排序算法:归并排序(Merge Sort)

使用C#详解常用排序算法(三):归并排序(Merge Sort) 结合C#代码讲解归并排序。 阅读详情

归并排序

归并排序采用了分治策略(divide-and-conquer),就是将原问题分解为一些规模较小的相似子问题,然后递归解决这些子问题,最后合并其结果作为原问题的解。

归并排序将排序数组A[1…n]分成两个各含n/2个元素的子序列,然后对这个两个子序列进行递归排序,最后将这两个已排序的子序列进行合并,即得到最终排好序的序列:

在这里插入图片描述

**归并排序的时间复杂度为:O(nlgn),其中 MERGE(a,b,c,d)的时间复杂度为O(n)。**如果这二组组内的数据都是有序的,那么就可以很方便的将这二组数据进行排序。

  • 将n个元素分成各含有n/2个元素的子序列.
  • 对两个子序列递归排序.
  • 合并两个已排序的子序列以得到排序结果

.

void merge(int x,int y){
    if(x==y)return;
    int mid=(x+y)/2,i=x,j=mid+1,k=x;
    merge(x,mid),merge(mid+1,y);
    while(i<=mid&&j<=y){
        if(a[i]<=a[j]){
            c[k++]=a[i++];
        }else{
            c[k++]=a[j++],ans+=mid-i+1;
        }
    }
    while(i<=mid)c[k++]=a[i++];
    while(j<=y)c[k++]=a[j++];
    for(int l=x;l<=y;l++){
        a[l]=c[l];
    }
}

归并排序的缺点:不是原地排序,需要额外申请空间来进行排序。

排序算法系列:归并排序(Merge sort)(C语言) 通俗理解:运用分而治之的思想,编写递归函数,将大数组排序转化为小数组排序,最后再将其合并。void merge_sort(int*p,int low,int high) { int mid = (low+high)/2; if (low <high) { merge_sort(p,low,mid); merge_sort(p,mid+1,high); merge(p,low,mi 阅读详情

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