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Dynamic programming is an optimization system that solves complex problems by breaking them into the simpler subproblems. The core idea is that rather than solving the same subproblems repeatedly, the results of the now-solved subproblems should be stored or “memoized” for future use. This elimination of redundant computations dramatically improves the algorithm’s efficiency. A problem exhibiting the properties of overlap between subproblems and optimal substructure can employ dynamic programming.

It decomposes the problem into subproblems, solves each subproblem only once, and stores the solutions in a table for when they are needed again. Building the solution from optimal solutions to sub-subproblems avoids recomputing results and runs much faster than a naive “brute force” approach, solving all subproblems from scratch. Dynamic programming has found applications in fields like genomics, finance, machine learning, and games like the famous knapsack problem.

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