Algorithms that use dynamic programming (from wikipedia) Backward induction as a solution method for finite-horizon discrete-time dynamic optimization problems Method of undetermined coefficients can be used to solve the Bellman equation in infinite-horizon, discrete-time, discounted, time-invariant dynamic optimization problems Many string algorithms including longest common subsequence, longest increasing subsequence, longest common substring, Levenshtein distance (edit distance). Many algorithmic problems on graphs can be solved efficiently for graphs of bounded treewidth or bounded clique-width by using dynamic programming on a tree decomposition of the graph. The Cocke-Younger-Kasami (CYK) algorithm which determines whether and how a given string can be generated by a given context-free grammar The use of transposition tables and refutation tables in computer chess The Viterbi algorithm (used for hidden Markov models) The Earley algorithm (a type of chart parser) The Needleman-Wunsch and other algorithms used in bioinformatics, including sequence alignment, structural alignment, RNA structure prediction. Floyd's All-Pairs shortest path algorithm Optimizing the order for chain matrix multiplication Pseudopolynomial time algorithms for the Subset Sum and Knapsack and Partition problem Problems The dynamic time warping algorithm for computing the global distance between two time series The Selinger (a.k.a. System R) algorithm for relational database query optimization De Boor algorithm for evaluating B-spline curves Duckworth-Lewis method for resolving the problem when games of cricket are interrupted The Value Iteration method for solving Markov decision processes Some graphic image edge following selection methods such as the "magnet" selection tool in Photoshop Some methods for solving interval scheduling problems Some methods for solving word wrap problems Some methods for solving the travelling salesman problem Recursive least squares method Beat tracking in Music Information Retrieval. Adaptive Critic training strategy for artificial neural networks Stereo algorithms for solving the Correspondence problem used in stereo vision. Seam carving (content aware image resizing) The Bellman-Ford algorithm for finding the shortest distance in a graph. Some approximate solution methods for the linear search problem.