Recursive vs. iterative approach

In computer science, recursion and iteration are both methods used to solve problems, but they are implemented in different ways.
Recursion is a method where a function calls itself in order to solve a problem. The function continues to call itself until it reaches a base case, at which point it stops and returns a result. Recursive solutions can be more elegant and concise, but they can also be less efficient as they may require more memory to keep track of multiple instances of the same function.
Iteration, on the other hand, is a method where a problem is solved by repeatedly executing a block of code until a certain condition is met. This is typically done using a loop, such as a for or while loop. Iterative solutions can be more efficient as they do not require as much memory, but they may not be as easy to understand or maintain as recursive solutions.
Both recursion and iteration can be used to solve the same problem, and the choice between the two often depends on the specific requirements of the problem and the preferences of the programmer.
I hope that my simple example in Python illustrates it well.
Do you know why the first version has O(n) memory complexity?
Best,
Albert
Ps: the runtime measurements were done via the timeit module on Intel i9-9880H based machine.
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