Spoiler for simple reasoning
Well, except that we are given the river as is, with a fixed width and a bridge perpendicular to its flow.
We do not know whether the line joining the cities lines up with the bridge - a very special case with a trivial solution.
We also do not know that the cities are equidistant from the river - a fact that bears on bridge placement if is not parallel to the joining line.
I'm curious to know the two different ways BMAD has to optimize the bridge placement.
You might've misunderstood me a little bit, I should have detailed a bit more, let the river be of width 1 unit, align the axis such that the x axis is parallel with and centered the river, in other words the river would be the area -0.5<y<0.5, now "removing" the river means collapsing it and so every point that was below it now goes up by 0.5 units and every point above it goes doen 0.5 units... Go to the full post