alibi's blog

Help me! (timus problem)
By alibi, history, 11 years ago, In English

Here is a link for the problem.

I found an approach in discussion: "You have to divide the participants into equal teams (rounded)", but I cannot understand why it's correct!

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11 years ago, hide # |
 
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In this problem you need to divide them into M teams, so you need to find an array a[1..M] such that its sum is N and its product is maximized.

Okay, suppose there is an optimal sequence of a[] such that there are two elements with difference greater than 1. Then, product is P * X * Y (X + 1 < Y), where P is product of other elements, while X and Y are these two elements with difference greater than 1 (X + 1 < Y).

Now, let's make X++ and Y-- and see what happens. Product becomes P * (X + 1) * (Y — 1) = P * X * Y + P * Y — P * X — P = P * X * Y + P * (Y — X — 1), we know that (Y > X + 1), thus Y — X — 1 at least 1, so answer becomes better.

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