An efficient reconstruction of 2D-tiling with t(1,2), t(2,1), t(1,1) tiles

We define the projection of a tiling as a matrix P = (p(ij)) where p(i1) is number of t(1,2) tiles in row i and p(i2) is the number of t(2,1) tiles in row i. We give an efficient algorithm to tile a 2D-square grid with only t(1,2), t(2,1), t(1,1) tiles such that the projection of this tiling is the same as the given projection.