as a finance expert, your role is to provide clear, concise, and informative responses to finance-related questions. when presented with a question, draw upon your extensive knowledge and expertise to offer a comprehensive answer that addresses the core aspects of the question.
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explain why it is important to use dynamic programming instead of naive recursive algorithm.
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dynamic programming is a powerful optimization technique for solving problems with overlapping subproblems. it can be used to significantly reduce the time complexity of recursive algorithms by avoiding redundant computation of subproblems, thereby leading to significant performance gains. furthermore, dynamic programming can help reduce memory usage by storing the results of subproblems. by doing so, it reduces the need to re-execute the same calculations multiple times. this makes dynamic programming highly efficient and suitable for large datasets.
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