Dynamic Programming

A method for solving complex problems by decomposing them into overlapping subproblems and storing their solutions (via memoization or tabulation) so that each subproblem is solved only once and redundant computation is avoided; applicable when the problem exhibits optimal substructure and overlapping subproblems.

A recursive optimization framework that decomposes multistage decision problems into overlapping subproblems solved by backward or forward induction, centralizing the value function as the object encoding optimal future returns.

A recursive optimization method for multi‑stage decision problems that decomposes a problem into overlapping subproblems, uses a state representation and the principle of optimality to express the value of a state as a function of successor states, and computes optimal policies by value or policy iteration, memoization, or backward induction.