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排序算法—归并排序【附代码】

排序算法—归并排序【附代码】

什么是归并排序?

  归并排序简单来讲,就是将两个有序的序列整合到一起。

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如何将两个有序的序列整合到一起呢?

  那么我们假设,现在有 M={m1 ,m2,m3,….,mx}序列和 N = {n1,n2,n3,….,ny}序列,这两个序列已经是有序的序列,首先创建一个空序列 K = {},那么接着将 m1 和 n1 进行比较,加入 m1 < n1 那么将 m1 放入 K 序列中,然后 M 序列游标后移,即下一次将进行 m2 和 n1 的比较,直到全部比较完毕,并填入序列 K 中。

既然归并排序是整合有序序列,那么岂不是不能排序无序序列,这条件也太苛刻了点吧?

  归并排序是建立在分治法的基础上进行操作的,也就是可以将一个完全无序的序列进行无线分割以达到有序序列,比如:现在有 M={m1 ,m2,m3,….,mx},M序列是完全无序的序列,那么此时可以将 M 序列分成若干个小序列——{m1,m2},{m3,m4}….{mx-1,mx};此时这些序列就是有序的,那么就可以通过归并操作进行排序,所以归并排序也可以排序无序序列,且速度仅次于快速排序,属于稳定排序。

如何分割序列?

  上个问题已经提过,归并排序是建立在分治的基础上进行操作的,其中分治的体现就体现在分割序列上,比如:现在有M={m1 ,m2,m3,….,mx},第一次分割:M1 = {m1,m2,…,m(x+1)/2},M2 = {m(x+1)/2 +1,m(x+1)/2 +2,…,mx},第一次分割之后得到 M1 和 M2 序列,然后再分割 M1 和 M2 ,分割若干次之后得到 x/2 + x%2 个序列,然后再逐一进行归并操作。

该算法具体步骤:

  1、规定首指针 left 和mid(left指向序列1的首元素,right 指向序列2的首元素)

  2、比较 left 和 mid 的大小,将小的元素放入新建的空间中

  3、重复步骤2,直到其中一个序列遍历完毕

  4、将剩下的未加入新建空间中的元素直接复制粘贴进新建空间

该算法的核心步骤:

  1、使用分治法(递归)分割序列

  2、比较 left 和 mid 的大小 , 将小的元素的添加进入新建空间

讲述完毕,贴上代码:

using System;using System.Collections.Generic;using System.Linq;using System.Text;using System.Threading.Tasks;namespace 排序__归并排序{    class 归并    {        public static int[] arr = { 6, 202, 301, 100, 38, 8, 1 ,-1,1000};        static void Main(string[] args)        {            Sort(arr, 0, arr.Length -1);            foreach (var item in arr)            {                Console.Write(item + "  ");            }            Console.ReadKey();        }        public static void Sort(int []a,int left,int right)        {            if (left >= right) return;            else            {                int mid = (left + right) / 2;                //@1                Sort(a, left, mid);                Sort(a, mid + 1, right);                MergeSort(a, left, mid, right);            }        }        public static void MergeSort(int []a,int left,int mid,int right)        {            int[] Arr = new int[right - left + 1];            int l = left, m = mid +1 , k = 0;           //@2            while ( m <= right && l <= mid )          //@3            {                if (a[l] > a[m]) Arr[k++] = a[m++];                else Arr[k++] = a[l++];            }            while (m < right +1)                           //@4            {                Arr[k++] = a[m++];            }            while (l < mid +1 )  Arr[k++] = a[l++];        //@4            for (k = 0, l = left; l < right + 1; k++, l++) a[l] = Arr[k];        }    }}

代码解读:

  @1 :Sort()函数完成了序列的分割,每一次递归都将序列分成两半,直到不能分隔为止。

  @2 :l 代表序列1的首元素,m 代表序列2的首元素,k代表新建数组Arr的已有元素个数

  @3 :序列1的首元素和序列2的首元素进行比较,将小的放入 Arr 中,且序列游标后移,直到其中一个序列的元素遍比较完毕

  @4 :在序列1 和序列2的比较过程中,可能出现序列1已经全部添加进了 Arr 中,但是序列2还没有,则将剩下的未比较的元素直接复制进入 Arr 中

总结:

  以上代码并不是真正意义上的分割数组,只是做了一个逻辑分割,没有像其他代码一样将分割后的数组填入一个新的数组,那样做的话会对速度和内存产生一点影响,虽然微乎其微,但是总归是没这么好的,在归并操作上,需要注意的是参数不要越界(我当时就想了很久为什么 @2 上面的 m 要等于 mid +1 而不是 mid ,其实道理很简单,因为mid是属于左序列,从 mid+1 开始才属于右序列,将m = mid +1 改成 m = mid 不是不行,只是后面的代码也需要改,但是没有必要多做一次无用比较,这个问题我当时真是想了半天…),其实只要理清楚其中的逻辑关系,这样代码就能做到信手拈来。

以上就是排序算法—归并排序【附代码】的详细内容,更多请关注求知技术网其它相关文章!

文章来源:智云一二三科技

文章标题:排序算法—归并排序【附代码】

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