合并排序

合并排序采用了“分治法”的思想：

分解：将n个元素分成各含n/2个元素的子序列

解决：用合并排序法分别对子序列递归地排序

合并：合并两个已排序的子序列

在对子序列排序时，其长度为1时递归结束。

下面是合并排序的C++代码：

/*合并已排序子数组a[begin...middle]，a[middle+1...end]*/
template <typename T>
void merge(T a[], int begin, int middle, int end) {
  int n1 = middle - begin + 1, n2 = end - middle;
  T *left = new T[n1],
    *right = new T[n2];

  for (int i = 0; i < n1; ++i) {
    left[i] = a[begin + i];
  }
  for (int i = 0; i < n2; ++i) {
    right[i] = a[middle + 1 + i];
  }

  int i = 0, j = 0, k = begin;
  while (i < n1 && j < n2) {
    if (left[i] <= right[j]) {
      a[k++] = left[i++];
    } else {
      a[k++] = right[j++];
    }
  }
  if (i == n1) {
    while (j < n2) {
      a[k++] = right[j++];
    }
  } else {
    while (i < n1) {
      a[k++] = left[i++];
    }
  }
  delete []left;
  delete []right;
}
  

/**/
template <typename T>
void mergeSort(T a[], int begin, int end) {
  if (begin < end) {
    int middle = (begin + end) / 2;
    mergeSort(a, begin, middle);
    mergeSort(a, middle + 1, end);
    merge(a, begin, middle, end);
  }
}