How do I distribute 48 items each with its own dollar value to each of 3 inheritors so that the value given to each is equal or nearly equal?
This is a form of partitioning problem with is NP-complete (or some such) and therefore impossible to perfectly answer with 48 items. I'm looking for a practical and generally acknowledged approximate algorithm to do this. It's a problem faced by many in resolving wills and estates. Answer must be out there somewhere! The answer could be a computer script or just a manual method.
A heuristic that is "Generally Accepted" would suffice. With my programmer hat on I seek a near-perfect solution. With my legalistic executor hat on I seek something for which there is a generally accepted or legal precedent as being "good enough".
Programming Language env: visual basic in LibreOffice Other research: Wikipedia, MathIsFun, CodingTheWheel
I have found a "good enough" answer from justanswer.com. Good enough for the legalities of dividing up the jewelry and close enough to being equal to satisfy all parties. The procedure:
Sort the items in descending order of value. Use greedy algorithm: start with 1st item (the most valuable) and fill the next bin (there are 3 inheritors so 3 bins) until that bin is no longer the bin of least value. Choose bin of subsequent least value and similarly fill it. Repeat.
Comments welcome.
来源：https://stackoverflow.com/questions/8317501/seeking-a-solution-or-a-heursitic-approxmation-for-the-3-partition-combinatorial