Editorial for DMOPC '20 Contest 1 P2 - Victor's Moral Dilemma

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Author: Kirito

A straightforward solution is to use prefix sum arrays.

Time Complexity: \mathcal O(N + D)

Alternate Solution

A more interesting question would be "why does brute force pass?"

Note that \min(F, S) \le F, S, thus 2 \min(F, S) \le F + S. That is, the total number of people remaining is at most half the number of people remaining on the previous day.

We start with \sum A_i people, and on the final day end with at least 1 person, so there are at most \mathcal O(\log\sum A_i) iterations.

Time Complexity: \mathcal O(N \log\sum A_i)


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