Hi, because of the situation right now i was thinking that when someone need to go out for any reason lets say that this person go out today, tomorrow no, the day after tomorrow yes and so on. How much bigger is the probability of getting sick if that person goes out every day?

I don't know if it's a silly question, but since i don't know much about probability i decided to post it. Also i think that the probability of getting sick one day is changing.

A friend talked me about this problem and i don't know how to solve it or if there is a judge to make submitions.

You will be given an array of $$$N$$$ integers $$$A$$$. You know that $$$ 1 \leq N \leq 2000$$$ and $$$1 \leq A_i \leq 10^6$$$.

Is there any way to know for a fixed $$$1 \leq k \leq N$$$ the maximum number of times you can choose $$$k$$$ different elements from $$$A$$$ with the condition that if you choose indexes $$$p_1,p_2,...,p_k$$$ then you have to do $$$A_{p_i}-=1$$$ for every $$$1 \leq i \leq k$$$ and $$$A_i \geq 0$$$ should hold.

My idea is that every time, you have to choose the currently $$$k$$$ greatest elements (but i don´t know if this is optimal, i did´nt prove it). And i guess that the time complexity for this would be $$$O( $$$$$$\sum_{i=1}^{n} A_i $$$$$$ ) \approx 10^9 $$$ worst case.

Another version

You are free to choose $$$k$$$ in such a way that at the end of the process with that $$$k$$$ (the process described above) the sum of the remaining elements should be minimum. You have to find the greatest $$$k$$$ meet this condition.

Any comment is welcome. Thank you.