Hi everyone,

I just joined Codeforces yesterday, but I’ve been working on a few problem ideas for a while before creating an account. I’d love to get some feedback on one of them to see if it’s any good.

The idea:

We have $$$n$$$ items ($$$n \le 2000$$$) and a budget $$$W \le 2000$$$. Each item $$$i$$$ has cost $$$c_i$$$, value $$$v_i$$$, and a discount $$$p_i$$$ (percentage left to pay).

We want to pick a set of items to maximize total value within budget $$$W$$$. Exactly one item in the chosen set gets a discount (new cost = $$$\lfloor c_i \cdot p_i / 100 \rfloor$$$).

The discounted item is chosen automatically using these rules:

1. Smallest original cost $$$c_i$$$
2. Smallest percentage $$$p_i$$$ (if tied)
3. Smallest index $$$i$$$ (if still tied)

Does this idea look interesting? What difficulty/Div would this fit?

Also, since Im completely new to how CF works from the author side, how does proposing problems actually work here? Do authors just write the statements and send them to coordinators, or do we need to make all the test cases ourselves first?

Thanks!