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back to boardShow all messages Hide all messagesThe product of natural numbers with a given condition in this problem will be maximal if and only if the middle arithmetic of these numbers is the most closely to the number e=2.71828... It's a mathematical sentence which are proved!
P.S. Sorry for my bad English Why is that true? You can get AC without math :P Well, you only need to understand that optimal partition can't contain any x >= 4(as 2*(x-2) >= x in this case), it obviously can't contain ones, and it can't contain more than 2 copies of 2, as 2*2*2<3*3. Surpisingly, there is only one way to express any x >= 2 as sum of 3's and not more than two 2's. That's a very nice idea. Let me clarify it for those who had problems understanding bsu.mmf.team's English. First of all, 'middle arithmetic' is an arithmetic mean. The thing is, the product will be maximal if (a_1 + a_2 + ... + a_n) / n ≈ e.
Well, it's not hard to figure out that the output of the program should be something like that: 3 * 3 * 3 * ... * ? |
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