排序算法的临界值是多少？

Question

I was asked to do the quicksort, cut off with insertion sort. But I did not understand the meaning of cut off value. I need someone to elaborate this concept with real-world examples.

Answer 1

It is hard to be sure without seeing the exact statement of requirements.

However, I think that this means that you should use insertion sort ( O(N^2) ) below a certain size (the "cut off") and quicksort ( O(NlogN) ) above that size.

• They could mean that you do this test on the size of the input array.

• They could also mean that you implement a hybrid sort, and use insertion sort on a subarray when a quicksort partition size is less than the threshold.

Either interpretation is plausible.

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I need someone to elaborate this concept with real-world examples.

I doubt that you need examples to understand this. If you understand the insertion sort and quicksort algorithms, then this is conceptually straightforward. (And if you don't understand them, there are lots of places to read about them, starting with your data structures & algorithms textbook.)

Answer 2

Some algorithms are asymptotically better than others. In your case, the asymptotic run time of Quicksort is O(N(logN)) while the asymptotic run time of insertion sort is O(N^2).

This means that for large values of N, Quicksort will run faster than insertion sort.

However, for small values of N, insertion sort may run faster. Hence, you can optimize the actual run-time of Quicksort by combining it with insertion sort for small array sizes.

Quicksort is a recursive algorithm, that breaks the original array into smaller arrays and runs recursively on each sub-array. Cut off with insertion sort means that once you reach array sizes smaller than some constant cut-off size, you sort these small arrays using insertion sort instead of continuing the recursion.