Question

For dynamic programming, we usually define a recursive (state) equation as we did for the subset sum problem or weighted interval scheduling. Write a recursive equation for the minimum total charging time.

Answer 1

For the minimum total charging time problem, a recursive equation can be defined using dynamic programming. The equation considers whether to include or exclude the charging time at each index in order to minimize the total charging time.

Step-by-step explanation:

For the minimum total charging time problem, we can define a recursive equation using dynamic programming. Suppose we have a list of charging times represented by t[i], where i represents the index of the charging time. Let's consider the first charging time, t[0]. In order to minimize the total charging time, we have two choices:

1. Include t[0] in the total charging time, which would mean the minimum charging time would be t[0] plus the minimum charging time for the remaining elements (t[1:], where t[1:] represents a slice of the list from the second element onwards).
2. Exclude t[0] from the total charging time, which would mean the minimum charging time would be the minimum charging time for the remaining elements.

We can represent this using the following recursive equation:

t[i] = min(t[i] + min_total_charging_time(t[1:]), min_total_charging_time(t[1:]))