11. Dynamic programming takes account of this fact and solves each sub-problem only once.12. To do so, methodologies based on dynamic programming and genetic algorithms were used. 13. There is use of mathematical programming, as well as dynamic programming . 14. In genetics, sequence alignment is an important application where dynamic programming is essential. 15. Rivas and Eddy published a dynamic programming algorithm for predicting pseudoknots. 16. This difference leads to elimination of dynamic programming at state-level in TI-HBM decoding process. 17. As with the optimal bitonic tour, this problem may be solved by dynamic programming . 18. Dynamic programming breaks a multi-period planning problem into simpler steps at different points in time.19. Popular dynamic programming languages include JavaScript, Lua and Perl. 20. I realize there is a fast dynamic programming algorithm, but it still seems mightily costly.