Counting depth or the deepest level a nested list goes to

Here is one way to write the function

depth = lambda L: isinstance(L, list) and max(map(depth, L))+1

I think the idea you are missing is to use max()

Let's first rephrase your requirements slightly.

The depth of a list is one more than the maximum depth of its sub-lists.

Now, this can be translated directly to code:

def depth(l):
    if isinstance(l, list):
        return 1 + max(depth(item) for item in l)
    else:
        return 0

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