How can I pair socks from a pile efficiently?

Question

Yesterday I was pairing the socks from the clean laundry and figured out the way I was doing it is not very efficient. I was doing a naive search — picking one sock and

Answer 1

Whenever you pick up a sock, put it in one place. Then the next sock you pick up, if it doesn't match the first sock, set it beside the first one. If it does, there's a pair. This way it doesn't really matter how many combinations there are, and there are only two possibilities for each sock you pick up -- either it has a match that's already in your array of socks, or it doesn't, which means you add it to a place in the array.

This also means that you will almost certainly never have all your socks in the array, because socks will get removed as they're matched.

Answer 2

As the architecture of the human brain is completely different than a modern CPU, this question makes no practical sense.

Humans can win over CPU algorithms using the fact that "finding a matching pair" can be one operation for a set that isn't too big.

My algorithm:

spread_all_socks_on_flat_surface();
while (socks_left_on_a_surface()) {
     // Thanks to human visual SIMD, this is one, quick operation.
     pair = notice_any_matching_pair();
     remove_socks_pair_from_surface(pair);
}

At least this is what I am using in real life, and I find it very efficient. The downside is it requires a flat surface, but it's usually abundant.

Answer 3

Non-algorithmic answer, yet "efficient" when I do it:

• step 1) discard all your existing socks

• step 2) go to Walmart and buy them by packets of 10 - n packet of white and m packets of black. No need for other colors in everyday's life.

Yet times to times, I have to do this again (lost socks, damaged socks, etc.), and I hate to discard perfectly good socks too often (and I wished they kept selling the same socks reference!), so I recently took a different approach.

Algorithmic answer:

Consider than if you draw only one sock for the second stack of socks, as you are doing, your odds of finding the matching sock in a naive search is quite low.

• So pick up five of them at random, and memorize their shape or their length.

Why five? Usually humans are good are remembering between five and seven different elements in the working memory - a bit like the human equivalent of a RPN stack - five is a safe default.

• Pick up one from the stack of 2n-5.

• Now look for a match (visual pattern matching - humans are good at that with a small stack) inside the five you drew, if you don't find one, then add that to your five.

• Keep randomly picking socks from the stack and compare to your 5+1 socks for a match. As your stack grows, it will reduce your performance but raise your odds. Much faster.

Feel free to write down the formula to calculate how many samples you have to draw for a 50% odds of a match. IIRC it's an hypergeometric law.

I do that every morning and rarely need more than three draws - but I have n similar pairs (around 10, give or take the lost ones) of m shaped white socks. Now you can estimate the size of my stack of stocks :-)

BTW, I found that the sum of the transaction costs of sorting all the socks every time I needed a pair were far less than doing it once and binding the socks. A just-in-time works better because then you don't have to bind the socks, and there's also a diminishing marginal return (that is, you keep looking for that two or three socks that when somewhere in the laundry and that you need to finish matching your socks and you lose time on that).

Answer 4

This is asking the wrong question. The right question to ask is, why am I spending time sorting socks? How much does it cost on yearly basis, when you value your free time for X monetary units of your choice?

And more often than not, this is not just any free time, it's morning free time, which you could be spending in bed, or sipping your coffee, or leaving a bit early and not being caught in the traffic.

It's often good to take a step back, and think a way around the problem.

And there is a way!

Find a sock you like. Take all relevant features into account: colour in different lighting conditions, overall quality and durability, comfort in different climatic conditions, and odour absorption. Also important is, they should not lose elasticity in storage, so natural fabrics are good, and they should be available in a plastic wrapping.

It's better if there's no difference between left and right foot socks, but it's not critical. If socks are left-right symmetrical, finding a pair is O(1) operation, and sorting the socks is approximate O(M) operation, where M is the number of places in your house, which you have littered with socks, ideally some small constant number.

If you chose a fancy pair with different left and right sock, doing a full bucket sort to left and right foot buckets take O(N+M), where N is the number of socks and M is same as above. Somebody else can give the formula for average iterations of finding the first pair, but worst case for finding a pair with blind search is N/2+1, which becomes astronomically unlikely case for reasonable N. This can be sped up by using advanced image recognition algorithms and heuristics, when scanning the pile of unsorted socks with Mk1 Eyeball.

So, an algorithm for achieving O(1) sock pairing efficiency (assuming symmetrical sock) is:

1. You need to estimate how many pairs of socks you will need for the rest of your life, or perhaps until you retire and move to warmer climates with no need to wear socks ever again. If you are young, you could also estimate how long it takes before we'll all have sock-sorting robots in our homes, and the whole problem becomes irrelevant.

2. You need to find out how you can order your selected sock in bulk, and how much it costs, and do they deliver.

3. Order the socks!

4. Get rid of your old socks.

An alternative step 3 would involve comparing costs of buying the same amount of perhaps cheaper socks a few pairs at a time over the years and adding the cost of sorting socks, but take my word for it: buying in bulk is cheaper! Also, socks in storage increase in value at the rate of stock price inflation, which is more than you would get on many investments. Then again there is also storage cost, but socks really do not take much space on the top shelf of a closet.

Problem solved. So, just get new socks, throw/donate your old ones away, and live happily ever after knowing you are saving money and time every day for the rest of your life.

Answer 5

Real-world approach:

As rapidly as possible, remove socks from the unsorted pile one at a time and place in piles in front of you. The piles should be arranged somewhat space-efficiently, with all socks pointing the same direction; the number of piles is limited by the distance you can easily reach. The selection of a pile on which to put a sock should be -- as rapidly as possible -- by putting a sock on a pile of apparently like socks; the occasional type I (putting a sock on a pile it doesn't belong to) or type II (putting a sock in its own pile when there's an existing pile of like socks) error can be tolerated -- the most important consideration is speed.

Once all the socks are in piles, rapidly go through the multi-sock piles creating pairs and removing them (these are heading for the drawer). If there are non-matching socks in the pile, re-pile them to their best (within the as-fast-as-possible constraint) pile. When all the multi-sock piles have been processed, match up remaining pairable socks that weren't paired due to type II errors. Whoosh, you're done -- and I have a lot of socks and don't wash them until a large fraction are dirty. Another practical note: I flip the top of one of a pair of socks down over the other, taking advantage of their elastic properties, so they stay together while being transported to the drawer and while in the drawer.

Answer 6

I've finished pairing my socks just right now, and I found that the best way to do it is the following:

• Choose one of the socks and put it away (create a 'bucket' for that pair)
• If the next one is the pair of the previous one, then put it to the existing bucket, otherwise create a new one.

In the worst case it means that you will have n/2 different buckets, and you will have n-2 determinations about that which bucket contains the pair of the current sock. Obviously, this algorithm works well if you have just a few pairs; I did it with 12 pairs.

It is not so scientific, but it works well:)