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The challenge in computer science is not just to solve problems, but to solve them in a way that is both efficient and elegant.

計(jì)算機(jī)科學(xué)中的挑戰(zhàn)不僅僅是解決問(wèn)題，而是以一種既高效又優(yōu)雅的方式解決問(wèn)題。

The intersection of mathematics and computer science is where some of the most exciting discoveries are made.

數(shù)學(xué)和計(jì)算機(jī)科學(xué)的交叉點(diǎn)是一些最激動(dòng)人心的發(fā)現(xiàn)產(chǎn)生的地方。

The development of efficient algorithms is not just a theoretical exercise; it has practical implications for the way we live and work.

高效算法的開(kāi)發(fā)不僅僅是一個(gè)理論練習(xí)；它對(duì)我們的生活方式和工作方式有實(shí)際影響。

The key to solving complex problems is often to find the right abstraction that simplifies the problem without losing its essential features.

解決復(fù)雜問(wèn)題的關(guān)鍵通常是找到正確的抽象，這種抽象可以在不丟失問(wèn)題本質(zhì)特征的情況下簡(jiǎn)化問(wèn)題。

The study of automata and formal languages is fundamental to understanding the limits of computation.

自動(dòng)機(jī)和形式語(yǔ)言的研究對(duì)于理解計(jì)算的極限是基礎(chǔ)性的。

The power of randomness in algorithms is that it can help us find solutions that are difficult to discover through deterministic methods.

算法中隨機(jī)性的力量在于它可以幫助我們找到通過(guò)確定性方法難以發(fā)現(xiàn)的解決方案。

In computer science, we often deal with problems that are too complex to solve directly, so we break them down into smaller, more manageable parts.

在計(jì)算機(jī)科學(xué)中，我們經(jīng)常處理那些過(guò)于復(fù)雜而無(wú)法直接解決的問(wèn)題，因此我們將它們分解成更小、更易管理的部分。

The beauty of mathematics is that it allows us to abstract away from the physical world and focus on the underlying principles.

數(shù)學(xué)的美在于它允許我們從物理世界中抽象出來(lái)，專(zhuān)注于基本原理。

A good algorithm is like a sharp knife—it does exactly what it is supposed to do with a minimum of effort.

一個(gè)好的算法就像一把鋒利的刀——它以最小的努力準(zhǔn)確地完成它應(yīng)該做的事情。

The concept of nondeterminism in computation is one of the most important ideas in computer science.

非確定性計(jì)算的概念是計(jì)算機(jī)科學(xué)中最重要的思想之一。