👉 Dynamic Programming (DP) is a method for solving complex problems by breaking them down into simpler subproblems and storing the results of these subproblems to avoid redundant calculations. It relies on the principle of optimality, where an optimal solution to a problem contains optimal solutions to its subproblems. DP typically involves two key steps: first, identifying overlapping subproblems where the same subproblem is solved multiple times; and second, solving each subproblem only once and storing its solution (memoization) to reuse it when needed. This approach significantly reduces time complexity, often transforming exponential time algorithms into polynomial time solutions. Common applications include sequence alignment in bioinformatics, the knapsack problem, and shortest paths in graphs. DP can be implemented using either a top-down (memoization) or bottom-up (tabulation) approach, depending on the problem's specifics and constraints.
