How to figure out if a certain algorithm has already been discovered or not? Suppose that I make a new algorithm to calculate something. How do I know that the exact algorithm has been found or not? I know that I can check scientific journals to figure that out. But surely checking every single journals available is not a feasible way to figure that out, especially since I'll have to read them before I can tell whether they use the same algorithm or not as the title can only tell the general idea of how the calculation is done. Also many journals requires one to subscribe or pay for their service. It'd be ridiculus to pay huge sum of money just to ensure whether my algorithm has been found or not.

So, how do I figure whether a certain algorithm has been found or not?
I'm afraid I have bad news:

Unless you are writing algorithms for entirely new scientific areas, you can safely assume that every algorithm anyone can come up without being familiar with the literature is either (i) already known, or (ii) inferior to already known algorithms. In other words, since you don't seem to be familiar with the literature in your field, I would think that the chances for your algorithm to be new and better are slim. It may of course be new, but inferior to existing methods, in which case it's not useful.

(The reason for this is that people who are familiar with the literature, have been thinking about these issues for a long time, and know about the limitations of the existing methods, are most likely to come up with improvements. It is unlikely that people who are not familiar with an area waltz in, come up with something, and it turns out to be better than what all of the experts have come up with. It probably happens every once in a while, but it's unlikely.)

This doesn't help you find out whether your algorithm has been found so far. But it helps you determine whether it's worthwhile pursuing this further -- which it is likely not. You are probably better off spending your time reading the literature in the field to understand what others have been doing, what the limitations of existing algorithms are, etc.