能？

麻省理工公开课 - 计算机科学及编程导论课程节选

But I want you to take away from this how we reason about the complexity of these algorithms. And I'll remind you, we said we're going to mostly talk about time.

但是我想你们理解我们,是怎么推出这些问题的复杂度的,提醒大家，我说过了我们主要讨论时间问题。

麻省理工公开课 - 计算机科学及编程导论课程节选