programming

Dynamic programming is a computer programming technique where an algorithmic problem is first broken down into sub-problems, the results are saved, and then the sub-problems are optimized to find the overall solution — which usually has to do with finding the maximum and minimum range of the algorithmic query. 

Richard Bellman was the one who came up with the idea for dynamic programming in the 1950s. It is a method of mathematical optimization as well as a methodology for computer programming. It applies to issues one can break down into either overlapping subproblems or optimum substructures.

When a more extensive set of equations is broken down into smaller groups of equations, overlapping subproblems are referred to as equations that reuse portions of the smaller equations several times to arrive at a solution.

On the other hand, optimum substructures locate the best solution to an issue, then build the solution that provides the best results overall. This is how they solve problems. When a vast issue is split down into its constituent parts, a computer will apply a mathematical algorithm to determine which elements have the most desirable solution. Then, it takes the solutions to the more minor problems and utilizes them to get the optimal solution to the initial, more involved issue.

This technique solves problems by breaking them into smaller, overlapping subproblems. The results are then stored in a table to be reused so the same problem will not have to be computed again. 

For example, when using the dynamic programming technique to figure out all possible results from a set of numbers, the first time the results are calculated, they are saved and put into the equation later instead of being calculated again. So, when dealing with long, complicated equations and processes, it saves time and makes solutions faster by doing less work.

The dynamic programming algorithm tries to find the shortest way to a solution when solving a problem. It does this by going from the top down or the bottom up. The top-down method solves equations by breaking them into smaller ones and reusing the answers when needed. The bottom-up approach solves equations by breaking them up into smaller ones, then tries to solve the equation with the smallest mathematical value, and then works its way up to the equation with the biggest value.

Using dynamic programming to solve problems is more effective than just trying things until they work. But it only helps with problems that one can break up into smaller equations that will be used again at some point.