V2EX exponential time

Exponential Time

定义 Definition

exponential time(指数时间)”指算法的运行时间随输入规模 \(n\) 按指数级增长,常见表示为 \(O(2^n)\)、\(O(c^n)\)(\(c>1\))。这类算法在 \(n\) 稍大时就会变得非常慢,通常被认为在计算上“不够可行/难以处理”(intractable)。除算法复杂度外,也可泛指“耗时呈指数式上升”的过程。

发音 Pronunciation (IPA)

/ekspnenl tam/

例句 Examples

The naive solution takes exponential time.
这个朴素的解法需要指数时间。

Although the algorithm is correct, its exponential time complexity makes it impractical for large inputs, so we prefer a polynomial-time approximation.
虽然该算法是正确的,但它的指数时间复杂度使其在大规模输入下不现实,因此我们更倾向于选择多项式时间的近似算法。

词源 Etymology

exponential 来自“exponent(指数)”,与拉丁语 exponere(“展示、列出、提出”)相关,后来在数学中发展为“用指数表示的增长/变化”。exponential time 作为计算机科学术语,源于对算法运行时间随输入规模增长方式的分析,用来强调“增长速度像指数函数一样快”。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Introduction to Algorithms(Thomas H. Cormen 等,常称 CLRS)讨论时间复杂度分类时常与 polynomial time 对比提及。
  • Computers and Intractability: A Guide to the Theory of NP-Completeness(Michael R. Garey & David S. Johnson)在 NP 完全性与不可解性语境中频繁出现。
  • The Art of Computer Programming(Donald E. Knuth)分析算法效率时会涉及指数级时间行为与其影响。
  • Computational Complexity: A Modern Approach(Sanjeev Arora & Boaz Barak)在复杂性理论中系统讨论指数时间与相关复杂度类。
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