递归函数中return 1 + sum(list[1:])的原理及报错问题咨询

First, let's clear up a quick mix-up: your function is named sum, but it doesn't calculate the sum of the list's values—it counts the number of elements in the list (just like Python's built-in len() function). That context makes the logic a lot easier to unpack. Let's walk through your questions one by one:

1. Why add 1 to the result of sum(list[1:])? #

Every time you call the function, you're focusing on the first element of the current list. Adding 1 is how you count that single element. The recursive call sum(list[1:]) takes care of counting all the remaining elements in the list, so adding 1 combines the count of the current element with the count of the rest.

For example, if your list is ["apple", "banana", "cherry"]:

• You count "apple" (add 1), then ask sum(["banana", "cherry"]) to count the rest.
• sum(["banana", "cherry"]) counts "banana" (add 1), then asks sum(["cherry"]) to count the rest.
• sum(["cherry"]) counts "cherry" (add 1), then asks sum([]) which returns 0.
• Adding those 1s together gives you 3, the total number of elements.

2. Why use the slice list[1:]? #

The slice list[1:] creates a new list containing everything from the second element onward (starting at index 1). This is how you shrink the problem with each recursive call—you remove the element you just counted, so the next call handles a smaller, simpler version of the original problem. Eventually, you'll reach the empty list [], which is your base case (returns 0, since there's nothing to count).

3. What happens after adding 1? #

The addition takes effect as the recursive calls "unwind" back up. Let's use [10, 20] as a concrete example:

1. First call: sum([10, 20]) → 1 + sum([20])
2. Second call: sum([20]) → 1 + sum([])
3. Base case: sum([]) → returns 0
4. Now we unwind: 1 + 0 = 1 (from the second call), then 1 + 1 = 2 (from the first call)
   The final result is 2, which is the length of [10, 20].

4. Why does adding 1 to list[1:] outside the recursive call throw an error? #

When you try something like list[1:] + 1 directly, you're trying to add an integer (1) to a list—Python doesn't allow mixing these data types in addition. But in your recursive function, you're not adding 1 to the slice itself—you're adding 1 to the return value of sum(list[1:]), which is an integer (the count of elements in that slice). Adding two integers together is a valid operation, so no error occurs.

内容的提问来源于stack exchange，提问作者Shit Coder