What is the primary purpose of dynamic programming in algorithms?

The primary purpose of dynamic programming in algorithms is to solve complex problems by breaking them down into simpler subproblems. This technique is particularly useful when the same subproblems are encountered multiple times during the computation. By solving each subproblem just once and storing its result, dynamic programming optimizes the overall efficiency, reducing the computational time significantly compared to naive recursive approaches.

This method focuses on two key principles: overlapping subproblems and optimal substructure. Overlapping subproblems occur when the same problem is solved multiple times, and optimal substructure means that an optimal solution to a problem can be constructed from optimal solutions of its subproblems. By leveraging these principles, dynamic programming allows for effective problem-solving in areas such as resource allocation, the longest common subsequence, and many others.