I am struggling with the following problem.
A college student has 7 days remaining before final examinations begin in her four courses, and she wants to allocate this study time as effectively as possible. She needs at least 1 day on each course, and she likes to concentrate on just one course each day, so she wants to allocate 1,2,3 or 4 days to each course. She decides to use dynamic programming to make these allocations to maximize the total grade points obtained from the four courses.
The following table shows the estimated points:
| Study Days | A | B | C | D |
|---|---|---|---|---|
| 1 | 3 | 5 | 2 | 6 |
| 2 | 5 | 5 | 4 | 7 |
| 3 | 6 | 6 | 7 | 9 |
| 4 | 7 | 9 | 9 | 9 |
Now my problem is that I also have an table that encodes the optimal solution. I know how to solve this problem step by step for each stage (Courses as stages starting with course D) however I don't understand how to calculate the table that encodes the optimal solution, nor do i understand what it expresses.
| 0 | 1 | 2 | 3 | |
|---|---|---|---|---|
| A | 16 | 18 | 19 | 20 |
| B | 16 | 18 | 19 | 20 |
| C | 16 | 18 | 21 | 23 |
| D | 16 | 18 | 21 | 23 |
