Incrementing the upper limit of range inside a loop doesn't make it run forever [duplicate]

Question

I'm an intro computer science student working in Python 3.7.1.

We were working with "Additorials" where you take a number and take get the sum of the number plus every number before it. Ie: for the number 10-- 10+1+2+3+4+5+6+7+8+9 = 55

I had to write a program that performed this operation as a function. However, I did it in a way that shouldn't work, but it does.

def bigAdd(n):
    for i in range(0,n):
        n+=i
    return n

for example, if I input the number 10, it returns 55

But... Why?

If the upper limit of this loop is n, and it is constantly being incremented by i, shouldn't it run forever because it is constantly raising its limit? Why does it return any answer, let alone the correct one?

Answer 1

You are adding to n, which initially is 10 (or whichever upper bound you are using). Thus your result is indeed 10 (the initial value) + 0 + 1 + ... + 9 (from the range).

Having said that, I'd still recomment not using the initial value of n and instead getting the sum of range(1, n+1), as that's much clearer.

>>> sum(range(1, n+1))
55

Or if you want to show off:

>>> n*(n+1)//2
55

---

About your second question:¹ No, the range(0, n) is evaluated only once, when the for loop is first entered, not in each iteration. You can think of the code as being roughly² equivalent to this:

r = range(0, n) # [0, 1, 2, 3, ..., n-2, n-1]
for i in r:
    n+=i

In particular, Python's for ... in ... loop is not the "typical" for (initialization; condition; action) loop known from Java, C, and others, but more akin to a "for-each" loop, iterating over each element of a given collections, generator, or other kind of iterable.

¹⁾ Which, I now realise, is actually your actual question...

²⁾ Yes, a range does not create a list but a special kind of iterable, that's why I said "roughly".

Answer 2

range(0,n) is evaluated once before the loop is entered.

This isn't like a typical for loop from other languages that has a condition that is constantly checked. range returns a range object that produces numbers, and the upper limit is set when the range object is created. Changing n has no effect on the range object that's already been constructed.