After being stuck at a problem for a while I look at editorial, In the editorial they provide the solution and sometimes the proof to why the solution works
But the problem I face is that a Proof for Solution $$$P\to Q$$$ assumes, if you already know $$$P \to Q$$$ you assume $$$P$$$ and try to prove $$$Q$$$. But in my mind I am unable to formulate $$$P\to Q$$$ and unless I formulate this, I cant Prove it. I am unable to discover the existence of $$$Q$$$. let alone combine them both. It's easy to prove "it" works, than to discover "it"
I can prove "it" but unable to discover "it"   A recent example for me would this:
B. Perfecto
In the editorial, we solve it by going through $$$A = [1, 2, 3, 4, ..., n]$$$
let $$$P_{i}$$$ denote prefix sum i.e $$$P_{i} = \sum_{k=1}^{i}A_k = \frac{i(i+1)}{2}$$$
if at any point the $$$P_i$$$ becomes a perfect square we swap $$$A_{i}$$$ with $$$A_{i+1}$$$ so $$$P_{i}$$$ becomes $$$P_{i}+1$$$
But how do the people who actually solved it and are not the authors of the question came to know "lets swap ith element with (i+1) element and (i+1)th element will not be a perfect square" it sounds so random. Now you can prove "it" works i.e $$$\exists x \in \mathbb{Z}^+ \ (\sum_{k=1}^{i} A_k = x^2) \to \neg\exists y \in \mathbb{Z}^+ \ \text{such that} \ \sum_{k=1}^{i+1} A_k = y^2$$$ we can use contradiction to prove it.
Another example would be this:
Combination Lock
In this question the if n is even then answer is -1, it was straight forward reasoning
But here is where I got stuck, if n is odd you have to come up with a permutation, in the editorial you simply print from $$$[n, n-1, n-2, ..., 1]$$$ After I looked at editorial I wasn't convinced with reverse order, I mean it worked, but there is no way I could have guessed printing reverse will give answer
But I wanted to do it without reversing so I came up with this
eg: [1, x, x, x, x]
curr=1
now perform a single rotation and increment the curr and set the curr index of permutation to curr;
repeat for all (n-1)
But this solution gave a TLE
This is has been happening for a while now, How do I overcome this?