role-algorithms:dynamic-programming

Dynamic programming solves optimization problems by breaking them into overlapping subproblems and optimal substructures. This skill implements both top-down memoization and bottom-up tabulation to compute efficient solutions for complex algorithmic challenges.

Memoization is a top-down dynamic programming approach that caches results of recursive calls, while tabulation is a bottom-up method that iteratively fills a table. This skill implements both techniques to handle overlapping subproblems based on the problem's structure.

Bitmask dynamic programming is supported to minimize state space when solving complex optimization problems. It enables efficient computation by representing subsets of data compactly, which is ideal for algorithmic challenges involving combinatorial state tracking.

Finding the longest common subsequence is a classic dynamic programming use case supported by this skill. It applies tabulation to compare string characters iteratively, building a matrix to identify the optimal substructure and overlapping subproblems efficiently.

Tree dynamic programming should be used when the optimal substructure relies on hierarchical dependencies rather than linear sequences. This skill handles tree DP and DP on DAGs to explore valid combinations efficiently when tasks have strict dependency graphs.

Advanced dynamic programming techniques for resource allocation include Convex Hull Trick optimizations, bitmask DP, and tree DP. These methods minimize state space and compute optimal substructures to find the minimum cost for completing tasks with dependencies.