lru_cache vs dynamic programming, stackoverflow with one but not with the other?

I’m doing this basic dp (Dynamic Programming) problem on trees (https://cses.fi/problemset/task/1674/). Given the structure of a company (hierarchy is a tree), the task is to calculate for each employee the number of their subordinates.

This:

import sys
from functools import lru_cache  # noqa
sys.setrecursionlimit(2 * 10 ** 9)

if __name__ == "__main__":
    n: int = 200000
    boss: list[int] = list(range(1, 200001))  
    # so in my example it will be a tree with every parent having one child
    graph: list[list[int]] = [[] for _ in range(n)]

    for i in range(n-1):
        graph[boss[i] - 1].append(i+1)  # directed so neighbours of a node are only its children

    @lru_cache(None)
    def dfs(v: int) -> int:
        if len(graph[v]) == 0:
            return 0
        else:
            s: int = 0
            for u in graph[v]:
                s += dfs(u) + 1
            return s

    print(*(dfs(i) for i in range(n)))

crashes (I googled the error message and it means stack overflow)

Process finished with exit code -1073741571 (0xC00000FD)

HOWEVER

import sys
sys.setrecursionlimit(2 * 10 ** 9)

if __name__ == "__main__":
    n: int = 200000
    boss: list[int] = list(range(1, 200001))
    # so in my example it will be a tree with every parent having one child
    graph: list[list[int]] = [[] for _ in range(n)]

    for i in range(n-1):
        graph[boss[i] - 1].append(i+1)  # directed so neighbours of a node are only its children

    dp: list[int] = [0 for _ in range(n)]

    def dfs(v: int) -> None:
        if len(graph[v]) == 0:
            dp[v] = 0
        else:
            for u in graph[v]:
                dfs(u)
                dp[v] += dp[u] + 1

    dfs(0)

    print(*dp)

doesn’t and it’s exactly the same complexity right? The dfs goes exactly as deep in both situations too? I tried to make the two pieces of code as similar as I could.

I tried 20000000 instead of 200000 (i.e. graph 100 times deeper) and it still doesn’t stackoverflow for the second option.

I’m using Python 3.11.1