GPU clusters: capacity left per day and the best K-switch plan

You run a few GPU clusters with fixed daily capacities, for example [10, 20]. Each day a list of usage records takes GPUs from clusters (a record names the day, the cluster and how many GPUs), and every cluster is back to full capacity the next morning.

1. Return, for each day, how many GPUs are left in every cluster (a list of lists, one row per day).
2. A new workload may sit on any cluster each day and switch freely between days. What is the most GPU-days it can collect?
3. Now it may switch clusters at most K times over the whole period. What is the most it can collect? Give the recurrence, then the time and space of your solution.

Parts 1 and 2 are warm-ups; most of the time belongs to part 3.