This paper analyses the implementation of the generalized finite differences method for the HJB equation of stochastic control, introduced by two of the authors in . The computation of coefficients needs to solve at each point of the grid (and for each control) a linear programming problem. We show here that, for two dimensional problems, this linear programming problem can be solved in O(p) operations, where p is the size of the stencil. The method is based on a walk on the Stern-Brocot tree, and on the related filling of the set of positive semidefinite matrices of size two.