Ah, didn't think to optimize constants. That did the trick. Thanks!

I used BFS (from neighboring points not in the given set) and still got TLE. Is this not the idea? Or is there a way to speed up my BFS? 149168850

If you print that test case, you can see it is:

A similar and simpler test that probably also catches your error is:

If we want to minimize $$$a+b$$$ and want $$$ab\ge n$$$, then we want $$$a$$$ and $$$b$$$ to be as close to each other as possible (just try a few values... it's very intuitive). That means each of $$$a,b$$$ must be around $$$\sqrt{n}$$$. In this problem, $$$a=1+x$$$ and $$$b=1+y$$$.

Suppose we perform the +1 operation $$$x$$$ times and the duplicate operation $$$y$$$ times. Clearly we want to perform all the $$$x$$$ operations first, so that each subsequent $$$y$$$ operation adds as much as possible. Then the sum of the array will be $$$(1+x)+y(1+x)=(1+x)(1+y)$$$. We want $$$(1+x)(1+y) \ge n$$$, so each of $$$(1+x)$$$ and $$$(1+y)$$$ is either $$$\lfloor \sqrt(n) \rfloor$$$ or $$$\lfloor \sqrt(n) \rfloor+1$$$. Then we can just try the cases.

94077437

At first I wasn't a huge fan of problem D because I thought Fenwick/segment tree was the only solution. Having seen this editorial though, I realize it's actually very creative and interesting.

Overall, I feel I learned a lot from this Educational Round. Thank you to all the problem writers!

I think mine failed on pretest 2 when I first submitted because of something like: 1 2 1 10 2 9

I also got WA on test 11 for my first submissions. For me it was because I had calculated the area of overlap between the two black papers, but didn't check that this overlap was within the white paper.