I am trying to create subsets from a list of data based on some constraints and optimize the subsets. I am trying to figure out how to go about it. I am hoping someone can help me come up with some equations, then Wolfram|Alpha can solve them, then I can follow Wolfram’s process and convert it into the programming language I am using. Here is an example of the problem:
Given:
- X_POSITIONMID = 3.5
- List where first item in each subgroup is the X_POSITION and the second item is the STRINGCOUNT: (0 2) (1 3) (2 3) (3 3) (4 3) (5 3) (6 3)
Constraints:
- Sum of STRINGCOUNT in each subset created must be less than or equal to 9
- Items in subsets created must be adjacent (based on X_POSITION, e.g. can’t make a subset of (0 2) and (2 3) without also having (1 3) in the subset)
- Create as few subsets as possible
- Lastly, this is hard to explain, but basically the subsets with the largest STRINGCOUNT sum shall be nearest to X_POSITIONMID
Example Solution:
- Subset 1: (0 2) (1 3) (sum of STRINGCOUNT is 5)
- Subset 2: (2 3) (3 3) (4 3) (sum of STRINGCOUNT is 9)
- Subset 3: (5 3) (6 3) (sum of STRINGCOUNT is 6)
Subset 2 is closest to the X_POSITIONMID so it has the highest STRINGCOUNT sum. 3 subsets were created which is the lowest number possible. Each subset has a STRINGCOUNT sum less than or equal to 9.