Merge sort for reverse order

Merge sort for reverse order

By MPs

"1" What is reverse order?

for a sequence to be ordered from small to large, if there is Ai,aj and meet Ai>aj and I<j Ai,aj for a set of reverse

"2" How to find the reverse order?

we find that we can force enumeration of i,j and then judge and accumulate the answer, time complexity O (N2)

But for a larger number of topics, the only way to keep the tle →_→

"3" merging sort for reverse order

The definition of reverse pairs (see "1") is a set of reverse pairs in the sequence that should be ordered, then we think of the sort, but because it is to 22 matches, we think of the merge sort

The merge sort roughly reads as follows:

a set of data is divided into a group, and then for each interval from the very large to make an orderly table merge (O (N)), and then back up, the main idea is divided

We found that, when merging, if a group of merge errors occur

(that is, not a direct A and then the B, but an AI in the middle is not in the right place, is replaced by a number in B, it proves that there must be mid-i+1 A reverse order, because the front must be orderly)

So the reverse is very simple for itself, only need to write a merge sort, in the process of merging, if not insert a element, but B, then the answer class plus mid-i+1

"4" Template

1 voidUnion (intLintMid,intR) {2     intI=l,j=mid+1, len=l-1;3      while(I<=mid && j<=R)4     {5         if(A[i]<=a[j]) b[++len]=a[i++];6         Else {7b[++len]=a[j++];8ans+=mid-i+1;9ans=ans%Mod;Ten         } One     } A      while(I<=mid) b[++len]=a[i++]; -      while(j<=r) b[++len]=a[j++]; -      for(i=l;i<=r;i++) a[i]=B[i]; the } -  - voidMerge_sort (intLintR) { -     if(l<R) { +         intMid= (l+r) >>1; - Merge_sort (l,mid); +Merge_sort (mid+1, R); A Union (l,mid,r); at     } - } -  - intMain () { - init (); -Merge_sort (1, n); inprintf"%d", ans); -   return 0; to}

"5" Summary

The time complexity of the algorithm is reduced from O (N2) to O (Nlogn)

Space complexity is raised from O (1) to O (N)

space Change Time

Merge sort for reverse order