public static int Reduce(List <int> list)
{
var maxSumSR = new MaxSum();
Opt <int, int> opt = new Opt <int, int>(maxSumSR, x => x);
return(opt.Reduce(list));
}
public static int Reduce(List <int> list)
{
var maxSumSR = new MaxSum();
var evenSumHP = new EvenSum();
// Generate the index map for the lifted multiplication op ahead of time
// This is the same information carried by the (+)p operator in the definition
// of a homomorphic predicate [Emoto def. 10]
var k_even = new List <Tuple <int, int> > {
new Tuple <int, int>(0, 0), new Tuple <int, int>(1, 1)
};
var k_odd = new List <Tuple <int, int> > {
new Tuple <int, int>(0, 1), new Tuple <int, int>(1, 0)
};
var multMap = new List <List <Tuple <int, int> > > {
k_even, k_odd
};
// Starting with our old Max Sum semiring, lift the even sum H-predicate into a lifted semiring
ISemiring <LiftedSet <int, char> > liftedSR = new LiftedSemiring <int, char, int>(maxSumSR, evenSumHP, multMap);
// Note this is the *same* Opt.Reduce we used for the normal maximum initial
// segment sum problem. It has no knowledge of our goal to filter the segment
// list to even sum segments only; we've embedded that filtering into a new,
// lifted semiring that we use as a replacement for the unlifted MaxSum one
var opt = new Opt <int, LiftedSet <int, char> >(liftedSR, Prepare);
var ycp = opt.Reduce(list);
return(ycp.coefficients.ElementAt(0));
}