Shortcut & Epta
Shortcut
Yo Epta, heard you’re brewing another code alchemy experiment, mind if I throw a speedrunning challenge at you? Whoever can squeeze the most cycles into the same function wins.
Epta
Sure thing, but just a heads‑up I won’t be using semicolons in my code or in my rant about it; that would be too easy for the compiler to bite back. Bring the challenge, I’ll craft a function that slashes cycles like a samurai with a well‑tuned blade. Just remember, I’ll hate any pop‑ups that try to interrupt my ritual. Ready when you are.
Shortcut
Cool, let’s see how fast you can slice this: write a function that returns the nth Fibonacci number in O(log n) time with no loops, just matrix exponentiation or fast doubling. No semicolons, no pop‑ups, pure code. Show me the trimmed‑down version, no fluff. Let's race!
Epta
Here’s the function, no loops, no semicolons, no pop‑ups, pure recursion:
def fib(n):
if n == 0:
return 0
def helper(k):
if k == 0:
return (0,1)
a,b = helper(k//2)
c = a*(2*b - a)
d = a*a + b*b
return (c,d) if k%2==0 else (d,c+d)
return helper(n)[0]
Shortcut
Nice cut, that’s tight and fast. Just one tweak: keep the helper outside the main to avoid redefining on every call if you plan to call it many times. But for a single call, you’re solid—no loops, no semicolons, pop‑ups handled. Ready to push the limit? Let's try a larger n and see how the stack holds.
Epta
Sure thing, stack depth is only about log₂n so a million isn’t a problem if you bump Python’s limit a bit. Just run it and watch the stack grow like a quiet mountain—no pop‑ups, no loops, just pure recursion. Let me know how far you push it.
Shortcut
If you crank it up to a million, you’ll hit Python’s default recursion limit (about 1000). Raise it first:
```
import sys
sys.setrecursionlimit(20000)
```
Then call `fib(10**6)`. The depth will be around 20, because each step cuts the problem size in half, so you’re good. Just keep an eye on memory – each stack frame stores a tuple and a few ints. No pop‑ups, no loops, just pure recursion. Give it a whirl.
Epta
That’s the trick – bump the limit, keep the recursion shallow enough. Just be careful with the memory cost of those tuples; a million frames will still be fine once you hit the ~20 depth you mentioned. Happy to watch your stack grow, just keep an eye on the heap, and you’ll avoid any pop‑up surprises. Give it a run and let me know how fast the numbers cascade.