Insert sort for decimal groups in merge sort

The complexity of a pure merge sort is: O (NLGN), whereas the time complexity of a pure insert sort is: O (n^2). Merge sort when data volume is large

But inserting a sort may run faster when n is smaller. Therefore, when the sub-problem becomes enough in the merge sort, the insertion sort is used to make the recursive leaves thicker, which can speed up the sorting. So how is this small enough to measure? Please see below:

So many I don't prove it, it's easier:

A, insert sort worst case can be ordered in O (NK) time each n/k sub-list of length K

B, in the worst case, these sub-tables can be combined in O (NLG (n/k)) time

C, the worst case run time complexity of the revised algorithm is O (nk + NLG (n/k))

Well, O (NK+NLG (n/k)) =o (NLGN). Only the maximum is K=o (LGN). The first item on the left side of the equation is a high-order item. If k is greater than LGN, it is more complex than merge sort. The left can be written as nk+nlgn-nlgk,k equals LGN, is 2nlgn-nlglgn. Ignoring the constant coefficients is the same as merging the sort.

Final conclusion: When K < LG (n) is used, insert sort

From At003_insertsort import insertsortfrom math Import log__author__ = ' Xiong Neng ' def mergesort (seq): Mergesortrange ( Seq, 0, Len (seq)-1, log (len)-1) def mergeorderedseq (seq, left, middle, right): "" "seq: to sort the sequence left <= Middle <= Right Sub-array Seq[left:  Middle] and Seq[middle+1..right] are ordered by the time complexity of the sort is O (n) "" "TEMPSEQ = [] I = left j = middle + 1 while I <=             Middle and J <= Right:if Seq[i] <= seq[j]: tempseq.append (seq[i)) i + = 1 Else: Tempseq.append (Seq[j]) J + = 1 if I <= middle:tempSeq.extend (Seq[i:middle + 1]) Els E:tempseq.extend (Seq[j:right + 1]) Seq[left:right + 1] = Tempseq[:]def mergesortrange (seq, start, end, Threshol d): "" "Merges the subsequence of a sequence start: The start subscript of the sub-sequence end: The end subscript of the subsequence threshold: to sort the length below this value, insert sort" "" if End-sta RT < THRESHOLD:TEMPSEQ = Seq[start:end + 1] insertsort (TEMPSEQ) Seq[start:end + 1] = tempseq[:] Elif Start < end: # If Start >= end terminates recursive call middle = (start + end)/2 Mergesortrange (SE Q, Start, middle, threshold) # line up the left half of the Mergesortrange (SEQ, middle + 1, end, Threshold) # and then half the right side Mergeord Eredseq (seq, start, Middle, end) # final Merge sort result if __name__ = = ' __main__ ': AA = [4, 2, 5, 1, 6, 3, 7, 9, 8] mergesort (AA ) Print (AA)

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