Time based rotation

I'm trying to figure out the best way of doing the following:
I have a list of values: L
I'd like to pick a subset of this list, of size N, and get a different subset (if the list has enough members) every X minutes.
I'd like the values to be picked sequentially, or randomly, as long as all the values get used.

For example, I have a list: [google.com, yahoo.com, gmail.com]
I'd like to pick X (2 for this example) values and rotate those values every Y(60 for now) minutes:

minute 0-59: [google.com, yahoo.com]
minute 60-119: [gmail.com, google.com
minute 120-179: [google.com, yahoo.com]
etc.

Random picking is also fine, i.e:
minute 0-59: [google.com, gmail.com]
minute 60-119: [yahoo.com, google.com]

Note: The time epoch should be 0 when the user sets the rotation up, i.e, the 0 point can be at any point in time. Finally: I'd prefer not to store a set of "used" values or anything like that, if possible. i.e, I'd like this to be as simple as possible.

Random picking is actually preferred to sequential, but either is fine. What's the best way to go about this? Python/Pseudo-code or C/C++ is fine.

Thank you!

Solution

You can use the itertools standard module to help:

import itertools
import random
import time

a = ["google.com", "yahoo.com", "gmail.com"]
combs = list(itertools.combinations(a, 2))
random.shuffle(combs)
for c in combs:
    print(c)
    time.sleep(3600)

EDIT: Based on your clarification in the comments, the following suggestion might help.

What you're looking for is a maximal-length sequence of integers within the range [0, N). You can generate this in Python using something like:

def modseq(n, p):
    r = 0
    for i in range(n):
        r = (r + p) % n
        yield r

Given an integer n and a prime number p (which is not a factor of n, making p greater than n guarantees this), you will get a sequence of all the integers from 0 to n-1:

>>> list(modseq(10, 13))
[3, 6, 9, 2, 5, 8, 1, 4, 7, 0]

From there, you can filter this list to include only the integers that contain the desired number of 1 bits set (see Best algorithm to count the number of set bits in a 32-bit integer? for suggestions). Then choose the elements from your set based on which bits are set to 1. In your case, you would use pass n as 2^N if N is the number of elements in your set.

This sequence is deterministic given a time T (from which you can find the position in the sequence), a number N of elements, and a prime P.