Path Cost
This video presents the same text shown beside it, spoken and on screen. It adds nothing the text does not say.
State
The cost of a path is the sum of its actions' costs, and the best solution is the cheapest — not necessarily the fewest steps.
Show
With road lengths added, Riverbend's three-road routes cost 12, 10, and 8 kilometers — same step count, different totals.
Watch for
Breadth-first happily returns the 12: its guarantee was about the wrong quantity. Ask what an optimizer optimizes.