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|> import Control.Monad.Tardis|
|let levels hs = evalTardis (traverse|
|(\h -> do x <- min <$> getFuture <*> getPast -- Get the height of the enclosing walls|
|modifyBackwards (`max` h) -- Send the right max back to the past|
|modifyForwards (`max` h) -- Send the left max into the future|
|pure (max 0 (x - h)) -- Calculate the height of the water itself|
|) hs) (0, 0)|
|> sum $ levels [5,3,7,2,6,4,5,9,1,2]|
Dec 10, 2019
@lalaithion Oh, you're right, well spotted! I think we could fix it perhaps by swapping those two lines?
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This code has a slight subtlety in it that I wouldn't call a bug, strictly speaking, but is perhaps inhibitory to understanding the exact semantics of the Tardis Monad.
If we have a situation where the max height in the Future direction is less than the current height, then the
getFutureon the previous line to return
h, not the actual max height in the future direction. In that case, we know that
h, because there is a bigger number in the Past, or
xis less than
h, because the Past was a smaller number. Therefore,
x - h <= 0, and we end up with the right answer in the end.
However, it's not quite what the code should be doing.