Off-topic: oh well, one day liver 4 chapters, yes you boy
1. What is merge sort
- Merge two or more ordered subsequences into one ordered sequence .
- You can understand it as, when I was in junior high school, I had a handicraft class, and the teacher said that two students should be in a group;
- Every 2 of us act as a group and choose the best work;
- Then the teacher said: Every two combinations are combined into a 4-person combination , and then the best work is selected;
- Next, every two combinations are merged into an 8-person combination until one of the best works is selected.
PS: The above example is not rigorous, just to let you understand the process of "merging" .
2. 2-way merge sort
- What is 2-way merge sort?
- As mentioned above, the merge sort is " 2 or more sequences xxxxx";
- Then we only choose 2 sequences and 2 sequences to merge , then it is 2-way merge sort .
- picture explanation
3. 2-way merge sort code implementation
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
namespace YoyoCode
{
internal class MSort
{
//辅助数组
static int[] sArray;
/// <summary>
/// 归并排序
/// </summary>
/// <param name="pArray">需要排序的数组</param>
public static void MergeSort(int[] pArray)
{
//辅助数组的初始化
sArray = new int[pArray.Length];
//步长限制1、2、4、8、16...
//如果数组长度为9，最大步长不能为4，必须是8
//因为8和剩下的一个元素需要合并
for (int step = 1; step < pArray.Length; step *= 2)
{
//在步长限制下，对数组的两两归并
for (int j = 0; j < pArray.Length - step; j += step + step)
{
Merge(pArray, j, j + step - 1, Math.Min(j + step + step - 1, pArray.Length - 1));
}
}
}
/// <summary>
/// 对两个子数组进行排序
/// </summary>
/// <param name="pArray">数组</param>
/// <param name="low">子数组1的起始index</param>
/// <param name="mid">子数组1的终止index，mid+1就是子数组2的起始index</param>
/// <param name="high">子数组2的终止index</param>
private static void Merge(int[] pArray, int low, int mid, int high)
{
//辅助数组赋值
for (int k = low; k <= high; k++)
{
sArray[k] = pArray[k];
}
//合并
int i = low;
int j = mid + 1;
for (int k = low; k <= high; k++)
{
//越界直接合并
if (i > mid)
{
pArray[k] = sArray[j++];
}
else if (j > high)
{
pArray[k] = sArray[i++];
}
else
{
//没越界则比较，两者中小的放进结果中
if (sArray[i] < sArray[j])
{
pArray[k] = sArray[i++];
}
else
{
pArray[k] = sArray[j++];
}
}
}
}
}
}
Explanation: It's all in the wine, ah no, it's all in the notes, read the notes, and then rub your hands together to understand the principle, it just looks disgusting~
4. Algorithm analysis
- time complexity
- O(nlogn)
- space complexity
- O(n)
- algorithm stability
- Stablize
Conclusion: so tired, so tired, so tired