已知f为单链表的表头指针，链表中存储的都是整型数据，试写出实现下列运算的递归算法和非递归算法：（1)求链表中的最大整数。（2)求所有整数的平均值

（1）递归算法求链表中的最大整数：

def find_max_recursively(head):
    # 基本情况：空链表返回None
    if not head:
        return None

    # 递归情况：比较当前节点值与当前最大值，取较大者
    max_val = head.val
    if max_val > find_max_recursively(head.next):
        max_val = head.val
    return max_val

# 非递归算法求链表中的最大整数（迭代）
def find_max_iteratively(head):
    max_val = head.val
    current = head.next
    while current:
        if current.val > max_val:
            max_val = current.val
        current = current.next
    return max_val

（2）递归算法求链表中所有整数的平均值：

def average_of_list_recursively(head):
    def sum_and_count(node):
        if not node:
            return 0, 0
        total, count = sum_and_count(node.next)
        total += node.val
        count += 1
        return total, count

    total, count = sum_and_count(head)
    if count == 0:
        return None  # 防止除以零的情况
    else:
        return total / count

# 非递归算法求链表中所有整数的平均值（迭代）
def average_of_list_iteratively(head):
    total = 0
    count = 0
    current = head
    while current:
        total += current.val
        count += 1
        current = current.next
    return total / count if count != 0 else None