Sonya - DP Formulation

$dp[i]$ as a function of the $i$-th value is convex and piecewise linear. Initially, $dp[0](v) = |v - b_0|$, a V-shape centered at $b_0$. Adding $|v - b_i|$ preserves convexity. The constraint "$v \geq \text{previous value}$" truncates the function on the left, keeping only where $v$ is at least the previous minimum.

After each step, the minimum of $dp[i]$ is at some breakpoint. You track breakpoints with a max-heap. The heap top is the best last value.