Dynamic programming is a method to solve complex problems by breaking them into overlapping subproblems, storing results to avoid recomputation and improve efficiency.

Dynamic programming (DP) is a technique used in competitive programming to solve problems that involve overlapping subproblems and optimal substructure. Instead of recalculating results for the same subproblems multiple times, DP stores these results in a table or array, allowing for efficient reuse and reducing time complexity. This approach is commonly applied in problems involving sequences, such as the longest common subsequence, knapsack, or Fibonacci sequence. DP is also valuable in pathfinding and optimization problems where choices need to be made to maximize or minimize a certain metric. There are two main approaches to DP: top-down (memoization) and bottom-up (tabulation). In top-down DP, recursive calls store results in a cache, while bottom-up builds the solution iteratively. Dynamic programming can seem challenging initially, but with practice, it becomes a powerful tool for solving a wide range of problems in competitive programming. Recognizing problems suited for DP and building a solution efficiently can make a significant difference in performance.