What is the primary goal of dynamic programming?

The primary goal of dynamic programming is to construct solutions from the results of subproblems. This approach involves breaking down a complex problem into simpler subproblems and solving each of those just once, storing their solutions — typically in a table. This method leverages the principle of optimality, which suggests that an optimal solution to a problem can be constructed from optimal solutions to its subproblems.

By using dynamic programming, a problem that might otherwise require an exponential amount of time to solve can often be solved in polynomial time, making it much more efficient. This is especially useful in optimization problems where the solution can be built up over time by combining the best solutions to smaller instances of the same problem.

In contrast, focusing solely on reducing time complexity does not capture the essence of dynamic programming, as time complexity reduction is often a by-product of the approach rather than its goal. Similarly, finding an optimal solution through iterative testing does not highlight the structured methodology of building solutions from subproblem results. Additionally, while dynamic programming can indeed avoid excessive recursion by using iterative approaches and storage of results, avoiding recursive functions is not a fundamental aim of this methodology.