一. 归并排序（Merge sorting）
归并排序（Merge sorting） 是一种将数据分而治之（divide and conquer）的算法，其实现过程如下：
- 将数据分为两部分（Divides the list into halves）；
- 每一半各自进行排序（Sort each halve separately）；
- 将排序结果汇总（Then merge the sorted halves into one sorted array）。
最差的情况如下图所示：
由图分析可知归并排序是一种稳定的排序算法，在最糟糕情况下的时间复杂度为O(n*log2(n))，平均时间复杂度为O(n*log2(n))。
二. C++ 代码
#include <iostream>
using namespace std;
void merge(int arr[], int first, int mid, int last, int arr_size, int order)
{
int tempArray[arr_size];
int first1 = first;
int last1 = mid;
int first2 = mid + 1;
int last2 = last;
int index = first1;
if(order == 1)
{
for(; (first1 <= last1) && (first2 <= last2); ++ index)
{
if(arr[first1] < arr[first2])
{
tempArray[index] = arr[first1];
++first1;
}
else
{
tempArray[index] = arr[first2];
++first2;
}
}
for(; first1 <= last1; ++first1, ++index)
tempArray[index] = arr[first1];
for(; first2 <= last2; ++first2, ++index)
tempArray[index] = arr[first2];
for(index = first; index <= last; ++index)
arr[index] = tempArray[index];
}
else
{
for(; (first1 <= last1) && (first2 <= last2); ++ index)
{
if(arr[first1] > arr[first2])
{
tempArray[index] = arr[first1];
++first1;
}
else
{
tempArray[index] = arr[first2];
++first2;
}
}
for(; first1 <= last1; ++first1, ++index)
tempArray[index] = arr[first1];
for(; first2 <= last2; ++first2, ++index)
tempArray[index] = arr[first2];
for(index = first; index <= last; ++index)
arr[index] = tempArray[index];
}
}
void MergeSort(int arr[], int first, int last, int arr_size, int order)
{
cout << "Split: ";
for(int k = first; k<= last; k++)
cout << arr[k] << " ";
cout << endl;
if(first < last)
{
int mid = (first + last) / 2;
MergeSort(arr, first, mid, arr_size, order);
MergeSort(arr, mid+1, last, arr_size, order);
merge(arr, first, mid, last, arr_size, order);
}
cout << "Merge: ";
for(int k = first; k <= last; k++)
cout << arr[k] << " ";
cout << endl;
}
int main()
{
int arr_size, order;
int *arr;
cout << "Enter the size of an integer array: ";
cin >> arr_size;
arr = new int[arr_size];
for(int i = 0; i < arr_size; i++)
{
cout << "Enter an integer to be stored at position " << i << " : ";
cin >> arr[i];
}
cout << "Choose the sorting order:\n 1 - Ascending\n 2 - Descending\n ";
cin >> order;
int first = 0;
int last = arr_size - 1;
MergeSort(arr, first, last, arr_size, order);
return 0;
}