O（log n）究竟意味着什么？

问题：

I am learning about Big O Notation running times and amortized times. 我正在学习Big O Notation运行时间和摊销时间。 I understand the notion of O(n) linear time, meaning that the size of the input affects the growth of the algorithm proportionally...and the same goes for, for example, quadratic time O(n ² ) etc..even algorithms, such as permutation generators, with O(n!) times, that grow by factorials. 我理解O（n）线性时间的概念，意味着输入的大小成比例地影响算法的增长...例如，二次时间O（n ² ）等也是如此。即使算法也是如此。，例如置换生成器，具有O（n！）倍，通过阶乘生长。

For example, the following function is O(n) because the algorithm grows in proportion to its input n : 例如，以下函数是O（n），因为算法与其输入n成比例增长：

f(int n) {
  int i;
  for (i = 0; i < n; ++i)
    printf("%d", i);
}

Similarly, if there was a nested loop, the time would be O(n ² ). 同样，如果有嵌套循环，则时间为O（n ² ）。

But what exactly is O(log n) ? 但究竟什么是O（log n） ？ For example, what does it mean to say that the height of a complete binary tree is O(log n) ? 例如，说完整二叉树的高度是O（log n）是什么意思？

I do know (maybe not in great detail) what Logarithm is, in the sense that: log ₁₀ 100 = 2, but I cannot understand how to identify a function with a logarithmic time. 我知道（可能不是非常详细）什么是对数，在这个意义上：log ₁₀ 100 = 2，但我无法理解如何识别具有对数时间的函数。

解决方案：

参考一： https://stackoom.com/question/9gEF/O-log-n-究竟意味着什么
参考二： https://oldbug.net/q/9gEF/What-does-O-log-n-mean-exactly

来源：oschina

链接：https://my.oschina.net/u/3797416/blog/3213659

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