If the tree is empty, the search ends in failure. If the tree is not empty, we compare v with the tree’s root K(r). If they match, a desired element is found and the search can be stopped; if they do not match, we continue with the search in the left subtree of the root if v < K(r) and in the right subtree if v > K(r). Thus, on each iteration of the algorithm, the problem of searching in a binary search tree is reduced to searching in a smaller binary search tree