// 归并排序：把数据分为两段，从两段中逐个选最小的元素移入新数据段的末尾。可从上到下或从下到上进行。

/*****************
    迭代版
*****************/
//整數或浮點數皆可使用,若要使用物件(class)時必須設定"小於"(<)的運算子功能
template<typename T>
void merge_sort(T arr[], int len) {
	T* a = arr;
	T* b = new T[len];
	for (int seg = 1; seg < len; seg += seg) {
		for (int start = 0; start < len; start += seg + seg) {
			int low = start, mid = min(start + seg, len), high = min(start + seg + seg, len);
			int k = low;
			int start1 = low, end1 = mid;
			int start2 = mid, end2 = high;
			while (start1 < end1 && start2 < end2)
				b[k++] = a[start1] < a[start2] ? a[start1++] : a[start2++];
			while (start1 < end1)
				b[k++] = a[start1++];
			while (start2 < end2)
				b[k++] = a[start2++];
		}
		T* temp = a;
		a = b;
		b = temp;
	}
	if (a != arr) {
		for (int i = 0; i < len; i++)
			b[i] = a[i];
		b = a;
	}
	delete[] b;
}

/*****************
    递归版
*****************/
template<typename T>
void merge_sort_recursive(T arr[], T reg[], int start, int end) {
	if (start >= end)
		return;
	int len = end - start, mid = (len >> 1) + start;
	int start1 = start, end1 = mid;
	int start2 = mid + 1, end2 = end;
	merge_sort_recursive(arr, reg, start1, end1);
	merge_sort_recursive(arr, reg, start2, end2);
	int k = start;
	while (start1 <= end1 && start2 <= end2)
		reg[k++] = arr[start1] < arr[start2] ? arr[start1++] : arr[start2++];
	while (start1 <= end1)
		reg[k++] = arr[start1++];
	while (start2 <= end2)
		reg[k++] = arr[start2++];
	for (k = start; k <= end; k++)
		arr[k] = reg[k];
}
//整數或浮點數皆可使用,若要使用物件(class)時必須設定"小於"(<)的運算子功能
template<typename T> 
void merge_sort(T arr[], const int len) {
	T *reg = new T[len];
	merge_sort_recursive(arr, reg, 0, len - 1);
	delete[] reg;
}