// Recursively construct a perfectly balanced BinarySearchTreeWithRank
// by repeated insertions in O( N log N ) time.
// t should be empty on the initial call.
public static void BuildTree(BinarySearchTreeWithRank <int> t,
int low, int high)
{
int center = (low + high) / 2;
if (low <= high)
{
t.Insert(center);
BuildTree(t, low, center - 1);
BuildTree(t, center + 1, high);
}
}
// Return the winner in the Josephus problem.
// Search Tree implementation.
public static int Jos2(int people, int passes)
{
BinarySearchTreeWithRank <int> t = new BinarySearchTreeWithRank <int>( );
BuildTree(t, 1, people);
int rank = 1;
while (people > 1)
{
rank = (rank + passes) % people;
if (rank == 0)
{
rank = people;
}
t.Remove(t.FindKth(rank));
people--;
}
return(t.FindKth(1));
}
