#include<iostream>using namespace std;void Merge(int[], int, int[], int, int, int)  void MergeSort(int numbers[], int length, int temp[], int begin, int end){  //1. 同样判断传入的参数是否有效  if (numbers == nullptr || length <= 0 || begin < 0 || end >= length)    throw new exception("Invalid input.");    //2. 作为递归的结束条件，开始下标和结束下标相等时，说明子序列中只有一个元素，看作有序的  if (end - begin == 0)    return;
  //3. 定义中间变量，将数组分半【如果有7个元素，下标0-6，则middle=3，数组分为长度为4和3的两段】  int middle = ((end - begin) / 2 ) + begin;  //4. 递归，先递归左半边，再递归右半边，将左右子序列不断分为长度为1的子序列才停止递归  MergeSort(numbers, length, temp, begin, middle);  MergeSort(numbers, length, temp, middle + 1, end);  //5. 再慢慢归并  Merge(numbers, length, temp, begin, end, middle);}
void Merge(int numbers[], int length, int temp[], int begin, int end, int middle){  //1. 判断是否有不符合要求的参数传入，有则抛出错误  if (numbers == nullptr || length <= 0 || begin < 0 || end >= length)    throw new exception("Invalid input.");
  //2. 将原序列从中分开  int leftIndex = begin;    //左边序列的开始（左边序列的结尾是middle）  int rightIndex = middle + 1;//右边序列的开始（右边序列的结尾是end）  int tempIndex = begin;    //辅助数组的下标  //3. 当左右子序列尚未到头时，循环  while (leftIndex <= middle && rightIndex <= end)  {    //4. 两两对比判断，谁大谁就放入辅助数组，同时指针后移    if (numbers[leftIndex] < numbers[rightIndex])      temp[tempIndex] = numbers[leftIndex++];    else      temp[tempIndex] = numbers[rightIndex++];    //5. 辅助数组下标++    ++tempIndex;  }
  //6. 当左边或右边子序列尚未到头时，直接放入辅助数组  while (leftIndex <= middle)    temp[tempIndex++] = numbers[leftIndex++];
  while (rightIndex <= end)    temp[tempIndex++] = numbers[rightIndex++];
  //7. 再将辅助数组中已经有序的元素覆盖掉原数组中无序的元素，使原数组变成部分有序  for (int i = begin; i <= end; ++i)    numbers[i] = temp[i];}
int main(int arvc, char* argv[]){  const int length = 9;  int nums[length] = { 18, 7, 23, 3, 9, 32, 10 , 99, 0};  int *temp = new int[length];
  MergeSort(nums, length, temp, 0, 8);
  for (int i = 0; i < length; i++)    cout << nums[i] << "  ";
  delete[] temp;  temp = nullptr;  cout << endl;  return 0;}