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

An interesting question! Here is my solution. It has the following properties:

• If there is no valid solution it should detect this and let you know
• The iteration is guaranteed to terminate so it should never get stuck in an infinite loop
• Any possible solution is reachable with nonzero probability

I do not know the distribution of the output over all possible solutions, but I think it should be uniform because there is no obvious asymmetry inherent in the algorithm. I would be surprised and pleased to be shown otherwise, though!

import random

def random_without_repeats(xs, ys):
    pairs = [[x,y] for x in xs for y in ys]
    output = [[object()], [object()]]
    seen = set()
    while pairs:
        # choose a random pair from the ones left
        indices = list(set(xrange(len(pairs))) - seen)
        try:
            index = random.choice(indices)
        except IndexError:
            raise Exception('No valid solution exists!')
        # the first element of our randomly chosen pair
        x = pairs[index][0]
        # search for a valid place in output where we slot it in
        for i in xrange(len(output) - 1):
            left, right = output[i], output[i+1]
            if x != left[0] and x != right[0]:
                output.insert(i+1, pairs.pop(index))
                seen = set()
                break
        else:
            # make sure we don't randomly choose a bad pair like that again
            seen |= {i for i in indices if pairs[i][0] == x}
    # trim off the sentinels
    output = output[1:-1]
    assert len(output) == len(xs) * len(ys)
    assert not any(L==R for L,R in zip(output[:-1], output[1:]))
    return output


nx, ny = 5, 5       # OP example
# nx, ny = 2, 10      # output must alternate in 1st index
# nx, ny = 4, 13      # shuffle 'deck of cards' with no repeating suit
# nx, ny = 1, 5       # should raise 'No valid solution exists!' exception

xs = range(1, nx+1)
ys = range(1, ny+1)

for pair in random_without_repeats(xs, ys):
    print pair