V2EX order of growth

Order of Growth

释义 Definition

“增长阶(数量级)”:指当输入规模增大时,函数(常见于算法运行时间或空间消耗)的增长速度类别,通常用大 O 记号等来描述(如 \(O(n)\)、\(O(n^2)\)、\(O(\log n)\))。也可泛指“增长的大致趋势/级别”。

例句 Examples

As the input gets larger, the order of growth tells you how fast the algorithm slows down.
当输入变大时,增长阶告诉你算法会以多快的速度变慢。

Although two programs may run equally fast on small tests, their orders of growth can differ dramatically for large data sets.
尽管两个程序在小测试上可能一样快,但在大数据集上它们的增长阶可能会有巨大差异。

发音 Pronunciation (IPA)

/rdr v roθ/

词源 Etymology

“order”源自拉丁语 ordo(“顺序、等级”),在数学与科学语境中常表示“级别/阶”;“growth”表示“增长”。合起来的 “order of growth” 在计算机科学与分析中用来表达“随规模增长时的数量级/阶”,强调的是主导增长趋势而非精确值。

相关词 Related Words

文学与著作 Literary Works

  • Introduction to Algorithms(Cormen, Leiserson, Rivest, Stein):用于讨论算法复杂度与渐近分析中的增长阶。
  • Algorithms(Robert Sedgewick & Kevin Wayne):以增长阶对比不同算法在大规模输入下的性能。
  • The Art of Computer Programming(Donald E. Knuth):在算法分析与渐近记号相关章节中涉及增长阶思想。
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