Create a random order of (x, y) pairs, without repeating/subsequent x's

Question

Say I have a list of valid X = [1, 2, 3, 4, 5] and a list of valid Y = [1, 2, 3, 4, 5].

I need to generate all combinations of every element in

Answer 1

For completeness, I guess I will throw in the super-naive "just keep shuffling till you get one" solution. It's not guaranteed to even terminate, but if it does, it will have a good degree of randomness, and you did say one of the desired qualities was succinctness, and this sure is succinct:

import itertools
import random

x = range(5)  # this is a list in Python 2
y = range(5)
all_pairs = list(itertools.product(x, y))

s = list(all_pairs)  # make a working copy
while any(s[i][0] == s[i + 1][0] for i in range(len(s) - 1)):
    random.shuffle(s)
print s

As was commented, for small values of x and y (especially y!), this is actually a reasonably quick solution. Your example of 5 for each completes in an average time of "right away". The deck of cards example (4 and 13) can take much longer, because it will usually require hundreds of thousands of shuffles. (And again, is not guaranteed to terminate at all.)