public void NRooksHarderTest()
{
var n = 8;
var p = new Problem("N rooks hard")
{
Timeout = 2000000
};
// rook(i, j) means there's a root at row i, column j
var rook = Predicate <int, int>("rook");
//
// Add constraint to the program
//
// There should be a total of n rooks
p.Exactly(n, Range(0, n).SelectMany(i => Range(0, n).Select(j => rook(i, j))));
// There should be at most one rook in each row
foreach (var i in Range(0, n))
{
p.AtMost(1, Range(0, n), j => rook(i, j));
}
// There should be at most one rook in each column
foreach (var j in Range(0, n))
{
p.AtMost(1, Range(0, n), i => rook(i, j));
}
var m = p.Solve();
//
// Test the constraint in the solution
//
m.Exactly(n, Range(0, n).SelectMany(i => Range(0, n).Select(j => rook(i, j))));
foreach (var i in Range(0, n))
{
m.AtMost(1, Range(0, n).Select(j => rook(i, j)));
}
foreach (var j in Range(0, n))
{
m.AtMost(1, Range(0, n).Select(i => rook(i, j)));
}
}