Examples
Given S = {3,1,1,2,2,1}, a valid solution to the partition problem is the two sets S1 = {1,1,1,2} and S2 = {2,3}. Both sets sum to 5, and they partition S. Note that this solution is not unique. S1 = {3,1,1} and S2 = {2,2,1} is another solution.
Not every multiset of positive integers has a partition into two halves with equal sum. An example of such a set is S = {2,5}.
Read more about this topic: Partition Problem
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