【Data Structure Learning Record 28】——Merge Sort

1. Principle

Our common merge sort, also known as 2路归并排序, is equivalent to the operation of combining two sequential lists or linked lists. If we achieve this through the dichotomy, dividing a long sequence table into the smallest subsequence all the way to the smallest subsequence, and then gradually merging from the smallest subsequence into a large table, then the final large table will be ordered.
So this is a recursive process with a time complexity of $nlo{g}_{2}n$

Two. Process

Because it is a recursive process, it is more convenient to show together

Suppose that the elements of an ordered list are n+1 elements from 0 to n, where the start represents l, the end represents h, and the middle element is represented by m=(l+h)/2. The
recursive expression can be written as:
$$sort(l,h)=\{\begin{array}{ll}l=h,& Handsgothe\; finalstop\\ l<h,& sort(l,m);sort(m+1,h);Andclosingand\end{array}$$

Three. Code

#include <stdio.h>
#include <stdlib.h>

#define MAXLEN  100
int temp[MAXLEN] = {
    
    0};     //创建一个临时变量数组


int Mergelist(int arry[], int low, int mid,int high)
{
    
    
    int tptr, lptr, hptr, i = 0;
    tptr = 0;                           // 临时数组储存下标
    lptr = low;                         // 左序列下标，low<=lptr<=mid
    hptr = mid + 1;                     // 右序列下标，mid+1<=hptr<=high

    while(lptr <= mid && hptr <= high)  // 这三个while就是循环合并两个线性表
    {
    
    
        // 将左序列或右序列中，较小的存入临时数组里
        if (arry[lptr] <= arry[hptr])
        {
    
    
            temp[tptr] = arry[lptr];
            ++lptr;
        }
        else
        {
    
    
            temp[tptr] = arry[hptr];
            ++hptr;
        }
        ++tptr;
    }
    // 检测左序列是否添加完毕
    while(lptr <= mid)
    {
    
    
        temp[tptr] = arry[lptr];
        ++lptr;
        ++tptr;
    }
    // 检测右序列是否添加完毕
    while(hptr <= high)
    {
    
    
        temp[tptr] = arry[hptr];
        ++hptr;
        ++tptr;
    }
    // 将新序列覆盖原数组
    for (; i < tptr; ++i)
    {
    
    
        arry[low+i]=temp[i];
    }
}

int MergeSort(int arry[], int low, int high)
{
    
    
    int mid;
    if (low < high) // 可递归部分
    {
    
    
        mid = (low + high) / 2;
        MergeSort(arry, low, mid);          // 左序列
        MergeSort(arry, mid+1, high);       // 右序列
        Mergelist(arry, low, mid, high);    // 合并两序列
    }
}


int main()
{
    
    
    int a[7] = {
    
    6,5,3,7,2,1,4};
    int i;
    MergeSort(a, 0, 6);
    for (i = 0; i < 7; ++i)
    {
    
    
        printf("%d ", a[i]);
    }
    return 0;
}