Dynamic programming stores solutions to subproblems for efficiency from "summary" of Data Structures and Algorithms in Python by Michael T. Goodrich,Roberto Tamassia,Michael H. Goldwasser
Dynamic programming involves breaking down a complex problem into simpler subproblems and solving each subproblem only once. The key idea behind dynamic programming is to store the solutions to subproblems so that they can be reused when needed, avoiding redundant computations. By storing the solutions to subproblems, dynamic programming can greatly improve the efficiency of algorithms. When applying dynamic programming to a problem, we first identify the subproblems that need to be solved. These subproblems are often smaller instances of the original problem. By solving these subproblems and storing their solutions, we can then combine them to solve the larger problem. Dynamic programming is particularly useful when there is overlap among the subproblems, as it allows us to avoid recomputing the same subproblem multiple times. By storing the solutions to subproblems, dynamic programming ensures that each subproblem is solved only once, leading to significant performance gains.- Dynamic programming effectively trades space for time. While it may require additional memory to store the solutions, this trade-off can result in faster runtime and improved efficiency overall. This approach is especially beneficial for problems with overlapping subproblems, where dynamic programming can avoid redundant computations and improve the overall efficiency of the algorithm.
