DYNAMIC PROGRAMMING Meaning and
Definition
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Dynamic programming is a method in computer science and mathematics that involves solving complex problems by breaking them down into smaller, more manageable subproblems. It is used to optimize computations and find efficient solutions to problems that would otherwise be computationally expensive or time-consuming.
In dynamic programming, the main idea is to store the solutions to subproblems in a table or memoization array, so that they can be easily retrieved when necessary. This allows for avoiding redundant computations and greatly improves the overall efficiency of the algorithm.
The term "dynamic programming" was originally used by American mathematician Richard Bellman in the 1950s. The "dynamic" part refers to the fact that the algorithm adapts and updates its computations based on the changing nature of the problem and the available information. It does not imply any relation to time or motion.
A key characteristic of dynamic programming is the concept of "optimal substructure," which means that finding an optimal solution to a problem involves finding optimal solutions to its subproblems. By solving these subproblems in a bottom-up manner, starting from smaller instances, the algorithm gradually constructs a solution to the overall problem.
Dynamic programming is employed in a wide range of areas such as computer science, operations research, economics, and bioinformatics. It is particularly useful in problems involving combinatorial optimization, resource allocation, graph algorithms, shortest path calculations, and many others. Its ability to efficiently solve complex problems by breaking them down into simpler subproblems makes it a powerful technique in algorithm design and optimization.
Etymology of DYNAMIC PROGRAMMING
The term "dynamic programming" was coined by Richard Bellman in the 1950s. However, its name can be a bit misleading, as it has nothing to do with programming in the traditional sense of computer programming.
The "dynamic" in dynamic programming refers to the process of breaking down a complex problem into simpler subproblems and solving them in a hierarchical manner. It emphasizes the idea of solving a problem by considering its optimal substructure.
The term "programming" comes from the use of the word in the mathematical sense, which means planning or organizing a set of tasks. Richard Bellman used the term "programming" because he was writing a memo on his new approach and knew that his ideas would be more accepted if he used a neutral term like "programming" instead of "mathematics".
