Vocabulary - Slope-Change Points

A slope-change point is where the slope of the function changes. For $f(x) = \sum |x - a_i|$, the slope changes at each $a_i$. These are the corners. Example: $f(x) = |x - 2| + |x - 5|$ has slope-change points at $2$ and $5$. Between them, $f(x) = (x - 2) + (5 - x) = 3$, constant with slope $= 0$.

Instead of storing $f(x)$ everywhere, you store breakpoints and compute slopes on the fly. Space drops from $O(V)$ to $O(n)$.