If I had to guess I would presume the OP has not done a formal analysis of the algorithm. This would undoubtedly be the contribution of the professor/researche

If I had to guess I would presume the OP has not done a formal analysis of the algorithm. This would undoubtedly be the contribution of the professor/researcher assuming the analysis proves it is an improvement over prior algorithms. This analysis/proof is certainly worth being a second author even if it is not a contribution to the algorithm itself.