Representative applications of dynamic-programming in different fields: Analysis on problems of shortest-path, 0/1 knapsack and longest common sub-sequence

This article mainly focuses on exploring the current application status, concrete things implemented by dynamic programming and advantages of dynamic programming in problems (the concept and operation of dynamic programming and the role it plays in programs) in different fields, future development trends and areas for improvement. It also introduces the gaps and problems currently encountered by dynamic programming, then provides corresponding solutions to make it more helpful and efficient in the future. In this regard, by consulting different references and online resources written by previous scientists, it finds out that they all have different points of view on dynamic programming and different solutions to its shortcomings. In the current research, dynamic programming is the most widely used algorithm with few limitations that can achieve the global optimal solution at any time; however, it does not mean that it can achieve the local optimal solution at any time, which also indirectly results in the memory space it requires being larger than other optimization algorithms. After analyzing the literature and researching and testing multiple applications, it is obvious that dynamic programming can make the code run easier and faster than traditional methods, even though it will take up more space.