用于复制子数组中的元素的合并排序算法循环

def merge_sort(arr):
    if len(arr) <= 1:
        return arr
    
    # 创建一个辅助数组用于存储排序结果
    aux = [0] * len(arr)
    
    # 设置初始子数组大小为1，逐渐增加子数组大小
    size = 1
    while size < len(arr):
        # 遍历数组，将相邻的子数组进行合并排序
        low = 0
        while low < len(arr) - size:
            mid = low + size - 1
            high = min(low + 2*size - 1, len(arr) - 1)
            merge(arr, aux, low, mid, high)
            low += 2*size
        size *= 2
    
    return arr

def merge(arr, aux, low, mid, high):
    # 将两个有序的子数组合并成一个有序的数组
    i = low
    j = mid + 1
    for k in range(low, high+1):
        if i > mid:
            aux[k] = arr[j]
            j += 1
        elif j > high:
            aux[k] = arr[i]
            i += 1
        elif arr[i] <= arr[j]:
            aux[k] = arr[i]
            i += 1
        else:
            aux[k] = arr[j]
            j += 1
    
    # 将辅助数组中的排序结果复制回原数组
    for k in range(low, high+1):
        arr[k] = aux[k]