in-place value updates

As you sweep through states you face a choice: compute all the new values from the old ones and swap at the end, or overwrite each value the instant you compute it, so later states in the same sweep already see the fresh number. The second style is "in-place", and it usually converges faster, because good information spreads within a single sweep instead of waiting for the next.

In-place evaluation keeps one array and writes a state's value immediately, so backups of later states use a mix of new and old values. The order of updates now matters — sweeping in a direction that follows the flow of value can speed convergence dramatically. It also halves memory, since you no longer keep two copies of the table. It is the default in most practical DP and a building block of asynchronous methods.