Exhaustive generation of positive lattice paths

We refer to lattice positive paths as to paths in the discrete plane constituted by different kinds of steps (north-east, east and south-east), starting from the origin and never going under the x-axis. They have been deeply studied both from a combinatorial and an algorithmic point of view. We propose some algorithms for the exhaustive generation of positive paths which are prefixes of Dyck, Motzkin and q-coloured Motzkin paths, according to their length. For each kind of path we define a recursive version as well an iterative one, specifying which path follows a given one in the lexicographic order. Furthermore we study the complexity of hese algorithms by using the relations between the number of paths of given size and the number of north-east steps appearing in the final rise.