Van Emde Boas Tree - How IT Works

How It Works

For the sake of simplicity, let log₂ m = k for some integer k. Define M=2m. A vEB tree T over the universe {0,...,M-1} has a root node that stores an array T.children of length M1/2. T.children is a pointer to a vEB tree that is responsible for the values {iM1/2,...,(i+1)M1/2-1}. Additionally, T stores two values T.min and T.max as well as an auxiliary vEB tree T.aux.

Data is stored in a vEB tree as follows: The smallest value currently in the tree is stored in T.min and largest value is stored in T.max. These two values are not stored anywhere else in the vEB tree. If T is empty then we use the convention that T.max=-1 and T.min=M. Any other value x is stored in the subtree T.children where . The auxiliary tree T.aux keeps track of which children are non-empty, so T.aux contains the value j if and only if T.children is non-empty.