The sorting algorithm of reading notes in the introduction of algorithms-merge sort merge sorting algorithm

Since the play ACM has been a sort of merger for a long time, now write a blog to introduce this algorithm:)

The picture is from Wikipedia, showing the complete merge sort process. For example, the array {38, 27, 43, 3, 9, 82, 10}.

In the introduction of algorithms, the chapter of Divide and conquer is referred to merge sort. First, the merge sort is a divide-and-conquer algorithm.

The merge (merge) Sort method combines two (or more than two) ordered tables into a new ordered table.

That is, the ordered sequence is divided into several ordered sub-sequences, and then the orderly subsequence is merged into a whole ordered sequence.

The Merg () function is used to merge two ordered arrays. is the key to the entire algorithm.

So what's the use of merge sorting?

1. Sorting elements in an array by row
2. Sorting the elements in the list by row, other sorting algorithms such as heap sorting and quick sorting cannot sort the list (refer to my blog http://www.cnblogs.com/wushuaiyi/p/4558391.html)
3. Can find the number of reverse order (refer to my blog http://www.cnblogs.com/wushuaiyi/p/4362149.html)
4. Sort outside

Below is a version of the merge sort that I wrote using the C + + implementation:

#include <iostream>using namespacestd;Const intMAXN =10900;intA[MAXN], TMP[MAXN], N;voidMerge (intLintMintr) {inti =l; intj = m +1; intK =l;  while(I <= m && J <=r) {if(A[i] <A[j]) {Tmp[k+ +] = a[i++]; } Else{tmp[k+ +] = a[j++]; }    }     while(I <=m) {tmp[k+ +] = a[i++]; }     while(J <=r) {tmp[k+ +] = a[j++]; }     for(inti = l; I <= R; ++i) a[i]=tmp[i];}voidMerge_sort (intLintr) {if(L <r) {intm = (L + r) >>1;        Merge_sort (L, M); Merge_sort (M+1, R);    Merge (L, M, R); }}intMain () {Std::ios::sync_with_stdio (false); intI, J, T, K, u, c, V, p, numcase =0;  while(Cin >>N) { for(i =0; I < n; ++i) {cin>>A[i]; } merge_sort (0N1);  for(i =0; I < n; ++i) {cout<< A[i] <<Endl; }    }    return 0;}

The efficiency of merge sort is relatively high, set the series length as N, divide the series into small series to Logn step,

Each step is a process of merging ordered series, and the time complexity can be recorded as O (N), so it is O (N*logn) altogether.

Because the merge sort is always done in the adjacent data,

So merge sort in O (N*logn) Several sort methods (quick sort, merge sort, hill sort, heap sort)

is also a high efficiency.

The sorting algorithm of reading notes in the introduction of algorithms-merge sort merge sorting algorithm