考虑一个红黑树。它具有O(log n)的访问、搜索、插入和删除操作。与数组相比，数组的访问权限为O(1)，其余操作为O(n)。

因此，对于一个插入、删除或搜索比访问更频繁的应用程序，并且只能在这两种结构之间进行选择，我们更喜欢红黑树。在这种情况下，你可能会说我们更喜欢红黑树更麻烦的O(log n)访问时间。

为什么?因为权限不是我们最关心的。我们正在权衡:应用程序的性能更大程度上受到其他因素的影响。我们允许这种特定的算法受到性能影响，因为我们通过优化其他算法获得了很大的收益。

So the answer to your question is simply this: when the algorithm's growth rate isn't what we want to optimize, when we want to optimize something else. All of the other answers are special cases of this. Sometimes we optimize the run time of other operations. Sometimes we optimize for memory. Sometimes we optimize for security. Sometimes we optimize maintainability. Sometimes we optimize for development time. Even the overriding constant being low enough to matter is optimizing for run time when you know the growth rate of the algorithm isn't the greatest impact on run time. (If your data set was outside this range, you would optimize for the growth rate of the algorithm because it would eventually dominate the constant.) Everything has a cost, and in many cases, we trade the cost of a higher growth rate for the algorithm to optimize something else.

我在这里的回答是，在随机矩阵的所有行的快速随机加权选择是一个例子，当m不是太大时，复杂度为O(m)的算法比复杂度为O(log(m))的算法更快。

当O(1)中的“1”工作单元相对于O(log n)中的工作单元非常高，且期望集大小较小时。例如，如果数组中只有两到三个项，那么计算Dictionary哈希码可能比迭代数组要慢。

or

当O(1)算法中的内存或其他非时间资源需求相对于O(log n)算法非常大时。

并行执行算法的可能性。

我不知道是否有O(log n)和O(1)类的例子，但对于某些问题，当算法更容易并行执行时，您会选择具有更高复杂度类的算法。

有些算法不能并行化，但复杂度很低。考虑另一种算法，它可以达到相同的结果，并且可以很容易地并行化，但具有更高的复杂度类。当在一台机器上执行时，第二种算法速度较慢，但当在多台机器上执行时，实际执行时间越来越短，而第一种算法无法加快速度。

There is a good use case for using a O(log(n)) algorithm instead of an O(1) algorithm that the numerous other answers have ignored: immutability. Hash maps have O(1) puts and gets, assuming good distribution of hash values, but they require mutable state. Immutable tree maps have O(log(n)) puts and gets, which is asymptotically slower. However, immutability can be valuable enough to make up for worse performance and in the case where multiple versions of the map need to be retained, immutability allows you to avoid having to copy the map, which is O(n), and therefore can improve performance.

在实时情况下，当你需要一个固定的上界时，你会选择一个堆排序，而不是快速排序，因为堆排序的平均行为也是它的最差情况行为。