排序功能的增长顺序? [英] Sorting the order of growth of the functions?

问题描述

请按从最快到最慢的增长率订购以下功能:

Please order the function belows by growth rate from fastest to slowest:

• n ^ 10
• 2 ^ n
• nlog(n)
• 10 ^ 6

我的答案是:

• 2 ^ n
• n ^ 10
• nlog(n)
• 10 ^ 6

我的答案正确吗?

推荐答案

这似乎是正确的.作为教育方式，请考虑当您输入不同的n值(使用10的近似幂而不是精确值)时会发生什么:

That seems about right. As way of education, consider what happens when you feed in different n values (using rough powers of 10 rather than exact values):

 n      2^n       n^10    n log n   10^6
 ----   -------   -----   -------   ----
    1   10^0.3    10^0    10^0      10^6
   10   10^3      10^10   10^1      10^6
  100   10^30     10^20   10^2      10^6
 1000   10^301    10^30   10^3      10^6
10000   10^3010   10^40   10^4      10^6

因此，就它们增长的速度而言，您的列表是正确的.

So, in terms of how fast they grow, you're list is correct.

• 10 6 根本没有增长.
• n log n每一步将其十进制功率增加一.
• n 10 每步增加十倍功率.
• 2 n 将其10乘幂乘以10.

• 106 doesn't grow at all.
• n log n increases its power-of-ten by one for each step.
• n10 increases its power-of-ten by 10 for each step.
• 2n multiplies its power-of-ten by ten each step.

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