I used to think they required some sort of strong math/logic understanding or proof writing. Now I'm convinced you just have to try random shit until it works and not worry about proving it. I think all the solutions to all the constructive problems rated under 1700 that I've practiced can be found by either writing a brute force program then identifying the pattern or by guessing something and submitting it if you can't find a counter-example.

For the problem you linked, I surprised myself came up with the idea in like 10 minutes. I was just like "Oh we need the max balance value to be exactly k, so let's just make a block of size k then try to minimize the balance value after that" then I was like "okay how to minimize the balance value? just alternate 0s and 1s?" and it worked.

I read the problem and my immediate reaction was we need alternating sequence. I think you just need experience.