Pattern - Slope Trick Recognition

Signal $1$: DP over a continuous or large discrete state $x$, with absolute value costs. Signal $2$: Transitions involve $\min_{y \leq x}$ or $\min_{y \geq x}$ (prefix/suffix operations). Signal $3$: The problem asks for non-decreasing, non-increasing, or bounded differences. Verify: sketch the DP function for small cases.

If it's piecewise linear with few breakpoints, Slope Trick applies. Absolute values create V-shaped functions. Prefix min flattens the right side. These operations hint at Slope Trick.