Waldo's World.
You arrive at Waldo's World Amusement Park with T minutes
remaining until the park closes. The park has n rides and your
objective is to complete as many rides as possible before the
park closes. (For this problem, taking the same ride twice counts
as 2 rides.) You are given a table W such that
W(i, t) gives you the waiting time for ride
i at time t. For convenience, assume that t
is expressed as minutes before the park closes. Ride i
itself takes r_{i} minutes and all times are
measured in integer minutes.
Describe a dynamic programming algorithm that produces a
schedule of rides with the maximum number of rides.
Additional Instructions: When you are asked to provide a dynamic
programming algorithm. You must provide the following:
- Define a function OPT that can be used to solve
this dynamic programming problem. To do this, you must describe
the input parameters to OPT and the "return value" using English
sentences. (Note: you are specifying the input-output relation
of the function. You should not describe how to compute
the function.)
- Give a mathematical formula that shows how OPT can
be computed recursively. Then, explain all the major parts of
the formula using English sentences. Remember to include the
base cases.
- Describe how OPT can be computed bottom up using
a dynamic programming table. Be sure to include a description
of the dimensions of the table and the order that the entries
of the table are to be filled. Draw a diagram. Which entry has
the solution to the original problem?
- Analyze and justify the running time of your dynamic
programming algorithm.
Finally, in case you thought this is a totally made up problem,
check out RideMax.