Merge sort was unique for its time in that the best, worst, and average time complexity are all the same: `Θ(N*log(N))`

. This means an almost-sorted list will take the same amount of time as a completely out-of-order list. This is acceptable because the worst-case scenario, where a sort could stand to take the most time, is as fast as a sorting algorithm can be.

Some sorts attempt to improve upon the merge sort by first inspecting the input and looking for “runs” that are already pre-sorted. Timsort is one such algorithm that attempts to use pre-sorted data in a list to the sorting algorithm’s advantage. If the data is already sorted, Timsort runs in `Θ(N)`

time.

Merge sort also requires space. Each separation requires a temporary array, and so a merge sort would require enough space to save the whole of the input a second time. This means the worst-case space complexity of merge sort is `O(N)`

.

### Instructions

Why does merge sort require so much space? Would it be possible to write an efficient sort that doesn’t require any additional space? Can you think of any trade-offs that would need to be made?

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