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Hello, I have a variation of the weighted activity selection problem I could use some help with. The problem is that there are activities that have a start time, finish time, and profit. I need to find the maximum profit achievable with the variation that there must be more "short" activities used than "long" activities. Where a short activity is an activity with duration less than 5 (finish time - start time). I have solved the problem without the variation, not sure how to implement the restrictions. This is homework so i am only looking for help with the recursion.
"...there must be more "short" activities used than "long" activities."
In the recursive step (where I assume you add another activity), just skip adding "long" activities when the number of short activities is less than or equal to the number of long activities minus one.
Presumably you are picking the best solution based on the final weight score.
And presumably you have an idea of what "more" means.
Then while spanning the graph you keep track of a count for long and short. Then at the end you provide an additional weight value based on the "more" calculation. So for example if you just need to do 'short > long' for the comparison then you might add a weight of '5' to the total if that is true. Or if you need to do a difference between long and short then you would multiple that difference by '5' and add it to the score. For that latter solution you should consider if you want to deal with a negative difference or not.
Here's one clue: when you want to have a loop that is guaranteed to be executed once, that construct is: Do ... While. In this case consider:
While (the user has not entered 9999)
"What Turing gave us for the first time (and without Turing you just couldn't do any of this) is he gave us a way of thinking about and taking seriously and thinking in a disciplined way about phenomena that have, as I like to say, trillions of moving parts.
Until the late 20th century, nobody knew how to take seriously a machine with a trillion moving parts. It's just mind-boggling." Daniel C. Dennett
Last Visit: 31-Dec-99 18:00 Last Update: 20-Dec-13 8:39