如果输入是排序的数据库还是未排序的，输入大小对算法时间复杂度是否重要？

Question

I have a theoretical question (if these are not allowed please direct me to the right place.) about time complexity.

Say I have a list sorted lexically, and one that isn't. I know that the linear search and binary search algorithms have vast differences in run-time (binary search being logarithmic so the input is halved each time), but other than that, will there be any significance about the size of the input for the sorted list versus the non-sorted list? Is there any other reason why the sorted list would be better, if the input is very large?

Really new at this stuff so any clarification would be much appreciated!

Answer 1

I know that the linear search and binary search algorithms have vast differences in run-time (binary search being logarithmic so the input is halved each time)

This, and other similar algorithms, is the main advantage

will there be any significance about the size of the input for the sorted list versus the non-sorted list

No, each element occupies the same amount of space in RAM regardless of order (for a standard list).

Is there any other reason why the sorted list would be better, if the input is very large?

Advantages:

• Some algorithms are faster on sorted input sets
• Sorted output can be more pleasing for end users if you are displaying it.
• Sorted data is easier to compress, so for storage on disk or specialized RAM storage it could be smaller, but it would make no difference if you just put it in a standard array or list.

There are probably more, this is what I can come up with offhand.