In my previous question on this, I managed to come up with a simple recursive algorithm for the sum-over-paths method. However, what other snatches of material I can find online don't use recursion when explaining it. I've tried to come up with a non-recursive form of the algorithm but it always seems to just look like the standard Schrodinger method. What is the non-recursive form of the sum-over-paths algorithm?

Also, how does such an algorithm map semantically onto a diagram like this, from Aaronson's quantum computing lecture 9?

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