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The analogy doesn't make sense for me. What if the shortest path from Waterloo to New York doesn't go through Toronto?

And if the point is that you already know that it does, then....the rest is beyond obvious?

What am I missing?



The analogy speaks to the number of paths that need be considered so that, later, we can find the overall shortest path (there are likely other intermediate places that we're also evaluating, along with Toronto). Once we know the shortest path from Waterloo to Toronto, that's the only one we need to consider (on that segment) from then on.


Strictly speaking this analogy doesn’t hold in real life since paths in road networks are not symmetric.




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