Dynamic Programming
Dynamic Programming is a powerful algorithmic paradigm for solving complex optimization problems by breaking them down into a collection of simpler, overlapping subproblems. The core principle is to solve each subproblem only once and store its solution, typically in a table or array, a process known as memoization or tabulation. When a subproblem is encountered again, its pre-computed solution is retrieved, thereby avoiding redundant calculations and dramatically improving efficiency. This technique is applicable to problems exhibiting optimal substructure, where an optimal solution can be constructed from optimal solutions of its subproblems, and it often reduces exponential time complexity to polynomial time.