Modifying a set while iterating over it

Question

I would like to iterate over a set while I'm deleting items from it. There are similar questions for deleting one item at the time or for lists , but they do not work for my case.

The code follows; I iterate over a set ZN and in the end of the iteration I'm removing a few items (the ones belonging to the set temp ). But the iteration is still happening over the "original" ZN.

How can I modify this code to change the set ZN while I'm iterating over it?

def CyclotomicCosets(q,n):
    N=q^n-1
    ZN=set(range(N))
    Cosets=[]
    for i in ZN:
        tmp=set([])
        for j in range(n):
            tmp.add( i*(q^j) %N)
        Cosets.append(list(tmp))
        ZN=ZN.difference(tmp) # <------------ Does not do what I want
    return(Cosets)

Answer 1

Use a while loop and .pop() values to process from the set:

def CyclotomicCosets(q, n):
    N = q ^ n - 1
    ZN = set(range(N))
    Cosets = []
    while ZN:
        i = ZN.pop()
        tmp = {i * (q ^ j) % N for j in range(n)}
        Cosets.append(list(tmp))
        ZN -= tmp
    return Cosets

Note that I replaced your inner for loop with a set comprehension to make it a little faster and more compact. These were introduced in Python 2.7 and Python 3, in earlier versions of python you can use a generator expression instead:

tmp = set(i * (q ^ j) % N for j in range(n))

Your original mistake was to replace ZN rather than update it:

ZN=ZN.difference(tmp)

This did not alter the original set you were using in the for loop. Rather, you are creating a new set and point the ZN reference to that.

However, you cannot modify a set while iterating over it, so even an in-place difference would not have worked; you would have to use ZN -= tmp or ZN.difference_update(tmp) but that would lead to exceptions instead:

>>> ZN = set(range(3))
>>> for i in ZN:
...     ZN -= set([2])
... 
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
RuntimeError: Set changed size during iteration

The corrected code gives:

>>> CyclotomicCosets(3, 5)
[[0], [0, 1, 2, 3], [0, 1, 4, 5], [0, 4, 5, 6]]

Alternatively, loop over range(N) instead, and keep a set of values you've already processed:

def CyclotomicCosets(q, n):
    N = q ^ n - 1
    Cosets = []
    seen = set()
    for i in range(N):
        if i in seen: continue
        tmp = {i * (q ^ j) % N for j in range(n)}
        Cosets.append(list(tmp))
        seen |= tmp
    return Cosets