Python Coding challenge - Day 535| What is the output of the following Python Code?

 

Code Explanation:

 Importing lru_cache from functools

from functools import lru_cache

This line imports lru_cache from Python's functools module.

lru_cache is used to cache results of function calls to avoid redundant calculations.

Useful for recursive functions like Fibonacci, which this problem is similar to.

Function Definition with Memoization

@lru_cache(None)

This is a decorator that applies caching to the function.

@lru_cache(None) means there’s no limit on the number of stored results (infinite cache size).

def climb_stairs(n):

Defines a function climb_stairs that takes an integer n (number of steps).

Base Case for Recursion

    if n <= 2:

        return n

This is the base case:

If there's 1 step, there's only 1 way to climb: (1)

If there are 2 steps, there are 2 ways: (1+1) or (2)

So for n = 1 → returns 1, for n = 2 → returns 2.

Recursive Case

    return climb_stairs(n - 1) + climb_stairs(n - 2)

For n > 2, the number of ways to climb n steps is the sum of:

Ways to climb n-1 steps (then take 1 step)

Ways to climb n-2 steps (then take 2 steps)

This mirrors the Fibonacci sequence.

Calling the Function

print(climb_stairs(5))

Calls climb_stairs(5)

The function computes:

climb_stairs(5)

= climb_stairs(4) + climb_stairs(3)

= (climb_stairs(3) + climb_stairs(2)) + (climb_stairs(2) + climb_stairs(1))

...

With memoization, repeated calls like climb_stairs(2) are cached.

Final Output

The number of ways to climb 5 stairs is:

8

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