Calculating total resistance?

No algorithm needed. Just start at the input and output and use the series/parallel formula up to common nodes.

Cheers

Google "circuit mesh analysis" or "circuit node analysis." The general method is to write a heap of loop equations and solve; it's essentially a matrix analysis thing.

Real engineers seldom or never do this. Relatively simple circuits can be solved by ad-hoc techniques, reducing series and parallel branches. Anything more complex, it's easier to just crank up LT Spice.

There are simple iterative numerical methods to solve a general resistor network, but they are compute-intensive, so you may as well use Spice.

I prefer to design things that are easy to analyze. One often has that option. With opamps being so cheap these days, it's easy to orthogonalize things instead of making a minimal-components hairball.

John