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It would help if you showed your work. Otherwise it really sounds like you're trying to get someone to do your homework for you. A rigorous proof for the correct algorithm is about 1/2 a page, by the way, so you can probably come up with it after a bit of thought.

2019年02月24日56分07秒

Hint: partial order.

2019年02月24日56分07秒

This may help you. It is another matching algorithm question.

2019年02月24日56分07秒

If the thread property of bottles and caps is comparable, you can sort the sets.

2019年02月24日56分07秒