Section Recap

You've learned Slope Trick. You can now solve DP problems with absolute value costs by tracking slope-change points instead of all values. You know:

$1.$ Piecewise linear functions are defined by breakpoints.

$2.$ Priority queues track these dynamically.

$3.$ Transitions shift or merge functions in $O(\log n)$ time.

$4.$ This turns $O(n \cdot V^2)$ into $O(n \log n)$. This is one of the harder DP optimizations. If it feels abstract, that's normal. Practice on the three problems above. Good work finishing here.